Disorder-Driven Collapse of the Mobility Gap and Transition to an Insulator in the Fractional Quantum Hall Effect

We study the $\nu =1/3$ quantum Hall state in the presence of random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to distinguish unambiguously between insulating and current carrying states in an interacting system. The mobility gap can be determined numerically this way and 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.