Qhe

quantum

1. QUANTUM HALL EFFECT SUBMITTED TO: Prof. R.S SINGH SUBMITTED BY: VISHAL KUMAR JANGID,M.Sc (Final) 2016-17 JNVU (Department of Physics)

2. Hall Effect (1897)

3. Quantum Hall Effect(1980)

4. Hall Resistivity

5. Integer Quantum Hall Effect

6. Explanation IQHE It can be explain by considering non interacting electron. At high magnetic field B, the electronic density of states becomes a set of discrete Landau levels due to the confinement produced by the field . When these levels are well resolved, if a voltage is applied between the ends of a sample, the voltage drop between voltage probes along the edge of a sample can go to zero in particular ranges of B, and the Hall resistance becomes extremely accurately quantised  

7. Continue …. The QHE can be described in terms of a set of states, one per Landau level, travelling along the edges. energy E=  

8. Fractional Quantum Hall Effect

9. Explanation By considering a two-dimensional system of strongly interacting electrons . At particular magnetic fields, the electron gas condenses into a remarkable state with liquid-like properties Filling factor: , where m is always turn out to be odd number FRACTIONALLY-CHARGED QUASIPARTICLES : consider   quasiparticles with charge  e * = e / q COMPOSITE FERMIONS : it attaches two (or, in general, an even number) flux quanta  h / e  to each electron, forming integer-charged quasiparticles called Composite Fermions  

10. Thank you