Algebraic and Geometric Mean Density of States in Topological Anderson Insulators

TL;DR

This paper investigates how algebraic and geometric mean densities of states can identify topological phases in disordered systems, revealing that disorder can induce topological Anderson insulators from trivial or nontrivial insulators.

Contribution

It introduces a method using density of states ratios to distinguish topological phases in disordered two-dimensional systems, including the disorder-induced topological Anderson insulators.

Findings

Topological phase characterized by quantized conductance and helical edge states.

Disorder can induce topological Anderson insulators from trivial or nontrivial phases.

Density of states ratio distinguishes topological phases in disordered systems.

Abstract

Algebraic and geometric mean density of states in disordered systems may reveal properties of electronic localization. In order to understand the topological phases with disorder in two dimensions, we present the calculated density of states for disordered Bernevig-Hughes-Zhang model. The topological phase is characterized by a perfectly quantized conducting plateau, carried by helical edge states, in a two-terminal setup. In the presence of disorder, the bulk of the topological phase is either a band insulator or an Anderson insulator. Both of them can protect edge states from backscattering. The topological phases are explicitly distinguished as topological band insulator or topological Anderson insulator from the ratio of the algebraic mean density of states to the geometric mean density of states. The calculation reveals that topological Anderson insulator can be induced by disorders from either a topologically trivial band insulator or a topologically nontrivial band insulator.