Landau levels and quantum Hall effect

The critical exponent ν of the localization length in the integral quantum Hall regime can be measured directly using small Hall-bar geometries with different sizes. We obtain a universal behaviour for the three lowest Landau levels. This is in agreement with the universality prediction of the field-theoretic approach to the metal-insulator-transition in the quantum Hall effect. The value of ν=2.3±0.1 agrees with recent numerical studies for the lowest Landau level. We review recent experimental findings on the basis of these results and discuss the situation in Landau levels where spin-splitting is not resolved.

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

Modern Physics Letters B ◽

10.1142/s0217984991000599 ◽

1991 ◽

Vol 05 (07) ◽

pp. 503-510 ◽

Cited By ~ 27

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.

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

International Journal of Modern Physics B ◽

10.1142/s0217979291001644 ◽

1991 ◽

Vol 05 (10) ◽

pp. 1739-1749 ◽

Cited By ~ 2

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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