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Springer Theses
Recognizing Outstanding Ph.D. Research
Condensed Matter
Applications of
AdS/CFT
Focusing on Strange Metals
Andrea Amoretti

Springer Theses
Recognizing Outstanding Ph.D. Research

Aims and Scope
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theses from around the world and across the physical sciences. Nominated and
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Andrea Amoretti
CondensedMatter
ApplicationsofAdS/CFT
Focusing on Strange Metals
Doctoral Thesis accepted by
University of Genoa, Italy
123

Author
Dr. Andrea Amoretti
Mathematical Physics of Fundamental
Interactions
UniversitéLibre de Bruxelles
Brussels
Belgium
Supervisors
Prof. Nicola Maggiore
Dipartimento di Fisica
Universitàdi Genova
Genoa
Italy
Prof. Nicodemo Magnoli
Dipartimento di Fisica
Universitàdi Genova
Genoa
Italy
ISSN 2190-5053 ISSN 2190-5061 (electronic)
Springer Theses
ISBN 978-3-319-61874-6 ISBN 978-3-319-61875-3 (eBook)
DOI 10.1007/978-3-319-61875-3
Library of Congress Control Number: 2017944314
©Springer International Publishing AG 2017
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microﬁlms or in any other physical way, and transmission
or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, express or implied, with respect to the material contained herein or
for any errors or omissions that may have been made. The publisher remains neutral with regard to
jurisdictional claims in published maps and institutional afﬁliations.
Printed on acid-free paper
This Springer imprint is published by Springer Nature
The registered company is Springer International Publishing AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To the memory of Lucio Calzia,
a good friend, a great warrior

Supervisors’Foreword
Gauge/gravity duality is one of the most powerful, ways to systematically tackle
problems regarding strongly correlatedﬁeld theories. It was discovered in 1997 by
Juan Maldacena in the context of string theory, but physicists very quickly realised
that this (still conjectured) duality might have a wider range of possible applica-
tions. To date it has been applied to analyse problems related to quark/gluon plasma
as well as condensed matter systems.
The work of Andrea Amoretti deals with the application of gauge/gravity duality
to the physics of high-temperature superconductive materials. These peculiar sys-
tems were discovered a long time ago, in the early 1980s. At present, despite strong
efforts made by the physics community to understand the mechanisms which
govern the physics of these materials, a complete theoretical explanation of their
behaviour is still lacking. In particular, the most inexplicable features appear in the
non-superconductive phase, where the temperature dependence of the thermo-
electric transport coefﬁcients differ signiﬁcantly from the one predicted by Fermi
liquid theory. It is commonly believed that a comprehension of this exotic beha-
viour is fundamental in order to understand the pairing mechanism which controls
the superconductive transition. In this book, Andrea Amoretti tackles the problem
from a phenomenological point of view by analysing the thermo-electric transport
properties of a wide class of gauge/gravity models. Speciﬁcally, since in order to
compare theoretical predictions with experimental results one needs to analyse DC
transport properties, mechanisms of momentum dissipation need to be included in
the holographic analysis in order to make the DC transport coefﬁcients of the model
ﬁnite. Andrea Amoretti has analysed carefully these mechanisms of momentum
dissipation in the context of gauge/gravity duality and has clariﬁed, for theﬁrst
time, the advantages and limitations of these models if applied to the phe-
nomenology of the phenomenon of high-temperature superconductivity.
The work of Andrea Amoretti has initiated unusual collaborations between
experimentalists and string theorists. Moreover, the present book constitutes one
of the few examples in the literature in which this topic is carefully reviewed both
vii

from experimental and theoretical points of view, including not only holographic
results but also standard condensed matter achievements developed over the past
decades. This work might be extremely useful both scientiﬁcally and pedagogically.
Genoa, Italy
April 2017
Prof. Nicola Maggiore
Prof. Nicodemo Magnoli
viii Supervisors ’Foreword

Abstract
In this book we analyse the properties of certain kinds of condensed matter systems
in which the electrons are strongly correlated. Among these systems, the most
well-known representatives are probably high-temperature superconductors, whose
properties are carefully analysed in Part I. The most exotic phase of these materials
is the non-superconducting one, where the behaviour of the thermo-electric trans-
port coefﬁcients abruptly deviate from those predicted by Fermi liquid theory—the
standard paradigm according to which we understand the majority of the existing
condensed matter systems. It is commonly thought that this exotic behaviour can be
explained by the strong correlations between electrons, even though, after forty
years since the discovery of theﬁrst example of this class of material, a complete
theoretical explanation is still lacking. The main topic of this treatise is to analyse
the properties of these materials using AdS/CFT (or holographic) correspondence—
mathematical tools developed in the context of string theory—representing one
of the most powerful techniques known to help understand strongly correlated
systems. Part II carefully introduces the basics of AdS/CFT which is required to
analyse strongly correlated condensed matter systems. Part III analyses the DC
themo-electric transport properties of certain kinds of holographic systems which
exhibit mechanisms of momentum dissipation. The holographic results are com-
pared with the phenomenology of high-temperature superconductors in order to
understand if these materialsﬁt in the class of strongly correlated systems described
by these holographic models.
ix

Acknowledgements
When writing a scientiﬁc manuscript, be it a journal article, a book, or a review, the
most challenging part is to consider who to acknowledge. It is extremely difﬁcult to
select, among the multitude of people I have interacted with, those who deserve
acknowledging the most. I think that the most fair thing to do is to start by
acknowledging all the human beings that have interacted with me over the past four
years, whether that be in the form of a small chat on the street, a complicated
philosophical conversation in a pub accompanied by a couple of beers, or a simple
scientiﬁc discussion in front of a blackboard. All of these people have contributed
and must be mentioned here.
If I really have to select speciﬁcally, there are probably three people that deserve
to be listed more than the others. This is because they have contributed the most to
the writing of this book. Theﬁrst two areNicoandNicola, my friends, collabo-
rators, and supervisors, who have patiently tolerated my complaints about searching
for postdoctoral jobs over the last year. The third person, probably the most
important, is my close friend and collaboratorDaniele Musso. I shared with him
most of my doubts, passions, and moments of happiness and sadness over the last
four years. It would not have been the same without him.
Aﬁnal thought goes tomy family, to whom I am grateful for the support and
encouragement that has always been given to me when following my dreams and
passions.
xi

Contents
Part I Condensed Matter Background
1 Preamble: Transport Coefﬁcients Deﬁnition
.................... 3
2 Standard Metals and the Fermi Liquid
........................ 5
References
................................................ 9
3 The Fermi Liquid Breakdown: High-T
cSuperconductivity........11
3.1 Cuprates: Crystalline Structure and Electronic Properties
........12
3.2 Cuprates: Phase Diagram
................................ 15
3.3 Cuprates: In-Plane Transport Properties in the
Non-superconducting Phase
.............................. 16
3.3.1 Resistivity and Hall Angle
......................... 18
3.3.2 Magneto-Resistance and the Koheler’s Rule
............ 21
3.3.3 Thermal Transport
................................ 23
References
................................................ 24
4 Theoretical Attempts
....................................... 29
4.1 Anderson’s Model
..................................... 29
4.2 Phenomenological Marginal Fermi Liquid
................... 30
4.3 Quantum Criticality
.................................... 33
References
................................................ 35
Part II Introduction to Holography
5 The Gauge Gravity Duality
................................. 39
5.1 Review: Conformal Field Theory
.......................... 39
5.1.1 The Conformal Group
............................. 39
5.1.2 Field Theory and Conformal Invariance
............... 42
5.1.3 Unitarity Bounds
................................. 48
5.2 Review: Anti-de Sitter Spaces
............................ 48
5.2.1 AdS as a Maximally Symmetric Solution
of Einstein’s Equations
............................ 48
xiii

5.2.2 Hyper-Surface Embedding and Geometric Properties.....50
5.2.3 Geodesic Motion inAdS
dþ1........................ 51
5.2.4 Carter-Penrose Diagram and Conformal Boundary
.......53
5.3 Motivating the Duality
.................................. 55
5.4 The GKPW Rule and Its Consequences
..................... 58
5.4.1 Holographic Renormalization and the Prescription
for the Correlators
................................ 61
5.5 An Example: Scalar Field inAdS
dþ1....................... 63
5.6 Thermal AdS/CFT
..................................... 72
5.6.1 Introducing Temperature in Holography
............... 75
5.6.2 Holography at Finite Charge Density
................. 78
5.7 Summa: The Holographic Dictionary
....................... 81
References
................................................ 82
Part III Thermo-electric Transport in AdS/CFT
6 Preamble: Linear Response Theory
........................... 85
Reference
................................................ 87
7 The Simple Raissner-Nordström Case
......................... 89
7.1 Bulk Solution
......................................... 89
7.2 Fluctuations
.......................................... 92
7.2.1 Renormalization of the Fluctuation Action
............. 93
7.3 Correlators and Transport Coefﬁcients
...................... 94
7.4 Physical Properties of Transport Coefﬁcients
................. 96
References
................................................ 98
8 Momentum Dissipation in Holography
........................ 99
8.1 Adding a Mass to the Graviton to Break Momentum
Conservation
.......................................... 99
8.1.1 The Massive Gravity Model
........................ 99
8.1.2 Background and Thermodynamic
.................... 100
8.1.3 Massive Gravity and Momentum Dissipation
...........102
8.1.4 Fluctuations and Transport in the Massive Case
.........103
8.1.5 Counter-Terms and Transport Coefﬁcients Deﬁnition
.....106
8.2 Spectral Properties of Transport Coefﬁcients
.................107
8.3 DC Transport Coefﬁcients
............................... 108
8.3.1 The Electric Conductivity and the Seebeck Coefﬁcient
....108
8.3.2 Thermal Conductivity and Onsager Reciprocity
.........112
8.3.3 DC Properties of the Transport Coefﬁcients
............114
8.4 Adding the Dilaton
..................................... 116
8.4.1 Properties of DC Transport Coefﬁcients
...............118
8.5 Holographic Magneto-Transport
........................... 119
8.5.1 Thermodynamics
................................. 120
8.5.2 Transport Coefﬁcients
............................. 122
xiv Contents

8.5.3 Structure of the Thermoelectric Transport Coefﬁcients ....128
8.5.4 Bulk Electromagnetic Duality and Its Consequences from
the Boundary Perspective
.......................... 130
References
................................................ 131
9 Physical Implications
....................................... 133
9.1 Criticality and Diffusion Bounds
.......................... 134
9.1.1 The Shear Viscosity Bound and the Concept of Planckian
Dissipation
..................................... 134
9.1.2 The Diffusivity Bounds Conjecture in Cuprates
.........137
9.1.3 On the Existence of Diffusivity Bounds in
Holography
..................................... 140
9.2 Holographic Inspired Phenomenology
...................... 145
References
................................................ 149
Appendix A: Basics of Fermi Liquid Theory
...................... 151
Appendix B: AsymptoticallyAdSSpace-Time:AdSBlack Holes
.......175
Appendix C: Radial Quantization and Unitarity Bounds
.............183
Appendix D: Effect of Linear Source in Time on DC Transport
.......189
Appendix E: Technical Aspects of Holographic
Magneto-Transport
................................ 191
Appendix F: Einstein Relations for Charge and Heat
Diffusion Constants
................................ 195
Curriculum Vitae
............................................ 197
Contents xv

Introduction
In the past century there has been great deal of progress made in understanding the
world around us by means of quantumﬁeld theory, an extremely powerful tool
which allows us to understand many different physical phenomena, from elemen-
tary particle physics to condensed matter physics. Our ability to extract results from
quantumﬁeld theory mostly relies on perturbation theory. In this framework, the
physical observables are usually evaluated as an expansion in powers of the cou-
pling constant, i.e., a dimensionless parameter which measures the departure from
free-ﬁeld theory.
However, in the last decades it has been realised that nature cannot always be
investigated by means of perturbation theory. One of the most well-known
examples of this fact is quantum chromodynamics (QCD). The asymptotically free
nature of QCD makes perturbation theory reliable at high energies. On the other
hand, at low energies, QCD becomes strongly coupled to phenomena such as
conﬁnement and chiral symmetry, which are non-perturbative in nature. In the
condensed matter framework, the prototypical example of a non-perturbative
phenomenon is that of high-T
csuperconductors, where strong coupling causes the
physical behaviour of these materials to abruptly deviate from the standard para-
digm according to which we understand normal metals in nature—the Fermi liquid
theory. Recently, one of the predominant ideas for explaining the strong coupling
nature of these materials has been that proposed by Sachdev [6], who suggested that
strong interactions between electrons atﬁnite temperatures are governed by the
existence of critical points at zero temperature. Systems in the vicinity of a critical
point are actually described by scale invariant quantumﬁeld theory because of the
inﬁnite correlation lengths which arise. Then, in this sense, the problem reduces to
that ofﬁnding a suitable strongly interacting scale invariant quantumﬁeld theory
which describes the physics of such strange metals. Unfortunately, at present we
know very few techniques to analyse strongly interacting quantumﬁeld theory. To
this end, most recently a mathematical tool has been developed in the context of
string theory, the so called Anti-de Sitter/conformalﬁeld theory (AdS/CFT) cor-
respondence(or gauge/gravity duality), which has acquired a prominent role in
helping to understand the general properties of strongly coupled systems. In brief,
xvii

the tool is based on a conjectured duality, discovered by Juan Maldacena [4] in
1997, between certain strongly coupled regimes of ordinary quantumﬁeld theories
indspacetime dimensions and classical (i.e., weakly coupled) theories of gravity in
at leastdþ1 dimensions. As a result, the correspondence maps difﬁcult quantum
problems inﬁeld theory to easier, classical ones on gravity. In its simplest form, the
correspondence relates a strongly coupled CFT to classical gravity on AdS
backgrounds.
To date, the gauge/gravity duality provides the closest connection between string
theory and the observable world. Simultaneously, it constitutes an extremely
promising environment for enlarging our theoretical understanding of strongly
interacting quantum systems and string theory itself. Despite the fact that this tool
was born out of string theory, in the last decade it acquired a prominent role to help
understand strongly interacting quantum systems by means of providing an effec-
tive description. Such an effective description does not take into account the string
theory origin of the duality. The main goal of this approach is to construct effective
toy models with features which are believed to be universal to many other strongly
interacting systems either with or without a stringy origin. Within this framework,
the duality has been used extensively to describe phenomena analogous to those
which occur in QCD and in high-temperature superconducting materials.
The holographic correspondence provides a relatively easy set-up for computing
properties of systems in and out of equilibrium, as well as phases with non-zero
fermionic densities and transport coefﬁcients. The latter are all difﬁcult to achieve
with other standard non-perturbative approaches. The main limitation of AdS/CFT
is that, at present, realisticﬁeld theories like QCD cannot be directly explored.
However, despite its limitation to toy models, the correspondence has provided
valuable insights at both the quantitative and qualitative level on properties of
strongly coupled systems realized in nature.
In the context of condensed matter, this duality has been applied to the study of
unconventional superconductivity. Assuming the existence of a quantum critical
point in the phase diagram of these materials, according to Sachdev’s proposal, the
theory governing these systems in the vicinity of this point has to be scale invariant,
allowing the gauge/gravity duality to be applied in its simplest form. Using holo-
graphic techniques, one can study the perturbations within the quantum critical
region in a controlled way using a holographic dictionary. As an example, studying
the system atﬁnite temperature is equivalent to placing a black hole at the center of
AdS spacetime. Analogously, one can analyze the system atﬁnite charge density or
include the effects of an external magneticﬁeld by introducing a Maxwellﬁeld in
the gravitational model. At present this is a very activeﬁeld of research with a
number of good reviews and books already available in the research literature (see,
e.g., [1–3, 5, 7–8])
The aim of this book is to consider how the AdS/CFT correspondence might
help in gaining some insight of strongly coupled condensed matter systems. In
particular, in the following Chapters 6, 7, 8 and 9, the holographic correspondence
is used to try to understand the peculiar properties of high-T
csuperconductors.
xviii Introduction

