Quantum transport and two-parameter scaling at the surface of a weak topological insulator

TL;DR

This paper demonstrates that the surface states of weak topological insulators remain metallic under disorder unless a time-reversal symmetric mass term is introduced, revealing a two-parameter scaling behavior in their transport properties.

Contribution

It shows that disorder alone does not localize weak topological insulator surfaces and introduces a two-parameter scaling framework when a mass term is present.

Findings

Surface states remain metallic without a mass term.

Transport follows one-parameter scaling in the absence of mass.

Two-parameter scaling emerges with a mass term.

Abstract

Weak topological insulators have an even number of Dirac cones in their surface spectrum and are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states, rather; the presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form.