Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect

TL;DR

This paper investigates how increasing disorder in the fractional quantum Hall state at nu=1/3 causes the mobility gap to collapse, leading to a transition from a conducting to an insulating phase, with results aligning with experimental data.

Contribution

It introduces a numerical method using the Chern number to distinguish insulating and conducting states in disordered fractional quantum Hall systems and characterizes the disorder-driven phase transition.

Findings

Mobility gap narrows with increasing disorder.

Critical disorder strength causes the gap and plateau to collapse.

Results agree semi-quantitatively with experimental observations.

Abstract

We study the nu=1/3 quantum Hall state in presence of the random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to unambiguously distinguish between insulating and current carrying states in an interacting system. The mobility gap can be determined numerically this way, which is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the mobility gap and plateau width narrow continuously and ultimately collapse leading to an insulating phase.