Since this is a line of research where techniques from very differentﬁelds of
physics come together, in order for the discussion to be self-consistent and com-
prehensible to scientists from different branches of physics, a large introductory text
is necessary. Consequently, the book is organised into three parts. Parts I and II are
introductory while Part III contains the original result of the treatise.
In Part I the basic features of high-T
csuperconductors are described. Initially the
book analyses the experimental properties of these peculiar materials, focusing in
particular on in-plane thermo-electric transport properties. At each step, the dif-
ferences between the behaviour of the strange metals and the Fermi liquid pre-
diction is commented upon. In the last chapter of Part I we focus on some
theoretical attempts, introduced in the past, to explain the exotic behaviour of these
materials, concentrating on the idea of the existence of a quantum critical point in
their phase diagram.
In Part II the AdS/CFT correspondence is introduced. This Part is constructed in
order to introduce the holographic duality as a series of computational rules, the so
calledholographic dictionary, the knowledge and comprehension of which is a
necessary step in order to understand the discussion in Part III of the book.
Part III contains the original results of the manuscript. In particular, the
thermo-electric transport properties of a strongly coupled bi-dimensional plasma in
the presence of an extrinsic mechanism of momentum dissipation is deeply analysed
using holography. The holographic results are compared with the phenomenology of
strange metals. In the last chapter of Part III a conclusion to the book, and the
physical implications of these holographic toy models, are discussed in details.
References
1. Martin Ammon and Johanna Erdmenger,Gauge/Gravity Duality(Cambridge University Press,
Cambridge, UK, 2015)
2. Sean A. Hartnoll, Lectures on Holographic Methods for Condensed Matter Physics. Class.
Quant. Grav.26, 224002 (2009)
3. Sean A. Hartnoll, Andrew Lucas, Subir Sachdev,Holographic Quantum Matter, Dec 21,
(2016), pp. 178.arXiv:1612.07324[hep-th]
4. Juan Martin Maldacena, The large N limit of superconformalﬁeld theories and supergravity. Int.
J. Theor. Phys.38, 1113–1133 (1999). [Adv. Theor. Math. Phys. 2,231(1998)]
5. Makoto Natsuume, AdS/CFT Duality User Guide. Lect. Notes Phys.903,1–294 (2015)
6. S. Sachdev,Quantum Phase Transitions(Cambridge University Press, 2001)
7. Jan Zaanen, Ya-Wen Sun, Yan Liu, Koenraad Schalm,Holographic Duality in Condensed
Matter Physics(Cambridge University Press, 2015)
8. A. Zaffaroni, Introduction to the AdS–CFT correspondence. Class. Quant. Grav.17, 3571–3597
(2000)
9. A. Amoretti and A. Braggio and N Maggiore, N Magnoli. Thermo-electric transport in
gauge/gravity models. In: Adv. Phys. X 2.2 (2017), pp. 409–427
10. A. Amoretti, N. Magnoli,On Conformal Perturbation Theory, May 9, (2017), pp. 20.arXiv:
1705.03502[hep-th]
Introduction xix

11. A. Amoretti, D. Arean, R. Argurio, D. Musso, Z. Pando, A. Leopoldo.A holographic
perspective on phonons and pseudo-phonons. In: JHEP 1705 (2017) 051.arXiv:1611.09344
[hep-th]
12. A. Amoretti, M. Baggioli, N. Magnoli, D. Musso.Chasing the cuprates with dilatonic dyons.
In: JHEP 06 (2016), p. 113.arXiv:1603.03029[hep-th]
13. A. Amoretti, D. Musso.Magneto-transport from momentum dissipating holography. In: JHEP
09 (2015), p. 094.arXiv:1502.02631[hep-th]
14. A. Amoretti, A. Braggio, N. Magnoli, D. Musso.Bounds on charge and heat diﬀusivities in
momentum dissipating holography. In: JHEP 07 (2015), p. 102.arXiv:1411.6631[hep-th]
15. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli.Introduction of a boundary in
topologicalﬁeld theories. In: Phys. Rev. D90.12 (2014), p. 125006.arXiv:1410.2728[hep-th]
16. A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli, D. Musso.Analytic dc thermoelectric
conductivities in holography with massive gravitons. In: Phys. Rev. D91.2 (2015), p. 025002.
arXiv:1407.0306[hep-th]
17. A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli, D. Musso.Thermo-electric transport in
gauge/gravity models with momentum dissipation. In: JHEP 09 (2014), p. 160.arXiv:1406.
4134[hep-th]
18. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli.Holography inﬂat spacetime:
4D theories and electromagnetic duality on the border. In: JHEP 04 (2014), p. 142.arXiv:
1401.7101[hep-th]
19. A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli, D. Musso.Coexistence of two vector order
parameters: a holographic model for ferromagnetic superconductivity. In: JHEP 01 (2014),
p. 054.arXiv:1309.5093[hep-th]
20. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli.3+1D Massless Weyl spinors
from bosonic scalar-tensor duality. In: Adv. High Energy Phys. (2014), p. 635286.arXiv:
1308.6674[hep-th]
21. A. Amoretti, A. Blasi, G. Caruso, N. Maggiore, N. Magnoli.Duality and Dimensional
Reduction of 5D BF Theory. In: Eur. Phys. J. C73.6 (2013), p. 2461.arXiv:1301.3688[hep-th]
22. A. Amoretti, A. Blasi, N. Maggiore, N. Magnoli.Three-dimensional dynamics of
four-dimensional topological BF theory with boundary. In: New J.Phys. 14 (2012), p. 113014.
xx Introduction

Part I
Condensed Matter Background

Chapter 1
Preamble: Transport Coefﬁcients Deﬁnition
In this manuscript we will analyse the thermo-electric transport properties of
two-dimensional condensed matter systems. Then, in order to ﬁx the notations in
this brief preamble we will deﬁne the transport coefﬁcients for the case at hand.
We will consider a two-dimensional system living in the planex−yand, in some
cases, we will analyse also the effects due to an external magnetic ﬁeldBapplied in
the direction perpendicular to thex−yplane,z(see Fig.1.1).
We are interested in the response of the electrical currentσJand the heat current
σQto an applied electric ﬁeldσEand a temperature gradientσ∇T. By deﬁnition, the
transport coefﬁcients relate the previous quantities in the following way:
σ
σJ
σQ
∇
=
σ
ˆσˆα
Tˆαˆ¯κ
ασ
σE
−σ∇T
∇
. (1.1)
In the presence of an external magnetic ﬁeldBin thez-direction (see Fig.1.1)the
transport coefﬁcientsˆσ,ˆαandˆ¯κare matrices, which, due to Onsager reciprocity,
assume the following form:
ˆσ=σ
xx
ˆ1+σ
xyˆε, (1.2)
whereˆ1 is the identity, andˆεis the antisymmetric tensorε
ij=−ε ji.σxxandσ xy
describe the longitudinal and Hall conductivity, respectively. The resistivityˆρis
deﬁned as the inverse of the conductivity matrix, namelyˆρ=ˆσ
−1
. Similarly, the
thermo-electric conductivityˆαhas a form analogous to (1.2), and determines the
Seebeck coefﬁcientSvia the relation:
S=
α
xx
σxx
, (1.3)
Finallyˆ¯κ, which governs thermal transport in the absence of electric ﬁelds, assumes
a similar structure to that described before forˆσandˆα. In contrast toˆ¯κ, the thermal
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A. Amoretti,Condensed Matter Applications of AdS/CFT, Springer Theses,
DOI 10.1007/978-3-319-61875-3_1
3

4 1 Preamble: Transport Coefﬁcients Deﬁnition
Fig. 1.1Schematic
illustration of a typical
experimental setup
conductivity,ˆκ, is deﬁned as the heat current response to−σ∇Tin the absence of
an electric current, namely, in the presence of electrically isolated boundaries. It is
given by
ˆκ=ˆ¯κ−Tˆα·ˆσ
−1
·ˆα. (1.4)
Eventually, the Nernst coefﬁcient is deﬁned as the electric ﬁeld induced by a thermal
gradient in the absence of an electric current. It is deﬁned by the linear response
relationσE=−ˆθσ∇T, with
ˆθ=−ˆσ
−1
·ˆα. (1.5)
With these deﬁnitions at hand, we are now ready to start the analysis of the exotic
and exciting properties of the cuprates superconductors, starting by understand how
they differ from the Fermi Liquid theory.

Chapter 2
Standard Metals and the Fermi Liquid
One of the milestones and great results of the 20
th
century isLandau’s Fermi liquid
theory, which underlines our present understanding of the majority of the known
states of matter, like normal metals, semi-conductors, superconductors and super-
ﬂuids. To better understand the differences between the predictions of this great
theory and the behaviour of the cuprate superconductors, strange states of matter
discovered since the early 80s, it is necessary to recall its basic properties in this
Introduction, referring the reader interested in the technical aspects to Appendix A
or to standard condensed matter textbook (e.g. [1,2]).
Let us start by recalling the basic properties of a system of free fermions in a box,
where the Pauli exclusion principle controls everything. In the ground-state of this
system all the single-particle states inside a sphere in momentum space with radius
k
F
1are ﬁlled, while the state outside the sphere are empty. The external surface of
this sphere is called theFermi surface. The system has two types of low energy
excitations. One can in fact ﬁll a state slightly outside the Fermi surface, creating
a particle, or remove a fermion from a ﬁlled state slightly inside the Fermi surface,
creating what is typically called a hole. These excitations are gapless by deﬁnition,
and have linear dispersion (fork−k
FεkF):
ε(k)=
k
2
2m
−μ=
k
F
2m
(k−k
F)≡v F(k−k F), (2.1)
wheremis the mass of the fermions,μ≡
k
2
F
2m
is the chemical potential, the quantity
v
F≡
kF
m
is called the Fermi velocity and particles and holes are distinguished by
the sign ofk−k
F. Rephrasing the previous statements in a more formal language,
1
kFis ﬁxed by the density of Fermions, as we will see below.
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5

6 2 Standard Metals and the Fermi Liquid
the existence of these kind of excitations manifests itself as a pole in the complex
frequency plane of the retarded Green’s functionG
R(ω,ψk)of the electron operator
ψ(ωψk):
G
0
R
(ω,ψk)≡ψ(ω,ψk)ψ(0,0)=
1
ω−ε(k)+i0
+
. (2.2)
Note that the retarded Green’s function (2.2) describes the response of the system to
the addition of a single electron. Fourier transforming the propagator (2.2) back in
time, in fact, one can notice that the resulting expression is exactly the one for the
usual Green’s function for the propagation of a free particle of energyε(k)(2.1):
G
0
R
(t,ψk)=i
√
2πθ(t)e
−iε(k)t
. (2.3)
The previous picture might not be any more valid in the case in which interactions
between electrons are turned on, since in this case the concept of particle is not well
deﬁned. Actually, one can naively expect that the qualitative picture of the non-
interacting gas should remain valid if the interactions are weak, but there are no
apparent reasons for this intuition to remain valid at strong coupling.
The basic assumption from which the phenomenological Landau theory is con-
structed, is that the qualitative picture for non-interacting Fermi gas remains actually
valid for a generic interacting fermionic system, also in the case of strong interactions
between the elementary constitutive fermions. Speciﬁcally, the Landau Fermi liquid
theory has two fundamental starting assumptions:
•There exists a Fermi surface which characterizes the ground state of a generic
interacting fermionic system. In momentum space, this surface lies atψk=ψk
Fand
is the locus at which the Green’s functionG
0
R
(ω,ψk)has a simple pole.
•The low energy excitations around the Fermi surface are weakly interacting parti-
cles, called quasi-particles, despite the (possibly strong) interactions between the
fundamental fermions. The quasi-particles are characterized by the same charge
and statistics of the underlying fundamental fermions.
Given these basic assumptions, one has to verify that the theory is stable, namely
that, when the interactions between quasi-particles are switched on, the quasi-
particles life-time is long enough such that an approximate particle picture still
applies. Eventually, it can be proven that, given a generic local interaction between
quasi-particles, the decay rate of a quasi-particle obeys (see Appendix A for details)
Γ∼
ε
2
μ
εε. (2.4)
Thus, despite the potentially strong interactions, there is a region sufﬁciently near
to the Fermi surface, where quasi-particles have long life-time and an approximate
particle pictures still applies.
This implies that, near the Fermi surface, the retarded Green’s function for quasi-
particles acquires the following form:

2 Standard Metals and the Fermi Liquid 7
GR(ω,ψk)=
Z
ω−v F(k−k F)+∗(≡,k)
, (2.5)
whereZ<1 is the quasi-particle residue, which, as we will see later, measures the
jump in the occupation number at the Fermi surface, and∗(≡,k)is called the free
energy. Finally, according to (2.1), the free energy∗has the following low energy
behavior:
Γ∗(≡,k)=
iΓ
2
∼iω
2
. (2.6)
Starting from these basic assumptions, it is possible to develop a general low
energy theory, independently of the precise microscopic details of the system. More-
over, just introducing some phenomenological prescriptions, one can derive the
behaviour of the thermodynamical quantities like the speciﬁc heatC
Vand the chem-
ical potentialμ, the entropysand the thermo-electric transport coefﬁcients (see
Appendix A for more details).
Regarding the thermodynamical quantities, considering only the quasi-particle
contribution, we obtain:
C
V=T
ε
∂s
∂T
≡
V
=s=
π
2
3
N(0)k
2
B
T, (2.7)
μ(n,T)=μ(n,0)−
π
2
4
k
B
ε
1
3
+
n
m
∗
∂m
∗
∂n
≡
T
2
TF
. (2.8)
wherek
Bis the Boltzmann constant,N(0)is the density of carriers at the Fermi
surface,nis the total density of quasi-particles andT
F=k
2
F
/(2m
∗
kB)is the Fermi
temperature.
The results previously described are extremely powerful and do not depend on the
microscopic details of the system at hand. However, when we have to compare the the-
oretical predictions with experiments, we have to keep in mind that the experimental
results provide us not only with the electronic contribution of the thermodynamical
quantities (2.7), but with the total contribution, which takes into account also the
effect of lattice vibrations, i.e.phonons, and defects. Since, as we will see in the
next Section, it is not always an easy task to extrapolate the electronic contribution
from the experimental data, in what follows we will try, if possible, to specify how
the external degrees of freedom like lattice vibrations and impurities modiﬁes the
properties of the electronic plasma. As an example, regarding the speciﬁc heatC
V,it
is known [2] that the phonons contribution to this quantity can be expanded in series
of odd powers of the temperatureT, namely:
C
ph=BphT
3
+EphT
5
+... . (2.9)
Then, the total speciﬁc heat in a normal metal should scale as:
C
V=γT+C ph. (2.10)

8 2 Standard Metals and the Fermi Liquid
Table 2.1Transport coefﬁcients temperature dependence predicted by the Fermi liquid theory
LowT,(TεT D) HighT,(T T D)
ρ Aimp+Be,eT
2
+Ce,phT
d+2
Ae,phT
S DT+E phdT
d
De,phT+Fphd
1
T
κ Hee
1
T
+LimpT+G e,phT
d−1
He,ph
As regards the thermo-electric transport coefﬁcients (see Chap.1for their deﬁni-
tion), the relevant quantities in experiments are the electric resistivityρ, the thermal
conductivityκand the Seebeck coefﬁcientS, which measure the voltage generated
due to the presence of an applied external thermal gradient. Keeping into account
the presence of phonons and defects, the Fermi liquid theory predicts the following
behaviours for these quantities:
wheredis the number of spatial dimensions in the system. In deriving the previ-
ous temperature scalings we have taken into account four different kind of scatter-
ing processes: the electron-impurity scattering (subscript imp), the electron-electron
scattering (subscript ee), the electron-phonon scattering (subscript e-ph) and the
phonon-drag mechanism (subscript phd), namely the process according to which
the heat transfer in the metal causes a ﬂux of phonons which carries the electron
with it. This mechanism is relevant only if one considers the Seebeck effectSand
can be neglected in the analysis of the electric and thermal transport. In normal
metals, the phonon-phonon scattering process is sub-dominant with respect to the
previously outlined scattering mechanism and can be neglected in the analysis of the
thermoelectric transport coefﬁcients (see Appendix A).
We have divided the whole temperature range into two intervals separated by
the Debye temperatureT
D. The coefﬁcients which multiply the powers of the tem-
peratureTin Table2.1, are constant which depends on the speciﬁc parameters of
the metal under consideration. In the regionT T
Dthe electron-phonon scattering
mechanism largely dominates the transport. In the opposite regime, at very lowT,
the scattering mechanisms are dominated by the effect of impurities. However, in
the transition region betweenT∼0 andT∼T
D, since the scattering rate of the
electron-phonon processes decreases faster than that of electron-electron processes
as the temperature is decreased, there may be a region in which the transport proper-
ties are dominated by the electron-electron interactions. In this region the resistivity
of the Fermi liquid scales asT
2
.TheT
2
scaling of the resistivity is considered a stan-
dard evidence of the presence of the Fermi liquid in the experimental measurements
(see Chap.3).
Finally, let us make some comments about the celebrated Wiedemann-Franz law.
This law states that in a Fermi liquid in the presence of elastic scattering processes,
the ratioκ/(σT)is constant in temperature and assumes the valueL
0=
π
2
3e
2.In
the analysis of Table2.1, the scattering processes considered are all elastic with the
exception of the electron-phonon interaction, under which a fraction of the energy
of the quasi-particles is transferred to the lattice. This is deﬁnitely true in the low-T

2 Standard Metals and the Fermi Liquid 9
region where, as one can see from the table, the Wiedemann-Franz law is not satisﬁed.
However, in the high-Tregime the fraction of energy transferred to the lattice is very
small and also the electron-phonon scattering can be considered as elastic. In this
region the Wiedemann-Franz law holds exactly.
References
1. A.A. Abrikosov, inIntroduction to the Theory of Normal Metals, Solid State Physics Series
(Academic Press, 1972)
2. L.P. Pitaevskii, E.M. Lifshitz, inPhysical Kinetics, vol. 10 (Elsevier Science, 2012)

