Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch

TL;DR

This paper explores quantum transport in quantum anomalous Hall bilayers with lattice mismatch, revealing complex phase boundaries, resonant tunneling, and in-gap bulk states influenced by lattice parameters and disorder.

Contribution

It introduces a theoretical framework for understanding transport in mismatched bilayers, highlighting fractal phase boundaries and mismatch-induced in-gap bulk states.

Findings

Resonant tunneling occurs at lattice-matched conditions.

Quantized conductance plateau persists with lattice mismatch due to Chern numbers.

Fractal transitional regions contain extended in-gap bulk states sensitive to disorder.

Abstract

We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in two layers), the inter-layer coupling results in resonant traversing between forward propagating waves in two layers. In the case of generic ratios, there is a quantized conductance plateau originated from two Chern numbers associated with two layers. However, the phase boundary of this quantization plateau consists of a fractal transitional region (instead of a clear transition line) of interpenetrating edge states (with quantized conductance) and bulk states (with unquantized conductance). We attribute these bulk states as mismatch induced in-gap bulk states. Different from in-gap localized states induced by random disorder, these in-gap bulk states are extended in the limit of vanishing random disorder. However, the detailed fine structure of this transitional region is sensitive to disorder, lattice structure, sample size, and even the configuration of leads connecting to it, due to the bulk and topologically trivial nature of these in-gap bulk states.