Mesoscopic transport in a Chern mosaic

TL;DR

This paper studies electronic transport in a patterned topological material with domains of varying Chern numbers, revealing diverse resistance behaviors and providing computational tools for experimental analysis.

Contribution

It introduces a semi-classical method to analyze mesoscopic transport in Chern mosaics with different domain configurations, aiding experimental understanding.

Findings

Simple domain patterns can produce zero, integer, or fractional quantum resistance.

The analysis applies to moiré heterostructures with local Chern number variations.

The method offers a comparative catalog for experiments in 2D topological materials.

Abstract

We analyze mesoscopic electronic transport in a Chern mosaic: a regular pattern of domains whose electronic bands carry differing local Chern numbers. An example platform where a Chern mosaic can arise is a moir\'e heterostructure, where variations in the local moir\'e parameters can produce such domains. We compute resistances at linear response for a variety of domain wall network geometries at zero temperature and magnetic field. Simple domain configurations can exhibit zero, integer, or fractional multiples of the quantum of resistance in both the longitudinal and transverse (Hall) responses. Our simple semi-classical analysis provides a useful computational method and comparative catalog for ongoing experiments in two-dimensional topological materials.