Chapter 3
The Fermi Liquid Breakdown: High-T c
Superconductivity
The Fermi liquid theory that we have outlined in the previous section has been
tremendously successful in explainingalmostall metallic states in nature. However,
fortunately nature hides always great surprises. In fact the ﬁrst big breakdown of
the Fermi liquid came in the early 80s, with the discovery of the phenomenon of
high-temperature superconductivity [1].
As the name suggests, highT
csuperconductors are metallic materials with a
transition temperature for superconductivity higher than 30 K (which is the maximum
critical temperature predicted by BCS theory [2]). Actually, high-T
csuperconductors
have been observed with transition temperatures as high as 138 K.
Moreover, in these peculiar materials both the transport properties of the non-
superconducting phase and the superconducting pairing mechanism differ signiﬁ-
cantly from whose predicted by the Fermi liquid and BCS theory.
1
Until 2008, the only materials believed to have high-T csuperconductors proper-
ties were certain kind of compound which include in their structure copper oxide
planse (the so calledcuprates), and the term high-temperature superconductor was
used interchangeably with cuprate superconductor for compounds such as bismuth
strontium calcium copper oxide (BSCCO) [3] yttrium barium copper oxide (YBCO)
[4], lanthanum strontium copper oxide (LSCO) and the mercury barium calcium
copper oxide (HgBa
2Ca2Cu3Ox)[5]. However, nowadays it is known that several
iron-based compounds (the iron pnictides) have a physical behaviour similar to that
of the cuprates [6–8].
Although the theoretical effort in explaining the mechanisms which govern the
physics of these materials has been remarkable, at present there is still no an accepted
theory which describes entirely of their peculiar properties.
1
See [2] for a theoretical review on BCS.
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DOI 10.1007/978-3-319-61875-3_3
11

12 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
This chapter is devoted to describe the experimental properties of these materials,
focusing particularly on the way in which the normal phase transport properties differ
from the Fermi liquid paradigm.
2
Since the iron pnictides superconductors have been discovered in very recent times
we will substantially focus on the cuprates, which are the best known materials from
the experimental point of view.
To have in mind the experimental properties of these materials is extremely impor-
tant. In fact in the lack of a solid theoretical model it is fundamental to face with the
experimental data in order to try to develop a serious theoretical starting point.
3.1 Cuprates: Crystalline Structure and Electronic
Properties
In this section we brieﬂy outline the basic crystalline structure of cuprate supercon-
ductors. This is far to be comprehensive. The main purpose of this brief introduction
is to make the reader familiar with the microscopic composition of the most popular
of these materials, and to highlight the common features of these large class of com-
pounds. In what follows, some standard concepts of Structure of matter, like tight
binding and crystalline unite cells appear. We refer the reader not familiar with these
concepts to standard condensed matter textbooks (see e.g. [9]).
There are two features that all the highT
csuperconductors have in common:
the CuO
2planes that form single-layer or multilayer conducting blocks per unit
cell, and the “charge reservoirs” in between the CuO
2planes that are responsible
for contributing either electrons or holes to the CuO
2planes. This structure typically
causes a large anisotropy in normal conducting and superconducting properties, since
electrical currents are generated by holes or electrons created due to the presence of
the oxygen sites of the CuO
2planes.
The ﬁrst superconductor found withT
c>77 K (liquid nitrogen boiling point) is
yttrium barium copper oxide (YBa
2Cu3O6+δ); the proportions of the three different
metals in the YBa
2Cu3O7superconductor are in the mole ratio of 1 to 2 to 3 for
yttrium to barium to copper, respectively. Thus, this particular superconductor is
often referred to as the 123 superconductor. The unit cell of YBa
2Cu3O7(see Fig.3.1)
consists of three pseudo-cubic elementary perovskite unit cells. Each perovskite unit
cell contains a Y or Ba atom at the center: Ba in the bottom unit cell, Y in the middle
one, and Ba in the top unit cell. Thus, Y and Ba are stacked in the sequence [Ba-Y-Ba]
along the c-axis. All corner sites of the unit cell are occupied by Cu [11]. One of the
key feature of the unit cell of YBa
2Cu3O6+δ(YBCO) is the presence of two layers
of CuO
2.
2
This is done in light of the holographic analysis of the normal phase transport properties, performed
in Part 3.

3.1 Cuprates: Crystalline Structure and Electronic Properties 13
Fig. 3.1Crystal structures of four hole-doped cuprates.aThe unit cells.bStructure of the CuO 2
sheets. Just the most important electronic orbitals, namely Cud
x
2
−y
2andOp σ, are shown. Figure
from [10]
The crystal structures of Bi-, Tl-, Hg- and La-based high-T csuperconductors
are very similar (see Fig.3.1)[12]. Like YBCO, the perovskite-type feature and
the presence of CuO
2layers also exist in these superconductors. However, unlike
YBCO, Cu-O chains are not present in these superconductors. Moreover, contrary to
the YBCO superconductor which, as previously said, has an orthorhombic structure,
the other high-T
csuperconductors have a tetragonal structure.
The cuprates previously discussed are all hole-doped, namely the “charge reser-
voirs” in between the CuO
2contributes in adding holes to the CuO2planes. Although
the majority of high-T
csuperconductors are hole-doped compounds, there are a small
number that can be doped with electrons (see [13] for a review on the topic). The
majority of these materials have the chemical formula RE
2−xMxCuO4where the
lanthanide rare earth (RE) substitution is Pr, Nd, Sm or Eu and M is Ce or Th. These
are single-layer compounds which, unlike their hole-doped parents, have a crystal
structure characterized by a lack of oxygen in the apical position (see Fig.3.2left).
As already mentioned, the common feature of all this compound is the presence
of CuO
2planes in their crystalline structure. Then, even though no ﬁrm evidence
has been provided, it is commonly believed that the superconductivity phenomenon
and all the peculiar properties of these materials are due to the presence of these
perovskite planes.

14 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
Fig. 3.2Crystal structures
of the electron-doped cuprate
RE
2xCexCuO4and of its
closest hole-doped
counterpart La
2xSrxCuO4.
Here RE is one of a number
of rare earth ions, including
Nd, Pr, Sm, or Eu. Figure
from [13]
a*
b*
c
a
b
c
RE
2-x
Ce
x
CuO
4
La
2-x
Sr
x
CuO
4
Cu
O
RE, Ce
La, Sr
Fig. 3.3Schematic ﬁgure of
the CuO
2plane showing the
spin alignments of the Cu
spins at half-ﬁlling and the
three principal hopping
parameterst,t
δ
andt
δδ
The electronic structure of the perovskite planes is sketched in Fig.3.3.Inthe
conducting partially-ﬁlled band the predominant orbitals are 3d
x
2
−y
2and O2px,y
.The
tight-binding representation of its energy dispersion is:
ε(σk)=ε
0−2t
δ
cosk x+cosk y
σ
+4t
δ
δ
cosk
xcosk y
σ
+4t
δδ
δ
cos 2k
x+cos 2k y
σ
.
(3.1)
The ratiot
δ
/tis known to affect the critical temperatureT cin a large number of
cuprates [14]. LowT
ccuprates like La2xSrxCuO4have a relatively lowt
δ
/t, whilst
those with highert
δ
/tvalues, such as YBa2Cu3O6+δ, have higherT c.

3.2 Cuprates: Phase Diagram 15
3.2 Cuprates: Phase Diagram
In the previous Section we have noticed that all the peculiar properties of the cuprates
superconductors are believed to be caused by the presence of the perovkite planes.
Consequently, this Section will be devoted to analyse the in-plane phase diagram of
the cuprates. Substantially, all the cuprates superconductors share the main features
of the in-plane phase diagram. In this section we will review schematically these
properties, postponing a more precise characterization to the next Section, where the
in-plane transport properties will be analysed.
The phase diagram of the cuprates is extremely reach and depends essentially on
the temperatureTand the doping concentrationp(for hole-doped cuprates) orn
(for electron-doped cuprates).
In Fig.3.4the schematic phase diagram for both electron and hole-doped cuprate
superconductor is plotted as a function of temperature and doping concentration. At
zero doping, the parent compound of both the electron-doped and the hole-doped
cuprates presents an anti-ferromagnetic Mott insulating state. Since we are speaking
of a 2D material, one might think that the Hohenberg-Mermin-Wagner theorem (see
e.g. [9]) could prevent an anti-ferromagnetic phase to exist. The experimental ﬁnding
of long-range anti-ferromagnetic ordering can be reconciled with theory by relaxing
the strict 2D picture and incorporating three-dimensional anisotropic effects [15–18].
As long as the concentration of hole is increased by doping the material, the
anti-ferromagnetic transition temperature of the system decreases rapidly and the
anti-ferromagnetic long-range order eventually disappears completely at around
p∼0.02. Above this doping level, spin ﬂuctuations replace the original anti-
ferromagnetic order and continue to survive in the superconducting phase. When
hole-doping is further increased, a superconductive dome appears fromp∼0.05
up top∼0.25. Generically, the superconducting transition temperatureT
cfor
Fig. 3.4Simpliﬁed doping
dependent phase diagram of
cuprate superconductors for
both electron (n) and hole (p)
doping. The phases shown
are the anti-ferromagnetic
(AF) phase close to zero
doping, the superconducting
phase (SC) around optimal
doping, and the pseudo-gap
phase. Doping ranges
possible for some common
compounds are also shown.
Figure from [19]

16 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
copper-oxide superconductors follows a parabolic dependence on the concentra-
tion of charge carriersp. The maximum of this parabola is called the optimal doping
level,p
opt. A universal formula forT c(p)can be proposed [20]:
T
c(p)=T c,max
ε
1−β(p−p
opt)
2
β
, (3.2)
where the parametersβandp
opthave the constant values,β=82.6,p opt=0.16
for a large number of compounds [21].
It is generally beleaved that the pairing symmetry of the superconducting order
parameter of hole-doped cuprates is mostlyd
x
2
−y
2-like in the under-doped and opti-
mally doped region [22,23]. In the over-doped limit, however, a signiﬁcants-wave
component has been measured [24]. In the normal state of the under-doped cuprates,
a partially suppressed density of states around the Fermi level and an opening of
the spectral gap in the spin and charge ﬂuctuations have been observed [25]. These
is thought to be the causes of several peculiar transport phenomena which will be
analysed in the following sections. This region is typically namedpseudo-gap phase.
Near the optimal doping, the pseudo-gap phase crosses over to an anomalous non-
Fermi liquid region where the transport properties differ signiﬁcantly from the Fermi
liquid paradigm (see the following Section). As we further increase the doping to the
over-doped range, some aspects of conventional Fermi liquid physics are eventually
recovered.
Finally, let us make some comments on the phase-diagram of the electron doped
cuprates. Even though the low doping region is characterized by an antiferromag-
netic long-range ordering as in the hole-doped compound, the phase diagram of the
electron-doped cuprates is not simply the specular reﬂection of the hole-doped one
(see Fig.3.4). Also near the zero doping region the symmetry between the hole-
doped and the electron-doped phase diagram is only approximative, since the anti-
ferromagnetic phase is more robust in the electron-doped material and eventually
persists to higher doping levels (see Fig.3.4). Probably due to this fact the super-
conductive dome of the electron-doped materials is almost ﬁve times narrower. In
addition, the superconducting and the anti-ferromagnetic orders occur in much closer
proximity to each other and may even cohexist, a phenomenon which never occurs in
the hole-doped materials. In what follows we will concentrate on the properties of the
hole-doped cuprates referring to the literature for the electron-doped cuprates [13].
3.3 Cuprates: In-Plane Transport Properties
in the Non-superconducting Phase
As noted before, the typical order of magnitude of the critical temperatureT cof
the superconducting phase transition is too high to be explained with the standard
BCS theory. This is the ﬁrst hint that the microscopic mechanisms that govern the
behaviour of the highT
csuperconductor must be different from that of the Fermi

3.3 Cuprates: In-Plane Transport Properties in the Non-superconducting Phase 17
Liquid described in Chap.2. In this section, we will analyse carefully the transport
properties in the non-superconducting phase, the so called strange metal phase. We
will note that, even though the known thermodynamical properties in this phase are
still Fermi liquid-like [26–28], the transport properties deviates signiﬁcantly from
the Fermi liquid prediction. Since it is commonly believed that a comprehension of
the transport properties in the non-superconducting phase is a fuundamental step to
understand the pairing mechanism which generates superconductivity, from now on
we will focus mainly on the properties of these phase.
In particular, also the basic assumption of the Fermi liquid theory, namely the
existence of stable quasi-particles, has to be questioned in these materials. This can
be seen by the analysis of the spectral electric conductivityσ
xx(ω). In the standard
Fermi liquid theory (see Appendix A), at low frequency this quantity has to follow
a Drude-like behaviour, namely:
σ(ω)β
N(0)e
2
τ
m
∗
1
1−iωτ
, (3.3)
whereτis the quasi-particle life-time, which in the Fermi liquid scales as 1/T
2
.As
noted in Chap.2, this temperature scaling ensure the stability of the quasi-particle
near the Fermi surface and leads to theT
2
resistivity scaling which is characteristic
of the Fermi liquid behavior.
By now optical conductivity data extending to temperatures up to and beyond
300 K are known for the majority of cuprates compounds (see [29,30]forareview)
and a universal and rather striking behaviour seems to emerges. This is illustrated in
Fig.3.5whereσ
xx(ω)data for under-doped La1.9Sr0.1CuO4are reproduced (without
the phonon peaks).
At lowT,σ
xx(ω)is dominated by a large Drude-like peak. AsTincreases, the
width of the drude peak becomes larger andσ(0)drops down. These behavior signal
an increase in the quasi-particle scattering rate and in some cases, a redistribution of
the spectral weight. As long asTapproaches the critical temperatureT
c(β400 K for
La
1.9Sr0.1CuO4) the charge dynamics changes. This is advised by the appearance of a
plateu in the low frequency limit ofσ(ω). AboveT
c, a dip appears in the far infra-red
limit ofσ(ω), signalling a transfer of the sprectral weight at energiesω>1eV.
The falloff ofσ
xx(ω)in the Drude-like regime is remarkably slower than the Drude
formula expectation (3.3). As observed in [32], the conductivity of a optimally doped
cuprate can be ﬁtted by using a Drude equation. However, if the scattering rate in
the Drude equation is set at a low value to reproduce the shape of the low-frequency
peak inσ
xx(ω), then the ﬁt is completely wrong at higher frequencies. If the width
of the Drude peak is chosen to be anomalously broad in accord with the behaviour
of the conductivity atωβ600 cm
−1
, then the model yields the wrong magnitude of
lowωbehaviour and reveals strong disagreement with the DC conductivity.
The lack of a well deﬁned Drude peak has led the physical community to argue
that the quasi-particle picture breaks down in these material (see Chap.4for more
details). This fact is reﬂected in the properties of the DC transport coefﬁcients, those

18 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
Fig. 3.5Spectral conductivityσ xx(ω)data for under-doped La1.9Sr0.1CuO4at various temperature
Twithout the phonon peak. Figure from [31]
behavior abruptly deviates from the Fermi Liquid picture, as we will illustrate in
what follows.
3.3.1 Resistivity and Hall Angle
In this section we will review the basic known properties of the in-plane resistivity
ρ
xx(T)and the Hall angle cotθ Hdeﬁned as the ratio between the electric conductivity
and the Hall conductivity, namely cotθ
H≡
σxx
σxy
.
Let us start from the resistivity. The temperature dependence ofρ
xx(T)can be
carefully characterized in terms of the doping level, as sketched in Fig.3.6. In par-
ticular, as one can see by comparing the temperature dependence ofρ
xx(T)with
that described for the Fermi liquid in Table2.1,theT
2
scaling, which is commonly
considered as a distinguish feature of a Fermi liquid behaviour, is recovered only in
speciﬁc regions of the phase diagram.
In particular, in Fig.3.6the solid lines determine the boundaries of proper phase
transitions, namely the crossovers between the normal state and the superconduct-
ing or anti-ferromagnetic ground state. On the other hand, the dashed lines indicate
changes in theρ
xx(T)behaviour which can not be uniquely associated with a funda-
mental change in the nature of the electronic states. The vertical dashed line which

3.3 Cuprates: In-Plane Transport Properties in the Non-superconducting Phase 19
Fig. 3.6Phase diagrams of the hole-doped cuprates. The different “phases” are mapped in terms
of the different temperature behaviours of the in-plane resistivity
lies at the maximum of the superconducting dome indicates the optimal doping level.
The left and the right regions with respect to the latter line are the under-doped and
the over doped region respectively.
In the under-doped regime,ρ
xx(T)is approximatively linear in temperature at
highT, but as the temperature is lowered it deviates from linearity. This change of
slope inρ(T)is a gradual, continuous process with no clear evidence of a phase
transition belowT
∗
[33–35]. The dashed line depictingTin Fig.3.6reﬂects this
ill-deﬁned nature.
At sufﬁciently low temperatures,ρ(T)of under-doped cuprates develops an
upturn, which might indicates some sort of electronic localization. This upturn is
characterized by log(1/T)dependence [36]. The critical doping levelp
cr i tat which
these upturns occur is not a universal feature of all the cuprates families [37,38].
The most stricking feature of the universality in the behavior of the cuprates is
theT-linear resistivity that at optimal doping, which survives for allT>T
c.This
is a common feature of all the cuprates, despite the large variations in optimalT
c
and in the crystallography of individual cuprate families, and is a strong hint that it
is an intrinsic feature of the CuO
2planes. Moreover, the value ofρ xxatT=300 K
normalized to a single CuO
2plane is largely independent of the chemical composition
of the charge transfer layers.
In the over-doped region,ρ
xx(T)increases in temperature faster thatT.Inthis
region its behavior can be ﬁtted with a sum of two contirbutions, oneT-linear, the

