Disorder Effects in Topological States -- Brief Review of the Recent Developments

TL;DR

This review summarizes recent research on how disorder impacts topological states, highlighting their robustness, disorder-induced topological phases, and disorder-driven metal-insulator transitions.

Contribution

It provides a comprehensive overview of recent developments in understanding disorder effects in topological states, including new mechanisms and phase diagrams.

Findings

Topological states are robust against weak disorder.

Moderate disorder can induce topological phases from normal states.

Strong disorder leads to metal-insulator transitions with complex phase diagrams.

Abstract

Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding recent developments in several topics about disorder effects in topological states. For weak disorder, the robustness of topological states is demonstrated, especially for both quantum spin Hall states with $Z_2=1$ and size induced nontrivial topological insulators with $Z_2=0$. For moderate disorder, by increasing the randomness of both the impurity distribution and the impurity induced potential, the topological insulator states can be created from normal metallic or insulating states. These phenomena and their mechanisms are summarized. For strong disorder, the disorder causes a metal-insulator transition. Due to their topological nature, the phase diagrams are much richer in topological state systems. Finally, the trends in these areas of disorder research are discussed.