Study of Scaling in the Fractional Quantum Hall Effect

TL;DR

This paper investigates how magnetic flux disorder affects localization in the fractional quantum Hall effect, finding that the critical behavior remains unchanged under certain conditions, implying a shared universality class with integer quantum Hall transitions.

Contribution

It demonstrates that flux disorder does not alter the localization length divergence exponent in the fractional quantum Hall regime, indicating the same universality class as integer quantum Hall transitions.

Findings

The localization length exponent remains unchanged with flux disorder.

Transitions between fractional and integer quantum Hall states share the same universality class.

Flux disorder does not significantly affect the critical properties of the system.

Abstract

In the composite fermion model of the fractional quantum Hall effect, composite fermions experience, in addition to the usual potential disorder, also a magnetic flux disorder. Motivated by this, we investigate the localization properties of a single fermion in two dimensions, moving in the presence of both potential and magnetic flux disorders, but with a non-zero average magnetic field. It is found that the exponent characterizing the divergence of the localization length is not changed upon the addition of the flux disorder, provided it is not too large, suggesting that the transitions between fractionally quantized Hall plateaus belong to the same universality class as those between the integrally quantized ones.