20 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
other quadratic, as well as with a single power lawT
n
, withncomprises within 1, at
optimal doping, and 2 at the superconducting transition boundary on the over-doped
side [39–41]. At sufﬁciently highThowever,ρ(T)becomesT-linear once more.
This crossover temperature [41]ismarkedinFig.3.6as the coherence temperature
T
coh, in line with the intuition from ARPES experiments, that this crossover in the
resistivity behavior coincides with the loss of a well deﬁned quasi-particles peak in
the energy dispersion relation [42].
A purely quadratic in temperatureρ
xx(T), characteristic of a Fermi liquid-like
behavior, is only observed beyond the superconducting dome. The dashed line
markedT
FLrepresents this crossover to strictlyT
2
resistivity. However, in this region
the phenomenon of quantum oscillations [43], which is considered one of the fun-
damental evidence of a Fermi liquid behaviour, has never been measured (Fig.3.7).
In systems immersed in an external magnetic ﬁeld, which is the common situ-
ation in measurements in cuprates, important physical quantities are the transverse
transport coefﬁcients (see Chap.1for their deﬁnitions).
In all hole-doped cuprates near optimal doping, the Hall resistivityρ
xy, which
measure the transverse electrical response to an external applied voltage, displays a
strong and complicated temperature dependence that persists to temperatures as high
as 500 K [33,44–46]. The origin of this anomaly can be understood by analysing the
Hall angle cotθ
Hrather thanρ xyor the Hall conductivityσ xy. The analysis of [44],
in which the dependence of cotθ
Hon the temperature and on the concentration of Zn
Fig. 3.7Left:The temperature dependence of the in-plane YBCO resistivity of single-crystal doped
with Zn.Right:Temperature dependence of the Hall angle cotθ
HvsT
2
for a series of Zn-doped
YBCO crystals. After [44]

3.3 Cuprates: In-Plane Transport Properties in the Non-superconducting Phase 21
impuritiesc Znin YBa2Cu3−xZnxO7−δhas been analysed, has outlined the following
functional form for cotθ
H:
cotθ
H=αT
2
+βc Zn. (3.4)
Studies of the Hall angle in different compounds [33,46] has revealed that the
temperature dependence od cotθ
Houtlined in (3.4) is valid (up to 500 K in some
cases). In some cases, deviations from theTbehaviour become signiﬁcant in the
under-doped or over-doped regimes [45].
Finally, whilst theT
2
dependence of cotθ Hholds for a wide range of doping in
most cuprates, it is not the case for the Bi-based cuprates Bi2212 and Bi2201. In
these systems, the power exponent of cotθ
His closer to 1.75 than 2 [47].
3.3.2 Magneto-Resistance and the Koheler’s Rule
According to Boltzmann transport theory (see Appendix A), the orbital transverse
magneto-resistance of a metalΔρ/ρis proportional to the cyclotron frequencyω
c=
eB/m
∗
and to the quasi-particles life-timeτ, namely
Δρ/ρ≡
ρ
xx(T,B)−ρ xx(T,0)
ρ(T,0)
∝(ω
cτ)∝(Bτ)
2
, (3.5)
Assuming that the only effect of a change in the temperature or in the impurity
density of the system is to alter the scattering timeτ(k)is such a way thatτ(k)→
λτ(k), whereλdoes not depend on the momentumk, thenΔρ/ρremains unaltered if
the magnetic ﬁeldBis rescaled toB/λ. Under this assumptions, the productΔρρ(=
Δρ/ρρ
2
xx
) is independent ofτand the quantityΔρ/ρis expected to be proportional
to(B/ρ)
2
with a temperature independent slope (if the carrier concentration remains
constant).
This relation is known asKohler’s rule, and is obeyed in a large number of standard
metals, provided that changes in temperature or purity simply alterτby the same
factor. In high temperature superconductors however, experiments has shown that
this rule is abruptly violated; in particular the slope seems not to be temperature
independent, as illustrated in the left panel of Fig.3.8for YBa
2Cu3O6.6[48].
Some progresses in the understanding of this violation were made in [48], where
the authors studied the temperature behaviour for the Hall angle cotθ
Hand the orbital
magneto-resistanceΔρ/ρfor YBCO and LSCO at different doping levels. Speciﬁ-
cally, they found the following temperature behaviour for the magneto-resistance:
Δρ
ρ
YBCO
∝
B
2
T
4
,
Δρ
ρ
LSCO
∝
B
2
(A+CT
2
)
2
, (3.6)
whereAandCare constants.

22 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
Fig. 3.8 a: Kohler plot for under-doped YBa2Cu3O6.6 at intermediate (main) and high (inset)tem-
peratures .bTemperature dependence of the orbital part of the magneto-resistance in YBa
2Cu3O6.6,
optimally doped YBa
2Cu3O7and La1.85Sr0.15CuO4.Theinsetshows the inverse Hall angle cotθ H
vsT
2
in optimally doped LSCO. Figures from [48]
Moreover, for the Hall angle they found:
cotθ
HYBCO∝T
4
,cotθ HLSCO∝D+ET
2
, (3.7)
whereDandEare also constants. These behaviours allow them to introduce the
following phenomenological modiﬁed Koheler’s rule:
Δρ
ρ
∝tan
2
θH, (3.8)
which seems to be satisﬁed (at least in the under-doped and optimally doped region
of the phase diagram) as as one can see in Fig.3.8. Interestingly, the only cuprates
that seems to recover, at least in some region of the phase diagram, the conventional
koheler’s rule behaviour is the LSCO in the over-doped non-superconducting region,
as pointed out in [49].
As a ﬁnal remark, we want to stress that in analysing the normal state orbital
magneto-resistance, one must not overlook contributions to the orbital magneto-
resistance from para-conductivity terms which can inﬂuence the in-plane magneto-
transport over a wide temperature range in HTC due to their small superconducting
coherence length and strong two-dimensionality (see e.g. [50] for a comprehensive
review on the topic).

3.3 Cuprates: In-Plane Transport Properties in the Non-superconducting Phase 23
3.3.3 Thermal Transport
The thermal transport properties, namely the thermo-electric (Seebeck) coefﬁcientS
and of the thermal conductivity matrixˆκhas been less studied than the electric trans-
port properties previously described. This is ﬁrstly due to the difﬁculty of performing
accurate measurements, and secondly, the problem of interpreting the ensuing results.
Their interpretation is compounded of course by the additional contribution toˆκfrom
heat carrying phonons and the effect of the phonon drag mechanism onS(See also
Appendix A). However, in recent time the developments of techniques for measure-
ments at high magnetic ﬁeld allowed the study of the Hall thermal properties. The
latter are not substantially affected by phonons effects and can be used to get insight
the electronic structure of the strange metals. In this brief section we will review
some of these results.
3.3.3.1 Seebeck Coefﬁcient
According to the simple Boltzmann theory of transport (see Appendix A), the
Seebeck coefﬁcientSdepends both on the transport scattering rate and the ther-
modynamic mass of the electrons. These two contributions are difﬁcult to separate
and it usually certain simplifying assumptions has to be applied that may obscure
some of the intrinsic physics especially in relation to the pseudo-gap. Even though
this iterplay of effect makes the interpretation of the Seebeck coefﬁcient quite hard, its
behaviour in the strange metals has been well documented. In particular, it is known
that all the cuprates presents a universal correlation between the room temperature
value ofSand the doping level [51]. This has been used to determine the doping con-
centration in a wide range of materials where determination of the hole concentration
is ambiguous. Whilst this relation is not found to hold in Bi
2Sr2−xLaxCuO6+δ[52],
its applicability to other high temperature superconductors appears robust.
In under-doped region of the cuprates,Shas a large positive value and presents
maximum whose peak temperature decreases with increasing doping. At optimal
doping,S(T)remains positive but has a negative linear slope,i.e.,
S
OD(T)=β−αT. (3.9)
As doping increases further,βcontinues to decrease while it is known that the
coefﬁcientαis almost doping independent. Eventually, in the most over-doped sam-
ples,S(T)is negative in the non-superconducting region.
3.3.3.2 Thermal Conductivity and Lorentz Ratio
The normal state in-plane thermal conductivityκ
xxof high-T csuperconductors is
dominated by the phonon contribution. Typical estimates of the electronic

24 3 The Fermi Liquid Breakdown: High- T cSuperconductivity
contribution are of order 10–20% of the total nearT=T c. Due to a lack of a solid
theoretical model to compare it is almost impossible to subtract the phonon contri-
bution and to analyse the pure electronic part; then the study of this quantity is not
very helpful in understanding the electronic properties of the strange metals.
A more interesting quantity is the thermal Hall conductivityκ
xywhich measure
the transverse response to an applied longitudinal thermal gradient when the system
is immersed in an external magnetic ﬁeld perpendicular to the plane. As all the
transverse contribution,κ
xyis almost unaffected by phonons and allows to deduce
some feature of the electronic structure of the strange metals.
The thermal Hall conductivityκ
xywas studied for the optimally doped YBCO in
[53,54]. In both the papers the authors found the following temperature dependence:
κ
xy∝
1
T
, (3.10)
and the two measurements agree also in the order of magnitude.
The two papers however disagree in the prediction of the Hall Lorentz ratioL
xy≡
κxy
σxyT
. This is an extremely interesting quantity since it has to be of the same order of
magnitude of the Lorentz rationL=
κxx
σxxT
and consequently it can provide an indirect
measurement of the Wiedemann-Franz law which is an indicator of how much the
system deviates from the Fermi liquid behaviour.
In [53] the authors found an Hall Lorentz ratio which varies approximatively lin-
ear in temperature and passes through several order of magnitude between 100 K and
300 K. On the over hand, the authors of [54] found a Hall Lorentz ratio approxima-
tively constant in temperature and higher than the Fermi liquid predictionL
0=
π
2
k
2
B
3e
2.
The discrepancy between the two results is not yet fully understood but it could be
due to the fact that the authors of [53] measured the Hall conductivityσ
xyand the
Hall thermal conductivityκ
xyin a different samples, while in [54] bothσ xyandκ xy
were measured in the same sample. However both the papers agrees in saying that
the Wiedemann-Franz law seems to be strongly violated in these materials [55–57].
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Chapter 4
Theoretical Attempts
The experimental scenario described in the previous sections strongly suggest that
the standard Fermi liquid paradigm is not valid for hight-T
csuperconductors. Several
attempts to explain the experimental observations within some modiﬁed Fermi liquid
framework had always provided unsatisfactory results (see [1] for a detailed review
on the topic).
Given this reliance on detail, other more exotic models, based on non-Fermi
liquid physics, have gained prominence within the community; in this review we
will concentrate on two model which provide inspiration also for the holographic
treatment of Part 3. These are the two-lifetime picture of Anderson [2] and the
Marginal Fermi liquid phenomenology of Varma and co-workers [3].
4.1 Anderson’s Model
In the two-lifetime approach, scattering processes involving momentum transfer
perpendicular and parallel to the Fermi surface are governed by independent transport
and Hall scattering rates 1/τ
tr(∝T)and 1/τ H(∝T
2
). In the usual Fermi liquidτ tr=
τ
H. To achieve different behaviours of the two scattering time, an effective Landau
interaction between up and down spins is introduced (see [2] for more details). The
effect of this interaction is not innocuous, and leads to separate Fermi velocities for
charge- and spin-waves which, as a consequence, generate the unusual independence
betweenτ
trandτ H.
Allowingτ
Hto be independent ofτ tr, the inverse Hall angle can now be written as
cotθ
H=
σ
xx
σxy
∝1/τ H. (4.1)
© Springer International Publishing AG 2017
A. Amoretti,Condensed Matter Applications of AdS/CFT, Springer Theses,
DOI 10.1007/978-3-319-61875-3_4
29

30 4 Theoretical Attempts
Thus the different behaviour ofρ xx(T)and cotθ H(T)reﬂects the differentTdepen-
dencies of 1/τ
trand 1/τ H.
Whilst the two lifetime model of Anderson has been successful in reproducing the
experimental situation in optimally doped cuprates, it does not appear to be consistent
with ARPES results and is does not explain the evolution of the transport phenomena
across the full cuprates phase diagram.
4.2 Phenomenological Marginal Fermi Liquid
The phenomenological marginal Fermi liquid developed by Varma and co-workers
has acquired great relevance with mounting evidence for a Fermi surface accumu-
lating from photoemission experiments.
In particular, we have learned in the previous sections that the correct theory has to
keep into account for the existence of a Fermi surface but with no sharp deﬁned quasi-
particles. This gave support to the idea of a “marginal” Fermi liquid. Essentially, this
is a theory that yields a Fermi surface in the weakest possible sense of the deﬁnition
but otherwise does not make the same predictions as Fermi liquid theory.
To underline the differences between Fermi liquid theory and the marginal Fermi
liquid let us recall brieﬂy what we have outlined in Chap.2for the Fermi liquid.
In the presence of interactions the quasi-particles propagator acquires corrections
due to the self-energy(ω,θk), namely:
G(ω,θk)=
1
ω−ε θk−(ω,θk)
, (4.2)
whereε
θkis the quasi-particle energy. The Fermi surface is deﬁned as the locus in
momentum space whereG
−1
(0,θkF)vanishes (θk Fis called the Fermi momentum).
In the vicinity of the Fermi surface one can safely expand in series the denominator,
obtaining:
G
−1
(ω,θk)σω
τ
1−
∂ρ
∂ω
θ
θ
θ
θ
ω=0
σ
−
ρ
ε
θk+ρ(ω,θk)

−i(ω,θk).(4.3)
The quantityz
−1
θk
(ω)≡1−
∂ρ
∂ω
is called the quasi-particle residue and measure the
amplitude of the jump in the quasi-particle distribution at the Fermi surfaceθk=θk
F,
whiletakes measures the decay rate of quasi-particles. In the standard Fermi
liquid theory one ﬁnds:
ρ∝ω,∝ω
2
. (4.4)
Then, in the Fermi liquid theory the quasi-particle residue, which for free fermions
is exactly equal to 1, assumes the following form

4.2 Phenomenological Marginal Fermi Liquid 31
zθk(ω=0)=
1
1+λ
<1, (4.5)
whereλmeasure the strength of the interactions. As we have proven in Appendix A,
ford≥2 spatial dimensions, the quasi-particle residue does not vanish independently
of the strength of the interactions. This implies that the Fermi surface is well deﬁned.
As we have previously said, we want to modify the Fermi liquid theory in order
to still have a Fermi surface, but deﬁned in a very weak sense. In order to do this, we
phenomenologically modify the real part of the self-energyas follow:
ρ(ω,θk)∝ωlog
θ
θ
θ
θ
ω
ωc
θ
θ
θ
θ
, (4.6)
whereω
cis a high energy cut-off. Consequently, the quasi-particle residue is given
by:
z
θk(ω)=
1
log
θ
θ
ωc
ω
θ θ
. (4.7)
Now, in order to compute the quasi-particle residue on the Fermi surface we need
to sendωto zero. In this limit we obtainz
θk→0. Hence, the jump in the quasi-
particle distribution tends to zero, but in a very weak way (i.e. logarithmically), and
thus a Fermi surface just barely remains in the weakest sense. However, from the
self-energy (4.6), all the other properties of the theory have a non-Fermi liquid like
behaviour. This is one way to deﬁne the marginal Fermi liquid.
In order to completely characterize the phenomenology of the marginal Fermi
liquid one has to ﬁnd a consistent behaviour also for. To take into account the
experimentally measuredT-linear andω-linear scattering rateτ
θk, one has to guess:
1
2τθk
=∝x, (4.8)
wherex=max{T,|ω|}. Using the Drude result to roughly estimate the resistivity,
namelyρ
xx=(ωpτθk)
−1
(whereω pis the plasma frequency), the linear in temperature
behaviour of the resistivity is recovered.
Having deﬁned the basic ideas which yield the correct phenomenology we need
to incorporate them in a consistent theory. Even though the attempt to construct a
consistent microscopic theory with the marginal Fermi liquid phenomenology were
numerous (see [4] for further details), a complete consistent way to microscopically
reproduce the marginal Fermi liquid has not yet been discovered.
Rather to take the microscopic approach, another possibility is to assume a phe-
nomenological model and should it work, then one would search for a microscopic
description of the phenomenology after the fact. This was the approach followed
by the authors of [3], where it was postulated that in the copper-oxide system there
are charge and spin density ﬂuctuations of the electrons which lead to a polarizabil-
ity of the electron medium that would renormalize the electron propagator trough

