Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems

TL;DR

This paper investigates how nonmagnetic disorder influences the quantum critical point in 3D $Z_2$ topological insulators, deriving phase diagrams and analyzing localization effects to understand the transition mechanisms.

Contribution

It provides a detailed phase diagram considering disorder effects and introduces a two-mode diffusion picture to explain the transition phenomena in 3D $Z_2$ quantum spin Hall systems.

Findings

Disorder modifies the phase diagram of 3D $Z_2$ insulators.

Identifies a two-mode diffusion process at the quantum critical point.

Discusses the microscopic origin of levitation and pair annihilation phenomena.

Abstract

In this paper, we studied the nonmagnetic disorder effects onto the quantum critical point (QCP) which intervenes an ordinary insulator and the 3-dimensional $Z_2$ quantum spin Hall insulator. The minimal model describing this QCP is the single-copy of the 3+1 Dirac fermion, whose topological mass $m$ induces the quantum phase transition. We derived the phase diagram spanned by this mass-term $m$, chemical potential $\mu$ and strength of the disorder within the self-consistent Born approximation. To infer the structure of the low-energy effective theory, we further calculated the weak localization (WL) correction to the conductivity. By way of this, we have found that the diffuson consists of the two quasi-degenerate contributions having the diffusion pole; one always behaves as the diffusion mode. The other becomes the massless mode only at $m=0$. Based on this "two-mode picture", we will discuss the possible microscopic picture of the "levitation and pair annihilation" phenomena, recently discovered by Onoda et al.