The strong side of weak topological insulators

TL;DR

This paper reveals that weak topological insulators have surface states protected from non-breaking time-reversal symmetric perturbations, maintaining metallic conductivity even under strong disorder, highlighting their robustness and anisotropic nature.

Contribution

It demonstrates that weak topological insulators' surface states are protected from certain perturbations, challenging previous notions of their fragility and emphasizing their robustness and anisotropy.

Findings

Surface states remain metallic under strong disorder.

Weak TIs are protected from time-reversal symmetric perturbations.

Anisotropy characterizes the difference from strong TIs.

Abstract

Three-dimensional topological insulators are classified into "strong" (STI) and "weak" (WTI) according to the nature of their surface states. While the surface states of the STI are topologically protected from localization, this does not hold for the WTI. In this work we show that the surface states of the WTI are actually protected from any random perturbation that does not break time-reversal symmetry, and does not close the bulk energy gap. Consequently, the conductivity of metallic surfaces in the clean system remains finite even in the presence of strong disorder of this type. In the weak disorder limit the surfaces are found to be perfect metals, and strong surface disorder only acts to push the metallic surfaces inwards. We find that the WTI differs from the STI primarily in its anisotropy, and that the anisotropy is not a sign of its weakness but rather of its richness.