Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant

TL;DR

This paper investigates the robustness of topological phases in 3D topological insulators under strong disorder, showing that the Z2 invariant remains quantized despite the closing of the spectral gap, and maps the phase diagram accordingly.

Contribution

It introduces an efficient numerical method to compute the Z2 invariant in disordered systems and reveals the persistence of topological order under strong disorder.

Findings

Delocalized bulk states persist at high disorder levels.

The Z2 invariant remains quantized despite dense localized states.

Phase diagram of Bi2Se3 mapped as a function of disorder and Fermi level.

Abstract

We study the effect of strong disorder in a 3-dimensional topological insulators with time-reversal symmetry and broken inversion symmetry. Firstly, using level statistics analysis, we demonstrate the persistence of delocalized bulk states even at large disorder. The delocalized spectrum is seen to display the levitation and pair annihilation effect, indicating that the delocalized states continue to carry the Z2 invariant after the onset of disorder. Secondly, the Z2 invariant is computed via twisted boundary conditions using an efficient numerical algorithm. We demonstrate that the Z2 invariant remains quantized and non-fluctuating even after the spectral gap becomes filled with dense localized states. In fact, our results indicate that the Z2 invariant remains quantized until the mobility gap closes or until the Fermi level touches the mobility edges. Based on such data, we compute the phase diagram of the Bi2Se3 topological material as function of disorder strength and position of the Fermi level.