scholarly journals The quantum Hall effect in the absence of disorder

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Kyung-Su Kim ◽  
Steven A. Kivelson
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Finite Interval ◽  
Quantum Hall ◽  
Wigner Crystal ◽  
Quasi Particle ◽  
Hall Conductance ◽  
Finite Extent

AbstractIt is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e., for the existence of “plateaus” in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal (QPWC) results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are also explored.

Quantum Hall effects

Quantum 20/20 ◽  
2019 ◽  
pp. 303-322
Author(s):  
Ian R. Kenyon
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Energy Gap ◽  
Quantum Hall ◽  
Free Electrons ◽  
Electron Gases ◽  
Hall Conductance ◽  
Hall Effects ◽  
The Stability ◽  
The Magnetic Field

It is explained how plateaux are seen in the Hall conductance of two dimensional electron gases, at cryogenic temperatures, when the magnetic field is scanned from zero to ~10T. On a Hall plateau σ‎xy = ne 2/h, where n is integral, while the longitudinal conductance vanishes. This is the integral quantum Hall effect. Free electrons in such devices are shown to occupy quantized Landau levels, analogous to classical cyclotron orbits. The stability of the IQHE is shown to be associated with a mobility gap rather than an energy gap. The analysis showing the topological origin of the IQHE is reproduced. Next the fractional QHE is described: Laughlin’s explanation in terms of an IQHE of quasiparticles is presented. In the absence of any magnetic field, the quantum spin Hall effect is observed, and described here. Time reversal invariance and Kramer pairs are seen to be underlying requirements. It’s topological origin is outlined.

CHIRAL ANOMALY IN EUCLIDEAN (2+1)-DIMENSIONAL SPACE AND AN APPLICATION TO THE QUANTUM HALL EFFECT

2008 ◽  
Vol 22 (17) ◽  
pp. 2675-2689 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Magnetic Field ◽  
Dirac Equation ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Zero Mode ◽  
Dimensional Space ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Regularization Procedure ◽  
Chiral Transformation

The chiral anomaly in (2+1)-dimensions and its relationship to the zero mode of the Dirac equation in the massless case is studied. Solutions are obtained for the Dirac equation under a vector potential which generates a constant magnetic field. It is shown that there is an anomaly term associated with the corresponding chiral transformation. It can be calculated by using the regularization procedure of Fujikawa. The results are applied to the quantum Hall effect.

scholarly journals WANNIER FUNCTIONS AND FRACTIONAL QUANTUM HALL EFFECT

1995 ◽  
Vol 09 (25) ◽  
pp. 3333-3344 ◽  
Author(s):  
R. FERRARI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Wannier Functions ◽  
Hartree Fock ◽  
Fock State

We introduce and study the Wannier functions for an electron moving in a plane under the influence of a perpendicular uniform and constant magnetic field. The relevance for the Fractional Quantum Hall Effect is discussed; in particular, it shown that an interesting Hartree–Fock state can be constructed in terms of Wannier functions.

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