Conductance fluctuations at the fractional quantum Hall plateau transitions

TL;DR

This paper models conductance fluctuations at fractional quantum Hall transitions using a mean field approach, identifying fixed points and their conductance distributions based on composite fermion theory.

Contribution

It introduces a mean field scaling flow for fractional quantum Hall conductivities, extending the integer quantum Hall scaling flow to fractional regimes.

Findings

Identifies unstable fixed points for fractional quantum Hall transitions.

Derives conductance distributions at critical points.

Discusses experimental implications for mesoscopic systems.

Abstract

We obtain a ``mean field'' scaling flow of the longitudinal and the Hall conductivities in the fractional quantum Hall regime. Using the composite fermion picture and assuming that the composite fermions follow the Khmelnitskii-Pruisken scaling flow for the integer quantum Hall effect, the unstable fixed points which govern the transitions between different fractional quantum Hall states are identified. Distributions of the critical longitudinal and Hall conductivities at the unstable fixed points are obtained and implications of the results for the experiments on mesoscopic quantum Hall systems are discussed.