Mesoscopic transport in a Chern mosaic

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.