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.

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.

scholarly journals Hall Effect in Neutron Star Crusts

2013 ◽  
Vol 9 (S302) ◽  
pp. 415-418
Author(s):  
K. N. Gourgouliatos ◽  
A. Cumming
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Large Scale ◽  
Initial Conditions ◽  
Free Electrons ◽  
Solid Crystal ◽  
Field Lines ◽  
Evolutionary Paths ◽  
The Magnetic Field ◽  
Turbulent Cascade

AbstractThe crust of Neutron Stars can be approximated by a highly conducting solid crystal lattice. The evolution of the magnetic field in the crust is mediated through Hall effect, namely the electric current is carried by the free electrons of the lattice and the magnetic field lines are advected by the electron fluid. Here, we present the results of a time-dependent evolution code which shows the effect Hall drift has in the large-scale evolution of the magnetic field. In particular we link analytical predictions with simulation results. We find that there are two basic evolutionary paths, depending on the initial conditions compared to Hall equilibrium. We also show the effect axial symmetry combined with density gradient have on suppressing turbulent cascade.

New Universality at the Magnetic Field Driven Insulator to Integer Quantum Hall Effect Transitions

1997 ◽  
Vol 78 (11) ◽  
pp. 2200-2203 ◽  
Author(s):  
S.-H. Song ◽  
D. Shahar ◽  
D. C. Tsui ◽  
Y. H. Xie ◽  
Don Monroe
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
The Magnetic Field

BREAKDOWN OF THE QUANTUM HALL EFFECTS IN HOLE SYSTEMS AT HIGH INDUCED CURRENTS

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3537-3540 ◽  
Author(s):  
J. D. GETHING ◽  
A. J. MATTHEWS ◽  
A. USHER ◽  
M. E. PORTNOI ◽  
K. V. KAVOKIN ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Eddy Currents ◽  
Energy Gap ◽  
Quantum Hall ◽  
Sweep Rate ◽  
Fractional Quantum Hall ◽  
Hall Effects ◽  
Highly Sensitive ◽  
Induced Currents

The magnetisation of two dimensional hole systems in the quantum Hall regime has been studied using a highly-sensitive torsion balance magnetometer. In a time varying magnetic field eddy currents are induced which become large around integer and fractional filling factors where ρxx takes a very low value. The sweep rate and temperature dependence of these induced currents are in good agreement with the model of quantum Hall effect breakdown proposed recently by Matthews et al. This model also allows comparison between the energy gap at different filling factors and so provides a measurement of the fractional quantum Hall effect energy gap, Δ1/3, and the spin split energy gap, g*μ B B.

NEW INSIGHT INTO THE INTEGER QUANTUM HALL EFFECT

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2783-2792
Author(s):  
VIPIN SRIVASTAVA
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Number Density ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Extended States ◽  
The Magnetic Field ◽  
Insight Into

By considering the degeneracies of the localized and extended states separately we have investigated the integer quantum Hall effect (IQHE) in terms of fraction of extended states in a Landau subband. The IQHE is found to manifest itself as saw-tooth oscillations in the number density of the extended electrons as a function of magnetic field. Preliminary results of an experiment are also presented that support this picture. It is found that contrary to the traditional theoretical belief, the extended states form a non-vanishing fraction of the states in a Landau subband. Significantly it is shown that if this was not so, the IQHE would not arise in the first place. This result is relevant in connection with the long standing question of nature of transition between plateaus, and also the recent discovery of intriguing electron density driven metal–insulator transition in two-dimensional systems. The results also show that extended states float up in energy in addition to being systematically destroyed as the magnetic field is reduced, and that the system can become completely localized at a nonzero magnetic field.

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