Topological invariant in three-dimensional band insulators with disorder

TL;DR

This paper investigates the topological invariant in disordered 3D insulators, demonstrating the emergence of a strong topological phase in trivial insulators with disorder, and characterizing phase boundaries through numerical and analytical methods.

Contribution

It introduces a method to study topological invariants in disordered systems by modeling them as super-cells, revealing the disorder-induced topological phase transition.

Findings

Disorder can induce a strong topological phase in trivial insulators.

The phase boundaries match predictions from SCBA and transport calculations.

The strong index remains robust in the presence of disorder.

Abstract

Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the topological invariant in disordered three-dimensional system by viewing it as a super-cell of an infinite periodic system. As an application of this method we show that the strong index becomes non-trivial when strong enough disorder is introduced into a trivial insulator with spin-orbit coupling, realizing a strong topological Anderson insulator. We also numerically extract the gap range and determine the phase boundaries of this topological phase, which ?ts well with those obtained from self-consistent Born approximation (SCBA) and the transport calculations.