scholarly journals Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect

1995 ◽  
Vol 93 (3) ◽  
pp. 503-518 ◽  
Author(s):  
N. Maeda
Keyword(s):  
Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Mean Field Theory ◽  
Quantum Hall ◽  
Mean Field ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

COLLECTIVE FIELD THEORY APPLIED TO THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (01n02) ◽  
pp. 417-426
Author(s):  
B. Sakita ◽  
Dong-Ning Sheng ◽  
Zhao-Bin Su
Keyword(s):  
Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Constraint Equation ◽  
Dynamical Theory ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Free Vortex ◽  
Fractional Quantum Hall

We present an application of collective field theory to the fractional quantum Hall effect (FQHE). We first express the condition, that the electrons are all in the lowest Landau level, as a constraint equation for the state functional. We then derive the fractional filling factor from this equation together with the no-free-vortex assumption. A hierarchy of filling factors is derived by using the particle-vortex dual transformations. In the final section we discuss an attempt at a dynamical theory of FQHE, which would justify the no-free-vortex assumption. A derivation of Laughlin’s wave function with and without quasi-hole excitations is also given.

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.

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.

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