32 4 Theoretical Attempts
Fig. 4.1Relevant diagrams for the self-energy computation in marginal Fermi liquid
the self-energy. Such a polarizability is drawn in terms of the Feynmann diagrams in
Fig.4.1. This is simply analogous to the electron-phonon interaction with the phonon
line being replaced by the polarizability. Their proposal for the polarizability is as
follows:
P(ω,θk)=
ω
−N(0)
ω
T
, for|ω|<T,
−N(0)signωfor|ω|>T,
(4.9)
whereN(0)is the single particle density of states at the Fermi energy. The form of
this polarizability is postulated to come from the vertex correction in the particle-hole
susceptibility shown in Fig.4.1.
The self-energy that arises from applying the Feynmann rules to the diagrams in
Fig.4.1is given by:
(ω,θk)σg
2
N
2
(0)
τ
ωlog
x
ωc
−i
π
2
x
σ
, (4.10)
which is consistent with that discussed previously and gives the correct phenomenol-
ogy for the Fermi surface, the DC resistivity and also for the spectral conductivity
(see [3] for further details on this quantity).
The basic marginal Fermi liquid assumption does not provide the correct behav-
iour for the magneto-transport. To get the correct prediction for the Hall angle and
the magneto-resistance, the authors of [5] introduced anisotropy into their marginal
Fermi liquid phenomenology via the elastic (impurity) scattering rate by assuming
small angle scattering off impurities located away from the CuO
2plane.
In other words, they phenomenologically modify the imaginary part of the self
energyas follows:
(T,θk)=Γ
0(θk)+λT. (4.11)
The anisotropic elastic partΓ
0(θk)has been ascribed to small-angle scattering from
dopant impurities lying between the CuO
2planes, an assumption supported by
ARPES measurements [6]. Referring for the technical details to [5], with the phe-
nomenological assumption (4.11) it is possible to reproduce the correct temperature
behaviour for the Hall angle and the magneto-resistance.
Whilst this hypothesis seems consistent both with ARPES and transport mea-
surements [7,8], it is not clear if the expansion in small scattering angle can be

4.2 Phenomenological Marginal Fermi Liquid 33
safely assumed, as pointed out in [9,10]. Speciﬁcally, it has been argued that the
conditions that lead to a separation in lifetimes are inconsistent with the violation of
Kohlers rule [9]. Moreover, although the predictions of marginal Fermi liquid theory
appear compatible with the empirical situation in optimally doped cuprates, their
applicability to the rest of the cuprate phase diagram is less evident.
4.3 Quantum Criticality
Although a tremendous effort has been made to understand the strange metal better
and beyond the phenomenology of the marginal Fermi liquid, only in one qualitative
aspect has progress been made. In particular, in recent times the idea that the phe-
nomenon ofQuantum Criticalitycould be the responsible of the Fermi liquid break
down in the strange metals has assumed growing importance. This is the critical
universal behaviour that occurs in the vicinity of aQuantum Phase transition(see
[11] for a review), which is a second order quantum phase transition. By deﬁnition, a
quantum phase transition is a transition which occurs at zero temperature, as a result
of varying some non-thermal control parameter, such as applied magnetic ﬁeld or
pressure. Since classically the entropy at zero temperature has to vanish, a quantum
phase transition can not be caused by the competition between energy and entropy,
like its ﬁnite-temperature counterpart. Rather, it is a result of competition between
different terms in the Hamiltonian describing the system.
Now, the relevant aspect is that, if this phase transition is second order, the absence
of a scale at the critical point (due to the diverging correlation length) means that the
quantum ﬁeld theory describing this point must be a conformal ﬁeld theory (See Part
2 for more details). The special aspect of a quantum critical theory compared to a
classical critical theory is that one now raises the temperature in the conformal ﬁeld
theory, the conformal constraints resonate through in the ﬁnite temperature physics.
A CFT at ﬁniteTis still very special in that all its dynamics are still controlled by
theT=0 conformal symmetry and in general the only aspect that changes is that all
dimension-full quantities are now given in terms of the only present scale T. To get
non-conformal (generic) behaviour one needs at least two scales. This means that
the phase diagram near a quantum critical point looks as in the left panel of Fig.4.2.
As one can see from the Figure, a common type of phase diagrams with a Quantum
Critical point has a line of ﬁnite-temperature critical points where the transition
temperature is depressed to zero by varying a coupling constant. Around this ﬁnite-
temperature critical line, the system can be described by a classical ﬁeld theory, even
though the transition temperature may be very low. This is due to the fact that close
to a critical point, the length scale above which the behaviour changes qualitatively
is very large. Around any non-zero temperature critical point, therefore, one has
k
BT≥˜ωwhere˜ωis some typical energy scale above which the behaviour of the
system changes (for example an energy gap). This reasoning clearly breaks down
for a quantum phase transition, where the temperature is strictly zero. The behaviour
at a Quantum Critical point is expected to be characterized by competition between

34 4 Theoretical Attempts
Fig. 4.2Left: schematic typical phase diagram in the vicinity of a Quantum Critical point as a
function of the temperatureTand a generic tunable parameterp.Right: approximative phase
diagram of the cuprates as a function of the temperatureTand the doping
low-lying states. This quantum critical behaviour is different from typical low energy
behaviour, which can be understood in terms of quasi-particles on a ground state.
This competition effect tends to break down away from the Quantum Critical point
on the zero temperature line, as an energy gap forms and the system chooses a ground
state. However, if the temperature is increased such that this gap may be overcome the
interplay between the different energy levels again becomes the dominant behaviour.
The ﬁnite temperature region of the phase diagram in which this quantum critical
behaviour is important is called the quantum critical regime.
Comparing the typical Quantum Critical point phase diagram with those of the
cuprates (right panel of Fig.4.2), it is very tempting to assume that the optimal doping
region atT=0 is associated with a quantum phase transition. Although the idea that
the physics underlying the strange metal is a ﬁnite T conformal ﬁeld theory, in detail
it is not so simple. In particular scale-invariance is only observed in terms of energy-
temperature scaling. In spatial directions one still notes a distinct Fermi surface with
ARPES data and we have learned in the previous Section that the idea of the marginal
Fermi liquid naturally takes into account this fact. This curious combination, scale-
less in the “time-direction”, but a distinct Fermi momentum in the spatial directions
has been coinedlocal quantum criticality.
It is important to note that the concept of local quantum criticality is naturally
implemented in the marginal Fermi liquid picture. In fact, as it is evident from the Self
energy (4.10) and from the polarizability (4.9), the spatial part of the susceptibility
exhibits ordinary mean-ﬁeld behaviour and the self-energy depends only on the
frequency and exhibits non-trivialω/Tscaling. As we have previously explained,
these are exactly the two basic ingredients to get local quantum criticality. For this
reason the idea that the non-Fermi liquid behaviour of the strange metals is due to
the inﬂuence of a quantum critical point is now predominant in the community.

4.3 Quantum Criticality 35
However, at present, the existence of a Quantum Critical point in the phase diagram
of the cuprates is still debated (see [12] for a review on the topic) and there are no
measurements which strongly corroborate or confute this idea. This is, above all,
due to the difﬁculty in performing measurements at very low temperature due to the
presence of the superconducting dome.
References
1. N.E. Hussey, Phenomenology of the normal state in-plane transport properties of high- t c
cuprates. J. Phys. Condens. Matter20(12), 123201 (2008)
2. P.W. Anderson, Hall effect in the two-dimensional luttinger liquid. Phys. Rev. Lett.67, 2092–
2094 (1991)
3. C.M. Varma, P.B. Littlewood, S. Schmitt-Rink, E. Abrahams, A.E. Ruckenstein, Phenom-
enology of the normal state of cu-o high-temperature superconductors. Phys. Rev. Lett.63,
1996–1999 (1989)
4. A.V. Narlikar, inStudies of High Temperature Superconductors: Advances in Research and
Applications, vol. 11, Advances in Research and Applications (Nova Science Publishers, 1993)
5. C.M. Varma, Elihu Abrahams, Effective lorentz force due to small-angle impurity scattering:
Magnetotransport in high-T
csuperconductors. Phys. Rev. Lett.86, 4652–4655 (2001)
6. T. Valla, A.V. Fedorov, P.D. Johnson, B.O. Wells, S.L. Hulbert, Q. Li, G.D. Gu, N. Koshizuka,
Evidence for quantum critical behavior in the optimally doped cuprate bi
2sr2cacu2o8+∂.Sci-
ence285(5436), 2110–2113 (1999)
7. A. Narduzzo, G. Albert, M.M.J. French, N. Mangkorntong, M. Nohara, H. Takagi, N.E. Hussey,
Violation of the isotropic mean free path approximation for overdoped la
2−xsrxcuo4.Phys.Rev.
B77, 220502 (2008)
8. T. Valla, A.V. Fedorov, P.D. Johnson, Q. Li, G.D. Gu, N. Koshizuka, Temperature dependent
scattering rates at the fermi surface of optimally doped bi
2sr2cacu2O8+δ. Phys. Rev. Lett.85,
828–831 (2000)
9. E.C. Carter, A.J. Schoﬁeld, Small-angle scattering in a marginal fermi liquid. Phys. Rev. B66,
241102 (2002)
10. R. Hlubina, Hall effect in the cuprates: The role of forward scattering on impurities. Phys. Rev.
B64, 132508 (2001)
11. S. Sachdev, inQuantum Phase Transitions(Cambridge University Press, 2001)
12. Subir Sachdev, Where is the quantum critical point in the cuprate superconductors? Phys. Status
Solidi B247, 537 (2010)

Part II
Introduction to Holography

Exploring the Variety of Random
Documents with Different Content

Τοιαύτα τινα, εν ολίγοις, κατηγορούσα η αντιπολίτευσις του
Καποδιστρίου, προσεπάθει να εξεγείρη τον λαόν κατά του
ανδρός εκείνου, ούτινος και το όνομα μόνον την σήμερον
αναφερόμενον αποσπά δάκρυα και λυγμούς παρά τοις τα
εθνικά συμφέροντα υπέρ πάντα άλλα έχουσι. Πάσας τας
κατά του Κυβερνήτου αιτιάσεις ταύτας της εγχωρίου
Αντιπολιτεύσεως εχρησιμοποίησαν και εξεμεταλλεύθησαν ο
ξένος τύπος και βραδύτερον οι ξένοι συγγραφείς, μεταξύ
των οποίων όμως πολλοί ηυδόκησαν ν' ανομονολογήσωσιν
ότι «ο κόμης Καποδίστριας ουδέποτε ηθέλησε το κακόν της
πατρίδος του εν επιγνώσει». Η Αντιπολίτευσις, έτυχεν
ενθαρρύνσεως και υπό του εν Παρισίοις «Επαναστατικού
συνδέσμου», κατά τινα Αυστριακήν έκθεσιν, κατ' Ιούλιον
του 1831, ιδία όμως παρά των αντιπρέσβεων Γαλλίας και
Αγγλίας. Η εξωτερική δ' αύτη ενθάρρυνσις εξώθησε την
Αντιπολίτευσιν επί την ανταρσίαν.
ΚΕΦΑΛΑΙΟΝ Η'.
Η αντιπολίτευσις οσημέραι καθίσταται σφοδροτέρα. —
Ανταρσία εν Μάνη — Ο Τσάμης Καρατάσος και η εν
Στερεά ανταρσία. — Οι συλληφθέντες παρεπέμφθησαν
εις το Στρατοδικείον. — Αφορμαί της ανταρσίας εν
Ύδρα. — Αι εφημερίδες «Απόλλων» και «Ηώς». — Ο
ποιητής Αλέξανδρος Σούτσος και αι κατά του
Καποδιστρίου σάτυραι. — Αφορμαί της εν Μάνη
ανταρσίας κατά του Κυβερνήτου. — Οποία τις ήτο η
Μάνη προ του 1821. — Η οικογένεια Μαυρομιχαλαίων.
— Αι περί Μάνης αξιώσεις αυτών. — Και πάλιν αι
εφημερίδες της αντιπολιτεύσεως — Αι αποζημιώσεις
των τριών ναυτικών νήσων. — Οικονομικά μέτρα του
Καποδιστρίου. — Τα περί συγκλήσεως της
Εθνοσυνελεύσεως.
Η σημαία της κατά του καθεστώτος ανταρσίας υψώθη το
πρώτον εν τω Λιμένι της Μάνης υπό της ηγεμονικής
οικογενείας των Μαυρομιχαλαίων και των ομοφρονούντων
αυτοίς. Οι κατοικούντες εν Λιμένι και Καρδαμύλη Σπαρτιάται
περιεφέροντο κρατούντες σημαίαν, εφ' ής ήσαν

απεικονισμένοι οι αρχαίοι αυτών ήρωες: ο Λυκούργος και ο
Λεωνίδας· αντήχει δε η κραυγή: Ελευθεροτυπία και
Σύνταγμα. Πανταχού εκυμάτιζεν η τρίχρους γαλλική σημαία,
και πάσα καρδία εν τη ευπαθεί και ευκαταφόρω Ελλάδι
έπαλλεν υπέρ της Γαλλίας.
Αυστριακαί εκθέσεις ισχυρίζονται, ότι το έναυσμα είχεν
αληθώς διαβιβασθή εκ Παρισίων: «Η αντιπολίτευσις έλαβεν
ενθαρρύνσεις παρά της επαναστατικής εταιρίας των
Παρισίων, ής ηγείτο ο στρατηγός Λαφαγέτ. Αυτός ούτος
προσηνέχθη να μεταβή εις την Ελλάδα, όπως ιδρύση εν αυτή
Σύνταγμα». Αλλ' εκείνος μεν ουδαμού εν τη Ελλάδι
εφαίνετο, άγρια δ' ουχ ήττον εγεννήθη στρατιωτική στάσις
κατά του Κυβερνήτου, ής αφορμή υπήρξεν, ως και άλλοτε
τοσάκις, η καθυστέρησις του μισθού, και παράπονα τινα
κατά των καταπιέσεων των εν τη Στερεά Ελλάδι ενοικιαστών
των φόρων.
Ο Τσάμης Καρατάσος, αυτός εκείνος, όστις επί Όθωνος
εγένετο η πρωτίστη αφορμή της διακοπής των σχέσεων
Ελλάδος και Τουρκίας, εξ ής τοσούτον εζημιώθη ο
Ελληνισμός, κατέλιπε κατά τον Μάιον του 1831 μεθ' όλου
αυτού του τάγματος το εν Ελευσίνι στρατόπεδον και
συνηνώθη παρά την Αταλάντην μετά σώματος του
συγγενούς αυτού Γρίβα Γαρδικιώτου. Σχέδιον υπήρχε να
συνέλθωσιν εν Αμφίσση πάντες οι δυσηρεστημένοι Έλληνες
οπλαρχηγοί. Επήλθε σύγκρουσις. Ανήγγελλον νίκας τα
κυβερνητικά όργανα, και ανεκοίνουν, ότι η στάσις εξερράγη
τη 1 Μαΐου. Την 8 Μαΐου ο αρχιστράτηγος του ελληνικού
στρατού Αυγουστίνος Καποδίστριας μετέβη επί τόπου και την
10 διέβη φεύγων ο Καρατάσος τα Τουρκικά όρια,
εξαλειφθέντος παντός ίχνους της στάσεως. Μόλις όμως
εβαυκάλισε την κυβέρνησιν η εκ της συνειδήσεως των
ηρωικών κατορθωμάτων του Αυγουστίνου γεννηθείσα
ασφάλεια και επέδραμε πάλιν ο Τσάμης Καρατάσος, κατά τας
αρχάς Ιουνίου, εκ των φαράγγων της Όθρυος. Μόνον δε
μετά σφοδρόν αγώνα υπέκυψεν εις τα ηνωμένα σώματα του
ηρωικού στρατηγού Ιωάννου Ράγκου και του Α. Μεταξά.
Ούτω δε μέρος μεν των στρατιωτών αυτού παρεκινήθη εις
λιποταξίαν διά χρηματικών υποσχέσεων, αυτός δε έφυγε και
εκ δευτέρου πέραν των ελληνικών ορίων.

