Theory of the topological Anderson insulator

TL;DR

This paper develops an effective medium theory explaining how disorder can induce a topological insulator phase in materials like HgTe quantum wells, highlighting a generic mechanism applicable to 3D semiconductors with strong spin-orbit coupling.

Contribution

It introduces a theoretical framework that explains the disorder-driven transition into a topological insulator phase, emphasizing the role of band edge crossing over mobility edges.

Findings

Disorder can induce a topological phase transition in quantum wells.

The phase boundary is determined by band edge crossing, not mobility edge.

The mechanism is applicable to 3D semiconductors with strong spin-orbit coupling.

Abstract

We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic corrections proportional to p^2 sigma_z to the Dirac Hamiltonian that can drive an ordinary band insulator into a topological insulator (having an inverted band gap). We calculate the location of the phase boundary at weak disorder and show that it corresponds to the crossing of a band edge rather than a mobility edge. Our mechanism for the formation of a topological Anderson insulator is generic, and would apply as well to three-dimensional semiconductors with strong spin-orbit coupling.