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.

scholarly journals MEAN FIELD DESCRIPTION OF THE FRACTIONAL QUANTUM HALL EFFECT NEAR ν=1/(2k+1)

1996 ◽  
Vol 11 (02) ◽  
pp. 329-342 ◽  
Author(s):  
STEPHANIE CURNOE ◽  
NATHAN WEISS
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Fractional Quantum Hall Effect ◽  
Finite Range ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Field Solution ◽  
The Mean

We study the nature of mean field solutions to the equations of motion of the Chern-Simons Landau-Ginzburg (CSLG) description of the fractional quantum Hall effect (FQHE). Beginning with the conventional description of this model at some chemical potential μ0 and magnetic field B corresponding to a “special” filling fraction ν=2πρ/ eB=1/n (n=1, 3, 5,…), we show that a deviation of µ in a finite range around μ0 does not change the mean field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy mean field solution but also for the vortex excitations. The vortex configurations do not depend on µ in a finite range about μ0 in this model. However, when [Formula: see text] the lowest energy mean field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of µ and ν over which the system of vortices is dilute.

THE CHERN–SIMONS–LANDAU–GINZBURG THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (01) ◽  
pp. 25-58 ◽  
Author(s):  
SHOU CHENG ZHANG
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Physical Consequences ◽  
Systematic Derivation ◽  
Chern Simons

This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. We first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern–Simons–Landau–Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin's wave function approach, their physical consequences are equivalent. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.

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.

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
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