Οι συλληφθέντες εκ των ανταρτών αιχμάλωτοι
παρεπέμφθημεν εις το Στρατοδικείον, αλλ' εδόθη αυτοίς
χάρις. Η παράδοξος αύτη επιείκεια ην ίσως υπαγόρευσις
αδυναμίας και φόβου. Διότι η κατά του Κυβερνήτου
εξέγερσις έβαινε δι' όλης της χώρας παραλλήλως τη
στρατιωτική ανταρσία, υποκινουμένη υπό των γαλλικών
ιδεών. Εύρε τα κύρια αυτής ερείσματα εν Ύδρα και εν Μάνη.
Αφορμή δε της κατά του Καποδιστρίου καταφοράς των τε
Υδραίων, των Σπετσιωτών και των Μανιατών ην ήδε: Ότε ο
Κυβερνήτης κατέπλευσεν εις Ελλάδα, «εύρεν εννέα
ναυάρχους και εκατόν πλοιάρχους, οίτινες επιλήσμονες του
χυθέντος αίματος χιλιάδων ηρώων της ξηράς, από της
αρματωλικής εποχής του Χρήστου Μιλιώνη μέχρι του
θανάτου του Καραϊσκάκη, αίματος σχηματίσαντος την λίμνην
εν ή αι μεγάλαι Δυνάμεις εβάπτισαν την ελευθερίαν του
Ελληνικού γένους, ως λέγει ο Στέφανος Ξένος,

συνεορτάσασαι αυτήν διά των εκλάμπρων και βομβοφώνων
Ναυαρινείων πυροτεχνημάτων, όταν ο Αιγυπτιακο-τουρκικός
στρατός και στόλος είχεν αποσβέσει την επανάστασιν,
κατέχοντες ολόκληρον την Πελοπόννησον και την Στερεάν,
επιλήσμονες, λέγω, ιστορικών πασιφανών γεγονότων, ως
μανιακοί φαντασιοπλήκται, αναιδέστατοι προς περιφρόνησιν
ολοκλήρου της Ελληνικής φυλής, εκόμπαζον ότι ούτοι μόνοι
ηλευθέρωσαν την Ελλάδα από των Τούρκων, ως άμοτοι
λύκοι απαιτούντες παρά του Καποδιστρίου ουχί ολιγώτερον
ή να μη ποιή βήμα άνευ της συμβουλής των, ή να τους δώση
να ροφήσωσιν ολόκληρον την Ελλάδα. Ενταύθα ηνεώχθη το
βάραθρον, εν τω οποίω η αλάστωρ της Ελλάδος Μοίρα
απεφάσισε να ρίψη τον Κυβερνήτην, διότι διαφωνήσασαι αι
τρεις κυριώτεραι ναυτικαί νήσοι, τα μεν Ψαρρά φανατικώς
εκηρύχθησαν υπέρ του Καποδιστρίου, η δε Ύδρα και αι
Σπέτσαι φανατικώς συνώμοσαν τον όλεθρον αυτού.
Οι Υδραίοι και Σπετσιώται, ιδιοκτήται μεγάλων πλοίων τα
οποία συνεισέφερον ηρωικώς και λυσιτελώς εις τον αγώνα,
δεν επεθύμουν η Ελλάς ν' απολαύση στρατιωτικού
ευρωπαϊκού ναυτικού, διότι εναύλουν τα πλοία των
επωφελώς προς την Κυβέρνησιν. Δεν επεθύμουν οργανισμόν
ευρωπαϊκόν και ναυτικήν γλώσσαν σύμφωνον προς τα
προστάγματα, τας κινήσεις και τας διεθνείς διατάξεις, αλλ'
απήτουν την αρβανίτικην γλώσσαν των και ναύτας μόνον εκ
της νήσου εξ ής κατήγετο ο κυβερνήτης του πλοίου. Το
πλήρωμα της «Ελλάδος» , ήν εκυβέρνα ο Μιαούλης,
συνεκροτείτο ολόκληρον εξ Υδραίων. Οι ναύται της
κορβέττας «Ύδρας», ήν εκυβέρνα ο Σαχίνης, ήσαν όλοι
Υδραίοι. Ο Ιωάννης Καποδίστριας εγκαίρως κατενόησεν ότι
τοιουτοτρόπως ο στόλος του Κράτους ευρίσκετο εις χείρας
των Υδραίων. Η δυσαρέσκεια των επιλοίπων νησιωτών της
ελευθέρας και δούλης Ελλάδος τότε όρια δεν είχε. Του
Καποδιστρίου κατορθώσαντος να σχηματίση τον στόλον περί
ού ανεφέραμεν, κατηργήθη το σύστημα τούτο αφ' εαυτού,
ούτω δ' ικανοποιήθη η ετέρα μερίς του Ελληνικού ναυτικού.
Αλλ' η Ύδρα και αι Σπέτσαι, υποδαυλιζόμεναι παρά του
Αλεξάνδρου Μαυροκορδάτου, ποιούντος άφθονον χρήσιν
του ονόματος της Αγγλίας και διασαλπίζοντος την ψευδή
φήμην, ότι η Αγγλία επιθυμεί ν' αποδιωχθή ο Καποδίστριας
εκ της Ελλάδος, αντέταξαν, αύται αι πρωταθλήτριαι του
επταετούς αγώνος, την αναρχίαν κατά της στερεωθείσης εν
τω Κράτει πειθαρχίας.

Εν τη ενάρξει του αγώνος ο Α. Μαυροκορδάτος είχεν
αντιπάλους ισχυροτάτους τον Δημήτριον Υψηλάντην, τον
Θεόδωρον Νέγρην, τον Καρατζάν και τον Καντακουζηνόν.
Κατά τον αγώνα ήσαν πάμπτωχοι εκτός του Καρατζά, ουδέν
έτερον έχοντες κεφάλαιον εκτός του γραψίματος, το οποίον
εν μέσω των αγραμμάτων παλληκαρίων της εποχής εκείνης
υπήρξε συχνότατα χείρον της πυρίτιδος των Τούρκων. Ο
Καρατζάς και ο Καντακουζηνός ήσαν ειλικρινέστεροι και
ικανώτεροι άνδρες· αλλ' απαυδήσαντες των ραδιουργιών του
Νέγρη και Μαυροκορδάτου εγκατέλειψαν πρόωρα τον
αγώνα. Ο Υψηλάντης και ο Νέγρης απεβίωσαν, έμεινε λοιπόν
ο Αλέξανδρος Μαυροκορδάτος, ούτινος αι μεγάλαι
αναμφισβήτητοι εκδουλεύσεις και το σταθερόν, φλεγματικόν
και ανδρείον ύφος δι' ού προσηνέχθη απέναντι των
φοβερών κινδύνων του Μεσολογγίου και της Σφακτηρίας επί
του «Άρεως», έδιδον δικαιώματα πρωθυπουργού της υπό
τον Ιωάννην Καποδίστριαν Δημοκρατίας. Ο εγωισμός και τα
πάθη ετύφλωσαν εν τη κρισιμωτέρα της Ελλάδος εποχή τον
άγαν πατριωτισμόν του Αλεξάνδρου Μαυροκορδάτου και τον
του Λαζάρου Κουντουριώτου, οίτινες συνώμοσαν την
καταστροφήν του Κυβερνήτου.
Η Ύδρα λοιπόν ην η εστία της σχηματισθείσης
«συνταγματικής επιτροπής», ήν συνεκρότουν ο
Κουντουριώτης, ο Μιαούλης, ο Δ Βούλγαρης, ο Μ. Τομπάζης,
ο Β. Βουδούρης, ο Α. Κριεζής, και ο Ν. Οικονόμου. Την
Ύδραν εμιμήθησαν και άλλαι νήσοι. Οι στρατιώται αυτών
επολλαπλασιάζοντο οσημέραι ερεθιζόμενοι, προ πάντων, υπό
τε της Ηούς» εκδιδομένης υπό του Εμμ. Αντωνιάδου, και του
«Απόλλωνος» του Αναστασίου Πολυζωίδου, όστις επολέμησε
δεινότατα τον Καποδίστριαν, είπερ τις και άλλος (από 16
Μαρτίου 1831) μέχρι της δολοφονίας αυτού.
Τον Αναστάσιον Πολυζωίδην υπεστήριζον προ πολλού ο τε
Α. Κουντουριώτης και ο I. Ορλάνδος, ως έκ τινος επιστολής
του Ορλάνδου και Λουριώτη γεγραμμένης εκ Λονδίνου προς
την Εκτελεστικήν Κυβέρνησιν τη 1)13 Οκτωβρίου 1824,
εξάγεται, αναφερούσης ότι εκ του δανείου του 1824 ο
Ορλάνδος εμέτρησε 500 τάλληρα προς τον Πολυζωίδην διά
την εφημερίδα αυτού. Ο Καποδίστριας από της αφίξεως
αυτού ενεθάρρυνε μεγάλως την ελευθεροτυπίαν, ίδρυσε δε
προς τούτο εν Ναυπλίω και εν Αιγίνη μεγάλα τυπογραφεία,
εν οίς επετρέποντο δαπάνη της Κυβερνήσεως η πληρωμή

του εκδότου εκδόσεις συγγραμμάτων οιωνδήποτε ελευθέρων
ιδεών. Ο Ε. Αντωνιάδης είχεν επίσης συστήσει
τυπογραφείον, εν ώ εδημοσιεύετο η «Ηώς». Της συνωμοσίας
εφηβαινούσης, η «Ηώς» και ο «Απόλλων» ήρξαντο να
επιτίθενται κατά του Καποδιστρίου δι' απρεπών ύβρεων.
Εκαλείτο προδότης της Ελλάδος και τύραννος. Τον
εκτραχαλισμόν τούτον των μερίδων ιδών ο Καποδίστριας,
ηναγκάσθη διά Διατάγματος (26 Απριλίου 1831) να
διαρρυθμίση τα του Τύπου δι' εννέα άρθρων συμφώνως τοις
περί Τύπου Νόμοις των μάλλον φιλελευθέρων και
πεπολιτισμένων Κρατών της Ευρώπης. Κατά το δεύτερον
άρθρον του Διατάγματος τούτου απήτει πας τυπογράφος να
παρακαταθέση τέσσαρας χιλιάδας φοινίκων εις την Εθνικήν
Τράπεζαν, ως εγγύησιν ότι δεν θα τυπώση τι κατά της
χριστιανικής θρησκείας ή των αρχών της δημοσίου ηθικής,
ούτε δημοσιεύση προσωπικότητας ή συκοφαντίας. Ο
Καποδίστριας προέβη εις τούτο, όπως παρακωλύση την
σύστασιν μικρών και αφανών, κρυφίως και εν παραβύστω,
λειτουργούντων τυπογραφείου, εν οίς ετυπούντο σάτυραι
και λίβελλοι, έμπλεω σατανικών συκοφαντιών και
αηδεστάτων φληναφημάτων, ών οι συντάκται επηγγέλλοντο
τους φιλελευθέρους, επωνομάζοντο συνταγματικοί και
εξήγειρον τον λαόν κατά του, υπ' αυτών Ρώσου τυράννου
της Ελλάδος αποκαλουμένου, Κυβερνήτου.

Ουχ ήττον δε διά της σατύρας ηγωνίσθη μανιωδώς κατά του
Κυβερνήτου και ο έτερος των αδελφών ποιητών ο
Αλέξανδρος Σούτσος, όστις διά πνεύματος λεπτού και
αμειλίκτου πικρώς προσέβαλλε πάσαν την Καποδιστριακήν
διοίκησιν· ως παράδειγμα δε της πικρίας των αρχιλοχείων
όντως σατυρών αυτού παρατίθεμεν ενταύθα την περί των
διατάξεων του τύπου σάτυραν αυτού, γραφείσαν κατά Μάιον
του 1831 και έχουσαν ώδε:
Ένας γερουσιαστής μας με το στόμα
γελαστό,
Σούτσ' ελεύθερε, με είπε, συγχαρίκια σε
ζητώ·
Πρόβαλα υπέρ του τύπου δεκαπέντε
άρθρα νόμου
Κατ' αυτό το σχέδιόν μου.

  Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη βλάψης
   Της Αρχής τους Υπαλλήλους
Τους Κριτάς, τους Υπουργούς μας και των
Υπουργών τους φίλους·
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη γράψης.
   Έχω έναν αδελφόν μου Έκτακτον
Διοικητήν,
Κ' έναν πρωτεξάδελφόν μου 'ς το
Πρωτόκλητο Κριτήν
Κ' εγώ ένα κοκκαλάκι σε μιαν κώχη
γλυκογλύφω·
Πλην τον Τύπο τον λατρεύω κατ' αυτού
δεν δίδω ψήφο·
Είν' ελεύθερος ο Τύπος φθάνει μόνον να
μη βλάψης
   Της Αρχής τους Υπαλλήλους,
Τους Κριτάς, τους Υπουργούς μας και των
Υπουργών τους φίλους·
Είν' ελεύθερος ο Τύπος φθάνει μόνον να
μη γράψης.
   Ένας μου συναδελφός,
Όπου έχει κάποιον λόγον να συχαίνεται το
φως,
Φώναζε κατά του Τύπου, φώναζε με
στόμα τόσο!
Ίδρωσα τον Εωσφόρο, ίδρωσα ν'
αποστομώσω . . . .
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη βλάψης
   Της Αρχής τους Υπαλλήλους,
Τους Κριτάς, τους Υπουργούς μας και των
Υπουργών τους φίλους·
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη γράψης.
Στο εξής κάθου και γράφε, κάθου και
κοπάνιζέ μας·
   Τραγουδάκια τύπωνέ μας

Ό,τι πράγμα δεν σ' αρέσει κι' όποιον
άνθρωπον θελήσης,
   Ημπορείς να σατυρίσης.
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη βλάψης
   Της Αρχής τους Υπαλλήλους,
Τους Κριτάς, τους Υπουργούς μας και των
Υπουργών τους φίλους·
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη γράψης.
   Τι λοιπόν φυλάγεις; Πάρε το
κονδυλομάχαιρό σου
Κονδυλάκια κόψε . . . Βάλε το χαρτί 'ς το
γόνατό σου·
Κόκκινη μελάνη θέλεις; Με την κόκκινη
αρχίνα·
Απ' το κόσκιν' όλους πέρνα, και κανένα μη
προσκύνα.
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη βλάψης
   Της Αρχής τους Υπαλλήλους,
Τους Κριτάς, τους Υπουργούς μας και των
Υπουργών τους φίλους·
Είν' ελεύθερος ο Τύπος, φθάνει μόνον να
μη γράψης.
Ο Σούτσος το κατ' αρχάς διά του «Απόλλωνος» και είτα διά
των εν τω «Πανοράματι της Ελλάδος» σατυρών επέπιπτε
λάβρως κατά του Κυβερνήτου. Εν τη ανωτέρω ποιητική
συλλογή εν Ναυπλίω τω 1833 εκδοθείση, ο Καποδίστριας και
η κυβέρνησις αυτού αποτελούσι το σταθερόν σημείον των
προσβολών αυτού. Παρωδεί τα ψηφίσματα, διακωμωδεί τα
σχέδια, τα μέτρα, τους σκοπούς αυτών, προσβάλλει τους
φίλους αυτού. Βραδύτερον δε προχωρεί και μέχρι της
εξυμνήσεως αυτής των δολοφόνων του Κυβερνήτου. Εν μια
των ωραιότερων αυτού ωδών ο Σούτσος, ωσεί νέος
Τυρταίος, παριστά αυτούς ως νέους Αρμοδίους και
Αριστογείτονας, ως θέλομεν ιδεί. Η ιστορία δεν επεκύρωσε
την κρίσιν του ποιητού και η νυν Ελλάς θλίβεται
αναγινώσκουσα τους ωραίους εκείνους στίχους.

