Levitation and percolation in quantum Hall systems with correlated disorder

TL;DR

This paper studies how correlated disorder affects the quantum Hall effect in a 2D lattice, revealing percolating current paths and a floating feature in Hall conductance related to experimental observations.

Contribution

It introduces a method to analyze the Chern number in correlated disordered systems and links the percolation of extended states to topological edge states.

Findings

Extended states form percolating paths at Landau band centers

Floating feature observed in Hall conductance with increasing disorder

Topological equivalence of percolating paths to edge states

Abstract

We investigate the integer quantum Hall system in a two dimensional lattice model with spatially correlated disorder by using the efficient method to calculate the Chern number proposed by Fukui \textit{et al}. Distribution of charge density indicates that the extended states at the center of each Landau band have percolating current paths, which are topologically equivalent to the edge states that exist in a system with boundaries. As increasing the strength of disorder, floating feature is observed in an averaged Hall conductance as a function of filling factor. Its relation to the observed experiments is also discussed.