Route towards Localization for Quantum Anomalous Hall Systems with Chern Number 2.

Zhi-Gang Song,Shu-Shen Li,Yan-Yang Zhang,Jun-Tao Song

doi:10.1038/srep19018

Abstract

The quantum anomalous Hall system with Chern number 2 can be destroyed by sufficiently strong disorder. During its process towards localization, it was found that the electronic states will be directly localized to an Anderson insulator (with Chern number 0), without an intermediate Hall plateau with Chern number 1. Here we investigate the topological origin of this phenomenon, by calculating the band structures and Chern numbers for disordered supercells. We find that on the route towards localization, there exists a hidden state with Chern number 1, but it is too short and too fluctuating to be practically observable. This intermediate state cannot be stabilized even after some “smart design” of the model and this should be a universal phenomena for insulators with high Chern numbers. By performing numerical scaling of conductances, we also plot the renormalization group flows for this transition, with Chern number 1 state as an unstable fixed point. This is distinct from known results, and can be tested by experiments and further theoretical analysis.

Highlights

As well as integer quantum Hall effect (QHE) under a magnetic field[1], the quantum anomalous Hall effect (QAHE) without an external magnetic field[2] is characterized by nonzero Chern number, a topological invariant associated with occupied bands[3,4]
Numerical calculations for a QHE with a high Chern number C > 1 show that, with the increasing of disorder strength, the Hall conductance σxy = C vanishes to 0 persistently without showing any intermediate Hall plateaus with Chern numbers C − 1, C − 2, 123–25, which are associated with stable fixed points and should be robust
After adjacent Landau levels are broadened enough to touch each other, their Chern numbers change from ± 1 to 0, which results in trivial localized bands

Summary

Introduction

As well as integer quantum Hall effect (QHE) under a magnetic field[1], the quantum anomalous Hall effect (QAHE) without an external magnetic field[2] is characterized by nonzero Chern number, a topological invariant associated with occupied bands[3,4]. The localization process with increasing disorder strength for a two-band model with C = 2 was investigated by transport calculations[32].

Results

Conclusion