Υπήρξε πάντοτε αδιάλλακτος. Ο πατριωτισμός αυτού
ουδέποτε έλαβεν υπ' όψιν τας απαιτήσεις των συμφερόντων
του Κράτους, ούτε υπέφερε τας βραδύτητας βαθμιαίας
κοινωνικής προόδου. Η πλήρης πάθους ιδιοσυγκρασία αυτού
καθίστα αυτόν αντίπαλον ανένδοτον, τα δε περιβάλλοντα
αυτόν στοιχεία δεν ήσαν τα αρμόδια όπως κατευνάσωσι τας
εξάψεις αυτού. Οι αντιπολιτευόμενοι εύρισκον εν αυτώ
ισχυρόν σύμμαχον, και επειδή τότε η Ελλάς είχεν ολίγας
εφημερίδας και αυτά δε τα βιβλία ήσαν σπάνια, αι σάτυραι
του Αλεξάδρου Σούτσου ήσαν ως άλλαι διακηρύξεις, αίτινες
αντιγραφόμεναι απεστηθίζοντο και ανέφλεγον έτι μάλλον τα
πάθη.
Ιδού και ετέρα σάτυρα γραφείσα κατ' Αύγουστον του 1831,
εν ή ο Καποδίστριας εικονίζεται ως δικαιολογών την
πολιτείαν αυτού ενώπιον της Εθνικής Συνελεύσεως:
Πληρεξούσιοι του έθνους, σεβαστόν
κριτήριόν μου,
να σας δώσω ήλθα λόγον των νομίμων
πράξεών μου.
Η Ελλάς, χάριτι θεία, βλέπετε, δεν
εδουλώθη
αν η Σάμος, αν η Κρήτη 'ς τους εχθρούς
μας παρεδόθη,
αν τα φρούρια δεν πήρα της Ευρώπης, της
Αθήνας,
και αν έπαιξα το πράγμα δεκαπέντε
σωστούς μήνας,
είχα λόγους ανωτέρους·
αι Αυλαί . . . Εγώ . . . το έθνος . . . εξ
ενός, εξ άλλου μέρους,
θεωρούντες . . . Είχα κι' άλλα να σας 'πώ .
. . 'πλην τι το κάμεις;
σ' εμποδίζουν να λαλήσης αι συμμαχικαί
δυνάμεις.
Αν κατώρθωσα να καύσω τον πολύτιμόν
μας στόλον
με την βίαν, με τον δόλον,
και αν έχυσα το αίμα των Ελλήνων εις τον
Πόρον,
με το μισθωτό μαχαίρι των πιστών μου

δορυφόρων,
αν με σκήπτρον ξένου κράτους θέλησα να
σας παιδεύσω,
και με όλην την Ευρώπην την Ελλάδα να
μπερδεύσω,
   είχα λόγους ανωτέρους·
αι Αυλαί . . . Εγώ . . . το έθνος. . . εξ
ενός, εξ άλλου μέρους
θεωρούντες . . . Είχα κι' άλλα να σας 'πώ .
. . πλην τι το κάμεις;
σ' εμποδίζουν να λαλήσης αι συμμαχικαί
δυνάμεις.
Θερμός είμαι δημοκράτης . . . για το
σύνταγμα πεθαίνω
αν με είδετε τρεις χρόνους τ' άρθρα του
να παραβαίνω
κι' απ' τους όρκους μου να λείπω,
γράμματα να κρυφανοίγω και να κυνηγώ
τον τύπο,
σπίτια να πατώ την νύκτα, και πολίτας
πριν τους κρίνω,
να 'ξορίζω, να ξυλίζω και τα νύχια τους να
χύνω,
   είχα λόγους ανωτέρους· κτλ.
Υπερπλούτισα το γένος (μάρτυρες οι
αδελφοί μου
   και τρεις τέσσαρες πιστοί μου,
όπου τρέχουν πουρνό βράδυ με τα
τάλληρα 'ς την τσέπη),
πλην τους πρώτους της Ελλάδος ο
καθένας πτωχούς βλέπει
πλην του Μπότζαρη ταις κόραις, τα παιδιά
του Καραΐσκου,
άφησα να ζουν μ' ελέη, με μαζώματα του
δίσκου
   είχα λόγους ανωτέρους κτλ
Ημπορεί να διη ο πλάστης εις των
σπλάγχνων μου το βάθος
η αγάπη της πατρίδος, και το μοναχό μου
πάθος·

πλην κατέτρεξα τα φώτα πλην διέφθειρα
τα ήθη·
πλην εις πλήθος κατασκόπων χρυσός
άφθονος εχύθη
πλην ηθέλησα να σβύσω και μεγάλους και
μικρούς,
πλην να δω τους πρώτους όλους
επεθύμησα νεκρούς.
Είχα λόγους ανωτέρους,
αι αυλαί . . . εγώ . . . το έθνος . . . εξ
ενός, εξ άλλου μέρους,
θεωρούντες . . . Είχα κι' άλλα να σας πω .
. . πλην τι το κάμεις;
σ' εμποδίζουν να λαλήσης αι συμμαχικαί
δυνάμεις.
Σας απέδειξα πώς είμαι άμεμπτος . . . Δεν
τ' αμφιβάλλω.
Σύνταγμά σας εγώ είμαι . . . μη ζητήτε
σύνταγμ' άλλο.
Δείξατέ με, 'σαν το Άργος αφοσίωσιν
τελείαν
Δόσετέ με 'σαν 'στο Άργος εντελή
Δικτακτορίαν,
Και ομνύω 'στου Βιάρου την ζωήν πως αν
'μπορέσω,
προκομμένους κι' απροκόπους χέρια πόδια
θα σας δώσω.
Έχω λόγους ανωτέρους
Αι αυλαί . . . Εγώ . . . το έθνος . . . εξ
ενός, εξ άλλου μέρους,
Θεωρούντες . . . Είχα κι' άλλα να σας πω .
. . πλην τι το κάμεις;
Σ' εμποδίζουν να λαλήσης αι συμμαχικαί
Δυνάμεις!
Ούτω γράφων ο ποιητής κατά του Καποδιστρίου εξηρέθιζε τα
πλήθη κατ' αυτού ως δήθεν ζητούντος να εκτελέση
ιδιοτελείς όλως σκοπούς, και ιδίως τους νησιώτας. Και των
μεν Υδραίων και Σπετσιωτών της κατά του Κυβερνήτου
καταφοράς αιτία ήτο όσα ανωτέρω ανεγράψαμεν, των δε
Μανιατών ήδε:

Η Μάνη προ της μεγάλης Ελληνικής επαναστάσεως της
παρασχούσης ημίν την ελευθερίαν, παρουσιάζει ιστορίαν
διάφορον της των άνω νήσων και της άλλης ελληνικής
φυλής· διότι, εν ώ μετά την κατάλυσιν της Βυζαντιακής
Αυτοκρατορίας (29 Μαΐου 1453) και την του Δεσποτάτου της
Πελοποννήσου (13 Απριλίου 1460) η πάσα Ελλάς σχεδόν
εδούλευσε τοις Τούρκοις, η Μάνη έχαιρεν είδος
ανεξαρτησίας εν ταις χερσί των Μουρζινάκων,
Ζαννεντάκηδων, Καπετανάκηδων, Δευτεράκων,
Κονμουνδουράκηδων, Διαβολάκων, Μαυρομιχαλαίων,
Πατριαρχέων, Κουκουβαλαίων, παρουσιάζουσα λαόν
μάχιμον, έχοντα πολλάς αρετάς των αρχαίων Σπαρτιατών
αναμίκτους μετ' αγρίων παθών και μεγάλης δεισιδαιμονίας.
Ο λαός ούτος ομιλεί υπέρ πάντα άλλον γλώσσαν ελληνικήν,
απηλλαγμένην τουρκικών και λατινικών λέξεων,
αποδεικνυουσών ότι οι διάφοροι κατακτηταί της Ελλάδος δεν
εξετάθησαν μέχρι του μέρους τούτου, ή δεν ηδυνήθησαν επί
χρόνον πολύν να διαμείνωσιν. Επί της επαναστάσεως του
1769-70 ως και εν τη του 1821, η οικογένεια Μαυρομιχάλη
διεκρίθη και εθυσίασε και χρήματα και άνδρας, οίτινες
προσέφερον μεγάλας και ανεκτιμήτους εκδουλεύσεις εις τον
ιερόν της Ελλάδος αγώνα. Ο διατρέχων την ιστορίαν των
χρόνων τούτων θα ίδη εν ταις σκηναίς της
Κωνσταντινουπόλεως τους ομήρους Μαυρομιχάλη ως και την
δραπέτευσιν αυτών. Εκ της εποχής ταύτης το αίμα των
Μαυρομιχαλαίων αφθόνως επότισε το δένδρον της
Ελληνικής ελευθερίας. Αλλ' ότε ο Κυβερνήτης ήρξατο της
χρησιμοποιήσεως των εθνικών γαιών, όπως προσπορισθή τα
μέσα της αναπτύξεως της χώρας, η Μάνη παρουσιάσθη ως
πρόβλημα ενώπιον αυτού. Απετέλουν άρα γε τα άγρια και
αδέσποτα όρη, αι βοσκαί και οι βάτοι της Μάνης μέρος των
εθνικών γαιών ή ου; Τίσιν ανήκον; Και διά τινων τίτλων η
Μάνη έπρεπε να μένη εξαιρέσιμος των γενικών μέτρων των
άλλων μερών της Ελλάδος, σχηματίση δε Κράτος εν Κράτει;
Ο βραχίων των νόμων της χώρας δεν έπρεπε να εκταθή
μέχρι της Μάνης; Δεν έπρεπε να ληφθώσι μέτρα, όπως μη η
Μάνη γίνη καταφύγιον των νόμων και των γενικών
μεταρρυθμίσεων αντιστρατευομένων;
Της Μάνης παρουσιαζομένης ως το δυσχερέστατον κατά την
λύσιν πρόβλημα τω Καποδίστρια, ο Πετρόμπεης και ο
Ζαννετάκης απεφάσισαν εκ συμφώνου ιδίαν αυτών λύσιν.

Ο Πετρόμπεης και ο Ζαννετάκης εψήφισαν, ίνα η Μάνη
διαιρεθή εις δύο, ανατολικήν και δυτικήν, και την μεν
κυριαρχίαν της ανατολικής ν' αναλάβη ο Ζαννετάκης, την δε
της δυτικής ο Μαυρομιχάλης.
Εκάτερος αυτών, όπως υποστηριχθή παρά των Μανιατών,
υπεσχέθη προς αυτούς θέσεις, στρατιωτικούς βαθμούς,
αποζημιώσεις, συντάξεις, και τον σχηματισμόν ταγμάτων
Μανιατών, τα οποία θα κυβερνώνται εξ ενός μέλους των δύο
οικογενειών. Τοιουτοτρόπως εκυμάτισεν εις Λιμένι η σημαία
του Λυκούργου και του Λεωνίδα. Ενεπιστεύθησαν δε την
αρχιστρατηγίαν τω στρατηγώ Κατσάκω (Ηλία) Μαυρομιχάλη
ανεψιώ του Πετρόμπεη, μικρού αποδράσαντι εκ των εν Άργει
φυλακών, συνεπεία αποφάσεως του δικαστηρίου προς ό
προσήχθη προδοθείς υπό του αδελφού αυτού Νικολάου
Πικουλάκη Μαυρομιχάλη, όστις, ως πρώτον συνταγματικόν
κατόρθωμα, επέδραμεν, ως άλλος Ιβραχίμ πασάς, κατά των
Καλαμών, άς, καίπερ φρουρουμένας υπό των Γάλλων,
ελεηλάτησεν.
Απέναντι τοιαύτης καταστάσεως πραγμάτων της τε Ύδρας
και της Μάνης, τι ώφειλε να πράξη ο Καποδίστριας; Δυοίν
θάτερον: ή να παραιτηθή αμέσως και επιστρέψη εις Γενεύην,
όπως διέλθη το γήρας αυτού μετά του φίλου Έυναρδ, ή η
υφισταμένη Κυβέρνησις αυτού εντός των δικαιωμάτων αυτής
να αντιτάξη δραστηρίως βίαν κατά της Ύδρας και Μάνης,
περιορίζουσα την κατ' αυτής ανταρσίαν της περαιτέρω
γενικεύσεως. Κατά μεν την πρώτην περίπτωσιν ώφειλε να
δώση την παραίτησιν προς τας τρεις Δυνάμεις, και να
εγκαταλείψη χάριν των Μανιατών και Υδραίων την πατρίδα
και λαόν ολόκληρον, όστις ευρών πόρους ζωής, εμπόριον,
ναυτιλίαν, κατάπαυσιν της πειρατείας και κιβδηλείας και
ευτυχίαν εν τη απελπισία ηυλόγει και ηγάπα αυτόν
υπερβολικώς. Κατά δε την δευτέραν ώφειλε να αντιτάξη βίαν
κατά των ανυποτάκτων, ίνα εξαναγκάση αυτούς εις
υποταγήν· δυστυχώς όμως ο μέγας εκείνος διπλωμάτης, ο
τας τύχας όλης της Ευρώπης κατά τας δύο πρώτας
δεκαετηρίδας του ΙΘ' αιώνος εις χείρας αυτού συγκρατήσας,
δεν ηδυνήθη να εννοήση, ως ώφειλε, χάριν της σωτηρίας
της πατρίδος, να προσοικειωθή τους ισχυρούς του τόπου και
διά μέσων, άπερ αυτός οίδε, να καταστήση αυτούς
χειροήθεις, αλλά προσοικειωθείς τον λαόν, εν αυτώ εζήτησεν
άπασαν αυτού την δύναμιν, ήν κατέθραυεν η των ισχυρών

επιβολή. Και εζήτησε μεν νυν, κατά το Ε' Ψήφισμα της εν
Άργει Δ' Εθνοσυνελεύσεως (7 Ιανουαρίου 1830), να
παράσχη τας αποζημιώσεις των τριών νήσων Ύδρας,
Σπετσών και Ψαρρών, του στρατού του Καραϊσκάκη, των
σωμάτων του Μεσολογγίου και της φρουράς της
Ακροπόλεως Αθηνών, αλλ' αι νήσοι εζήτουν δύο
εκατομμύρια και εννεακοσίας χιλιάδας ταλλήρων Ισπανικών
ως αποζημιώσεις και οι της ξηράς στρατιωτικοί πεντήκοντα
τέσσαρα εκατομμύρια τουρκικών γροσίων.
Πάντες ούτοι εζήτουν αυτά άνευ τίτλων, αποδείξεων
δαπάνης και βασίμων μαρτυριών. Τεσσαράκοντα πλοιοκτήται
ήσαν Υδραίοι ζητούντες 1,220,000 ταλλήρων, τριάκοντα
Σπετσιώται 1,000,000 ταλλήρων και οι Ψαρριανοί 700,000.
Προς δε την αποσταλείσαν προς εξέλεγξιν των παραπόνων
αυτών πενταμελή επιτροπήν εκ του Μεταξά, Γενοβέλη,

Μαυρογένη, Μαγγίνα και Αντωνοπούλου, οι ταραχοποιοί
δημοτικοί σύμβουλοι της Ύδρας παρέστησαν και πάλιν
κομπορρημονούντες και αξιούντες ούτε ολίγα ούτε πολλά
18,000,000 φοινίκων!
Η Εθνοσυνέλευσις καθώς και ο Καποδίστριας απεφάσισαν να
πληρώσωσιν 1,000,000 ταλλήρων ταις νήσοις εις γαίας,
χρήματα και γραμμάτια, ή το όλον των 2,900,000 ταλλήρων
εις μόνον γαίας. Αλλ' ο μέγας αληθώς πατριώτης
Κουντουριώτης εύρε την ευκαιρίαν να θέση την μάχαιραν εις
τον τράχηλον της Ελλάδος, ζητών το όλον ποσόν 2,900,000
ταλλήρων εις χρήματα και τόκον μέχρις ού αποπληρωθή το
ποσόν τούτο (τόκον ετήσιον 1,400,000 φοινίκων). Φυσικώς
ούτε η Κυβέρνησις ούτε η Γερουσία, απεδέξατο την
τοκογλυφικήν ταύτην αίτησιν, ήτις δεν εβασίζετο επί
αποδείξεων, αλλ' επί των παραλόγων φωνασκιών των
πλοιοκτητών, τινές των οποίων ελαχίστας υπέστησαν ζημίας.
Διότι, κατά τινας υπολογισμούς, τα μεγαλείτερα πλοία της
εποχής εκείνης των νησιωτών δεν ήσαν μεγαλείτερα των
300 τόννων, έν δε πλοίον των 300 τόννων κατά τας
υψηλοτέρας διατιμήσεις των τότε ναυπηγών της Γαλλίας,
δεν ηδύνατο να στοιχίση εν τη ναυπηγία αυτού
περισσότερον των 25,000 φράγκων. Άρα πάντα τα πλοία,
άπερ δεν ήσαν βεβαίως και πάντα των 300 τόννων, και δεν
απωλέσθησαν πάντα κατά τον επταετή αγώνα, δεν ηδύναντο
να απαιτήσωσιν αποζημίωσιν ούτε 1,000,000 ταλλήρων.
Εν τούτοις, ο Καποδίστριας, όστις ήλπισεν, ότι ηδύνατο να
ευχαριστήση αυτοίς διά πληρωμής μικρού τινος ποσού
απέναντι των απαιτήσεων απέστειλεν, επί τη γνωμοδοτήσει
της πενταμελούς επιτροπής, προς τας δημοτικάς αρχάς των
τριών νήσων 50,000 ισπανικών ταλλήρων συγχρόνως δε
εκήρυξε (12)24 Μαρτίου 1830) την Ύδραν ελεύθερον λιμένα
επί πενταετίαν, όπως ανορθώση το καταπεπτωκός εμπόριον.
Τα εκ του τελευταίου όμως τούτου μέτρου πλεονεκτήματα
ανηρέθησαν όλως διά της αυξήσεως των επί της εισαγωγής
και εξαγωγής δασμών, οι δε κεχολωμένοι Υδραίοι ούτε διά
του δώρου της ατελείας κατεπραΰνθησαν, ούτε διά της
πληρωμής μέρους τινός των απαιτήσεων αυτών.
Ενεκολπώθησαν χωρίς της ελαχίστης ευγνωμοσύνης τας
25,000 ισπανικών ταλλήρων, άτινα εδόθησαν τη Ύδρα —
16,000 εδόθησαν ταις Σπέτσαις και 9,000 τοις Ψαροίς — και
εξηκολούθουν έτι μεγαλοφωνότερον απαιτούντες την υπό

του Κράτους πληρωμήν ολοκλήρου του χρέους. Τέλος
απεφάσισεν ο Κυβερνήτης να προτείνη αυτοίς οριστικήν
εξόφλησιν δι' 6 εκατομμυρίων φοινίκων, ών έν τρίτον
έμελλε να δοθή εις κτήματα, έτερον εις ομολογίας και το
υπολειπόμενον εις μετρητά εκ του ελπιζομένου δανείου, ή
και σύμπασα η ποσότης εις εθνικά κτήματα, αλλ' οι νησιώται
ουδέν ήθελον να ακούσωσι περί του συμβιβασμού εκείνου,
και επέμενον απαιτούντες την υπό του Κράτους αναγνώρισιν
ολοκλήρου του χρέους, και την παρά τη εθνική χρηματιστική
τραπέζη κατάθεσιν του φανταστικού αυτού κεφαλαίου επί
τόκω 8 ο)ο, ού οι ετήσιοι τόκοι ήθελον αναβαίνει, ως
είπομεν ανωτέρω, εις 1,440,000 φοινίκων. Την αξίωσιν
ταύτην απέκρουσεν εντόνως ο Καποδίστριας διότι εν τη κακή
τότε καταστάσει της τραπέζης δικαίως εφοβείτο ο
Κυβερνήτης, ότι ήθελε παντελώς καταστραφή η πίστις
αυτής, αν επεβαρύνετο διά νέου χρέους. Ούτω το περί
αποζημιώσεως ζήτημα έμεινεν άλυτον, η μεταξύ της
κυβερνήσεως και των Υδραίων διάστασις παρετείνετο, και αι
ιδέαι της Ιουλιανής επαναστάσεως εύρον στήριγμα εν Ύδρα
απτά υλικά συμφέροντα.
Τοιαύται ήσαν αι απαιτήσεις των νησιωτών και η αδιάσειστος
αυτών απόφασις, όπως, εάν μη αποζημιωθώσιν αντιστώσι
κατά της Κυβερνήσεως. Και δεν εμιμήθησαν οι γεννάδαι
τους απαιτητάς αποζημιώσεων των κατά ξηράν
στρατευμάτων, οίτινες ήσαν ουκ ολίγοι. Αλλ' αι απαιτήσεις
αύται ήσαν δίκαιαι και συγκαταβατικαί. Ο δε στρατηγός
Ιωάννης Ράγκος, λέγει φιλέλλην ιστοριογράφος της εποχής,
έδειξε πρώτος το παράδειγμα της αποδοχής των δοθεισών
αποζημιώσεων και τοιουτοτρόπως εξώφλησαν οι πλείστοι
απαιτηταί.
Οι Υδραίοι όμως απορρίψαντες τας προτάσεις του
Καποδιστρίου εξέφραζον αγανάκτησιν κατ' αυτού,
επιλαθόμενοι, ότι κατέστρεφον ου μόνον την πατρίδα, αλλά
τα ίδια αυτών ανδραγαθήματα, τας ιδίας αυτών, κατά τον
μακρόν αγώνα, θυσίας. Υπάρχουσι χιλιάδες Ελλήνων τού τε
εξωτερικού και εσωτερικού και εκατοστύες φιλελλήνων, εκ
των ευγενεστέρων της Ευρώπης οικογενειών, δουκών,
λόρδων και κομητών, χύσαντες το αίμα αυτών και
θυσιάσαντες την ουσίαν υπέρ της Ελλάδος, και όμως τα
τέκνα αυτών ουδέποτε εζήτησαν ούτε οβολόν.

