scholarly journals Quantum Hall Conductivity in the Presence of Interactions

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 200
Author(s):  
Xi Wu ◽  
Mikhail Zubkov
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Interaction Strength ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Hall Conductivity ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that, irrespective of the interaction strength, the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. This conclusion remains valid for both the integer and fractional quantum Hall effect.

NUMERICAL STUDY OF JASTROW-SLATER TRIAL STATES FOR THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (07) ◽  
pp. 503-510 ◽  
Author(s):  
NANDINI TRIVEDI ◽  
J.K. JAIN
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Numerical Study ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Correlation Factors

We study the recently proposed trial states for the fractional quantum Hall effect, which are constructed by multiplying the wavefunction for filled Landau levels with Jastrow correlation factors. In spite of the essential use of higher Landau levels, we demonstrate the validity of the variational states using Monte Carlo methods by showing that the Jastrow factors ensure (i) these states lie predominantly in the lowest Landau level and (ii) they have very low interaction energies.

NON-1/m FRACTIONAL QUANTUM HALL EFFECT IS A MANIFESTATION OF ANYON SUPERCONDUCTIVITY

1991 ◽  
Vol 05 (10) ◽  
pp. 1739-1749 ◽  
Author(s):  
Chia-Ren Hu
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Statistical Correlation ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
The Mean

Regarding electrons as anyons of index αs pierced with -(m+αs) flux quanta per particle, and letting the mean field of these fluxes cancel the external magnetic field B, we obtain the filling factor ν=1/(m+αs), where m must be odd. Demanding the resulting system of anyons to exhibit "anyon supercanductivity", we obtain αs=±(1-q/n) where q is odd, and n>q is relatively prime to q. For q=1 we recover a formula due to Jain, and resolve the mystery why, for a state with ν=n/(2pn±1)<1 he requires use of the statistical correlation of n filled Landau levels. For q=3,5,⋯, we obtain the fractions 4/11, 4/13, 5/13, etc., which are missing from Jain's list. Thus this non-heirarchical approach to the non-1/m fractional quantum Hall effect has the strengths of Jain's composite-fermion approach, but not its (potential) weaknesses.

Fractional quantum Hall effect in hole Landau levels

1990 ◽  
Vol 41 (2) ◽  
pp. 1290-1293 ◽  
Author(s):  
S.-R. Eric Yang ◽  
A. H. MacDonald ◽  
D. Yoshioka
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

scholarly journals Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

2007 ◽  
Vol 3 (8) ◽  
pp. 561-565 ◽  
Author(s):  
Jeffrey B. Miller ◽  
Iuliana P. Radu ◽  
Dominik M. Zumbühl ◽  
Eli M. Levenson-Falk ◽  
Marc A. Kastner ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum Hall Effect ◽  
Quantum Point Contact ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Point
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