Anderson localization in a two-dimensional random gap model

TL;DR

This paper investigates Anderson localization in a 2D disordered lattice, demonstrating a transition from delocalized to localized states and showing that suppressed backscattering does not prevent localization in topological insulators.

Contribution

It provides a transfer-matrix analysis of localization transition and proves the existence of an Anderson localized phase in a 2D topological insulator model.

Findings

Transition from delocalized to localized states at critical disorder strength

Existence of an Anderson localized phase with exponential decay

Suppressed backscattering does not prevent localization

Abstract

We study the properties of the spinor wavefunction in a strongly disordered environment on a two-dimensional lattice. By employing a transfer-matrix calculation we find that there is a transition from delocalized to localized states at a critical value of the disorder strength. We prove that there exists an Anderson localized phase with exponentially decaying correlations for sufficiently strong scattering. Our results indicate that suppressed backscattering is not sufficient to prevent Anderson localization of surface states in topological insulators.