Την τοιαύτην κατάστασιν της Ελλάδος καθίστων έτι
δεινοτέραν, ως και ανωτέρω είπομεν, αι εφημερίδες της
αντιπολιτεύσεως ο εν Σμύρνη εκδιδόμενος υπό του Βλακ
(78) «Ταχυδρόμος της Σμύρνης» η εν Ναυπλίω «Ηώς» του
Ε. Αντωνιάδου και ο εν Ύδρα «Απόλλων» του Αναστασίου
Πολυζωίδου, νέου Θεσσαλού άρτι εκ Παρισίων
επανακάμψαντος και εμπεφορημένου υπό επαναστατικών
ιδεών. Ούτος ζητήσας να εκδώση εν Ναυπλίω την εφημερίδα
αυτού κατεδιώχθη και φυγών μετέβη εις Ύδραν, ένθα έτυχε
της αναγκαίας υποστηρίξεως και εξέδιδε τον «Απόλλωνα». Αι
κατά του Κυβερνήτου αδολεσχίαι των εφημερίδων τούτων
επί τοσούτον επιθετικότητος ίκοντο, ώστε ο Αντωνιάδης,
συντάκτης της «Ηούς» κατεδιώχθη δικαστικώς, ένεκα της
ελευθέρας γλώσσης της εφημερίδος αυτού, κατηγορήθη επί
εγκλήματι εσχάτης προδοσίας και προυφυλακίσθη· η δε Ηώς
επαύθη. Μόλις μετά πολύμηνον κάθειρξιν εξεδόθη απόφασίς
τις, δι' ής ο κατηγορούμενος ηθωώθη. Το δικαστήριον
εθεώρησε την στέρησιν της προσωπικής ελευθερίας, ήν
υπέστη ο Αντωνιάδης, ως προσήκουσαν ανταπόδοσιν της
ελευθέρας πολιτικής κρίσεως, ήν είχε τολμήσει ο συντάκτης
της «Ηούς». Η προς τον άνδρα τούτον συμπεριφορά της
Κυβερνήσεως ενέπνευσε μεν τρόμον και αγανάκτησιν τοις
δημοσιογραφούσιν, αλλά δεν εφόβισεν ούτε απέτρεψε και
άλλους της οδού, ήν εκείνος εβάδισεν.
Ο εν Ύδρα εκδιδόμενος «Απόλλων» επετίθετο λάβρως κατά
του Κυβερνήτου αποκαλών αυτόν τύραννον, ρωσόφρονα και
παροτρύνων τον λαόν εις ανταρσίαν.
Αφειδώς μετεχειρίσθη παρακλήσεις και απειλάς ο
Καποδίστριας, όπως στερήση τον «Απόλλωνα» της
προστασίας των νησιωτών. Επίτροπος της κυβερνήσεως
μετέβη εις Σπέτσας και Ύδραν και υπέβαλε προς τους
δημογέροντας τον τύπον αναφοράς, δι' ής παρεκάλουν ούτοι
την κυβέρνησιν να απομακρύνη της νήσου το σκάνδαλον,
όπερ κατήσχυνε τας κοινότητας αυτών, απαλλάττουσα αυτάς
του «Απόλλωνος». Αλλ' οι νησιώται έμειναν κωφοί προς τας
παρακλήσεις του Κυβερνήτου, οι Υδραίοι δε μάλιστα
διέταξαν την ημέρας και νυκτός ένοπλον φρούρησιν του
τυπογραφείου του Α. Πολυζωίδου, εν ώ εξετυπούτο ο
«Απόλλων» , προς αποτροπήν βιαίας τινός από της Στερεάς
επιθέσεως. Η βιαιότης της γλώσσης του «Απόλλωνος»
ηύξησε μετά του απειλούντος αυτόν κινδύνου, η χειρίστη δ'

αυτού μομφή κατά του Κυβερνήτου ήν ο φόβος αυτού προς
την κοινήν γνώμην. «Ο ελεύθερος τύπος, επανελάμβανεν
αδιακόπως υπό διαφόρους φράσεις το αντιπολιτευόμενον
φύλλον, υπήρξε πάντοτε η αιωνία πέτρα του σκανδάλου διά
τους αυθαιρέτους δεσπότας.»
Αλλά πλην των εφημερίδων οι αντιπολιτευόμενοι,
θρασύτεροι γενόμενοι, ήρξαντο γράφοντες και αναφοράς, άς
υπερεπλήρουν διά πλαστών υπογραφών, εν αίς εξετίθετο η
αντεθνική δήθεν πολιτική του Κυβερνήτου. Τούτο δ' έχων
υπ' όψει: «Ας κατασκευάζωνται, έγραφεν ο Καποδίστριας
προς τον πρίγκηπα Σούτσον εις Παρισίους, αναφοραί εν
Ύδρα και άλλοις δήμοις του Αιγαίου, εκ Πελοποννήσου αφ'
ετέρου και εκ της Στερεάς δεν παύει ο λαός γράφων προς
εμέ τα αντίθετα. Επί του παρόντος έχομεν έτι μόνον
εμφύλιον πόλεμον διά του καλάμου· αλλοίμονον αν
καταντήση ούτος εις πυροβολισμούς!»
Οι φόβοι ούτοι εφάνησαν ταχέως δικαιολογούμενοι υπό των
γεγονότων. Η κατά το Αιγαίον στασιαστική κίνησις, ιδίως της
Σύρου, ελάμβανεν οσημέραι σοβαρωτέραν μορφήν. Ο
Αλέξανδρος Μαυροκορδάτος, όστις είχε τέως διαμείνει εν τω
βάθει της σκηνής και συνεδαύλιζε μόνον εκ Τήνου, ένθα είχε
καταφύγει, την φλόγα, ήλθεν εις Ύδραν, ο επίτροπος της
κυβερνήσεως έφυγεν εκείθεν, και οι τω Κυβερνήτη
αφωσιωμένοι δημοτικοί σύμβουλοι εδιώχθησαν. Επταμελής
συνταγματική επιτροπή, αποτελουμένη, ως είπομεν, εκ των:
Κουντουριώτου, Μιαούλη, Β. Βουδούρη, Μ. Τομπάζη, Δ.
Βούλγαρη, Α. Κριεζή και Ν. Οικονόμου, ανέλαβεν, ως
ηγγέλλετο την διοίκησιν της νήσου, και διέκοψε πάσαν
σχέσιν προς την καθεστηκυίαν κυβέρνησιν. Το παράδειγμα
της Ύδρας παρηκολούθησαν, εντός ολίγου, και άλλαι νήσοι
του Αιγαίου. Ο σκληρότερος όμως κατά του Κυβερνήτου
κτύπος ην η αποστασία της Σύρου, ής η δυσαρέσκεια
οσημέραι αύξουσα από των τελευταίων ταραχών,
εκορυφώθη νυν μετά το δοθέν παράδειγμα της Ύδρας εις
εκφανή στάσιν. Τα τελωνεία Σύρου είχον τέως αποτελέσει
τον κυριώτατον οικονομικόν πόρον της κυβερνήσεως. Διότι
επί της Στερεάς δεν εισεπράττοντο οι φόροι τόσον τακτικώς
ως επί των νήσων. «Η δυσάρεστος συνέπεια πάντων των
σκευωρημάτων, έγραφεν ο Κυβερνήτης, είναι η εξής: αι υπό
των δήθεν πατριωτών υποκινούμεναι ταραχαί παρέχουσιν εις
τους ενοικιαστάς την πρόφασιν να αναβάλωσι την εις το

δημόσιον πληρωμήν· οι φορολογούμενοι αφ' ετέρου
ουδεμιάς αμελούσιν ευκαιρίας, όπως υστερώσι της
καταβολής των οφειλομένων. Εκ τούτου εννοείτε την
αξιοθρήνητον θέσιν μου».
Κατά την εποχήν ταύτην ο Καποδίστριας, εις απελπισίαν
περιελθών ένεκα της καθυστερήσεως των αναγκαιοτάτων
χρηματικών πόρων, κατέφυγεν εις το έσχατον μέτρον
κυβερνήσεως παλαιούσης προς την χρεωκοπίαν· έπλασε
νέους φόρους, μη πληρωνομένων των παλαιών· διέταξε κατ'
απομίμησιν του παρά πάσι τοις πεπολιτισμένοις έθνεσιν
υπάρχοντος τέλους χαρτοσήμου, την πληρωμήν τοιούτου
φόρου παρά παντός τίτλου ιδιοκτησίας, παντός συμβολαίου
εκμισθώσεως και πάσης υπό της κυβερνήσεως διδομένης
αδείας· ανεβίβασε τους τελωνειακούς δασμούς, τον μεν της
εξαγωγής εις 8, τον δε της εισαγωγής εις 10 ο)ο, επί
προφάσει ανακουφίσεως των εκ Κρήτης δυστυχών
μεταναστών· εψήφισε δε τέλος την έκδοσιν 3,000,000
φοινίκων ατόκου χαρτονομίσματος.
Τω ρώσω ναυάρχω Ρίκορδ τοσούτον κρίσιμος εφαίνετο η
των πραγμάτων κατάστασις, ώστε έγραφε κατ' Ιούλιον του
1831 τον Νέσσελροδ: «Τα συμβάντα επέρχονται ενταύθα
ουχί της ισχύος των πεποιθήσεων, αλλά διά της δυνάμεως
των ταπεινοτάτων ορμών. Πας ο μετασχών της
υπερασπίσεως της πατρίδος, ζητεί νυν αποζημιώσεις και
δώρα, και ζητεί αυτά ανώτερα των εν τω πολέμω ζημιών
αυτού. Πάντες λησμονούσι την πτωχείαν του δημοσίου
ταμείου και την αρχήν, ότι οι ικανώτατοι πρέπει να
καταλάβωσι τας καλλίστας των θέσεων. Τούτου ένεκα έχει
τοσούτους εχθρούς η κυβέρνησις. Οι αντιπρέσβεις Αγγλίας
και Γαλλίας κατακρίνουσι μεν εν τω φανερώ την
αντιπολίτευσιν, αλλ' εν τω κρυπτώ δεν παύουσιν
υποστηρίζοντες αυτήν, και συνδαυλίζουσιν ούτω το πυρ, εξ
ού γενική κινδυνεύει να προέλθη και καταστρεπτική
πυρκαϊά».
Η αμηχανία του Κυβερνήτου ταυτοχρόνως τοσούτον είχε
κορυφωθή, ώστε ησθάνθη την ανάγκην να ενδώση, κατά τι,
εις τας απαιτήσεις των πολεμίων, αφού μάλιστα η
αντιπολίτευσις είχεν ισχυρόν έρεισμα τους αντιπρέσβεις των
δυτικών Δυνάμεων, οίτινες προβαλλόμενοι ως ασπίδα τας
ταπεινοτάτας ορμάς Ελλήνων σπουδαρχών υπό τον τύπον

ευλόγων δικαίων, τας ανάγκας των αληθώς την πατρίδα
κατά την επανάστασιν ευεργετησάντων, τους πτωχούς τους
οπωσδήποτε πάσχοντας, τους πολιτικής επικουρίας
επιδεομένους και πάντας εν γένει τους ένεκα τούτου ή
εκείνου του λόγου αφορμάς κατά της κυβερνήσεως έχοντας,
κατεπενέβαινον τοις των Ελλήνων πράγμασιν επί ιδίοις
τέλεσιν, οι μεν ως συμπολιτευόμενοι, εν οίς πρώτιστοι οι
Ρώσοι οι δε ως αντιπολιτευόμενοι, εν οίς οι Άγγλοι και
Γάλλοι. Τη παρακινήσει των αντιπροσώπων των ευεργετίδων
Δυνάμεων ήλθον περί τας αρχάς Ιουλίου, πέντε προύχοντες
της Ύδρας εις Ναύπλιον, όπως συνεννοηθώσι μετά της
Κυβερνήσεως. Επανέλαβον την περί εθνοσυνελεύσεως και
συντάγματος απαίτησιν, ήν πλείσται πόλεις, εν αίς και αι
Αθήναι, τοσούτον ενεργώς είχον ασπασθή. Αλλ' ο
Κυβερνήτης ηρνήθη να δεχθή αυτούς και να συνομιλήση
μετ' αυτών προσωπικώς, εδέησε δε να γείνωσιν αι
διαπραγματεύσεις τη μεσιτεία των αντιπρέσβεων. Ο
Καποδίστριας εθεώρει τους Υδραίους ως απλούς αποστάτας,
και μεγάλως εδυσχέραινεν, ότι των Δυνάμεων αντιπρόσωποι
συγκατέβαινον εις προσωπικήν προς αυτούς κοινωνίαν.
Ούτω δε κατεδείκνυε την αγανάκτησιν αυτού, γράφων προς
τον Σούτσον:
»Αι απαιτήσεις, άς οι κύριοι αντιπρέσβεις έσχον την
υπομονήν να ακούσωσι παρά των Υδραίων εν τη μετ' αυτών
συνεντεύξει, χαρακτηρίζουσιν εντελώς τα τε πρόσωπα και
πράγματα. Δεν δύναμαι να ελπίσω, ότι η ημιεπίσημος
ανάμιξις των κυρίων αντιπρέσβεων εις τα της Ύδρας θέλει
φέρει ευχάριστόν τι αποτέλεσμα.» Ουχ ήττον δεν
κατώρθωσεν ο Καποδίστριας να αντιστή εκφανώς εις την
γενικήν συνταγματικήν πίεσιν. Απεφάσισε να ορίση κατ'
Οκτώβριον 1831 την έναρξιν της Εθνοσυνελεύσεως, υπό τον
όρον: «αν μέχρις Οκτωβρίου δεν μετέβαλλε την κατάστασιν
των πραγμάτων η εν Λονδίνω σύνοδος. »
Συνάμα δ' επέμεινε προφορικώς ο έμφρων ηγεμών, απέναντι
των συνταγματικών ορέξεων των νησιωτών, εις το αξίωμα,
ότι δεν είχε το δικαίωμα να διαθέση το μέλλον της Ελλάδος,
και ότι μόνος ο μέλλων Βασιλεύς ηδύνατο να αποφασίση
περί της σκοπιμότητος συνταγματικού πολιτεύματος. Οι
Υδραίοι επανέκαμψαν άπρακτοι· αλλ' ο Κυβερνήτης διήνοιξε
τους οφθαλμούς αυτών, και αι ψευδείς παραχωρήσεις
κατέστησαν οξείαν την κρίσιν. Η μερίς της αντιπολιτεύσεως

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Condensed Matter Applications Of Adscft Focusing On Strange Metals Andrea Amoretti Auth

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