Quantum Hall - insulator transitions in lattice models with strong disorder

TL;DR

This paper uses numerical simulations of a lattice model to explore how strong disorder affects the quantum Hall effect, revealing a universal pattern of transition to an insulator and connecting lattice results to continuum theories.

Contribution

It provides a detailed numerical analysis of quantum Hall-insulator transitions in disordered lattice models, highlighting the universal destruction pattern of current-carrying states.

Findings

Current carrying states are destroyed by increasing disorder, leading to an insulating phase.

A universal pattern describes the transition process across different disorder strengths.

The study connects lattice model results to continuum quantum Hall physics.

Abstract

We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field applied perpendicular to the lattice. We consider field magnitudes such that the area per flux quantum is commensurate with the lattice structure. Topological properties of the single electron wave functions are used to identify current carrying states that are responsible for the quantized Hall conductance. We study the interplay between the magnetic field and the disorder, and find a universal pattern with which the current carrying states are destroyed by increasing disorder strength, and the system driven into an insulating state. We also discuss how to interpolate results of lattice models to the continuum limit. The relationship to previous theoretical and experimental studies of quantum Hall-insulator transitions in strongly disordered systems at low magnetic fields is discussed.