Quantized bulk conductivity as a local Chern marker

Abstract

Chern insulators display a remarkable insensitivity to spatial disorder and imperfections. Despite this, the Chern number itself is defined in momentum space, and can only be calculated in a clean crystalline material. The authors propose here a spatial Chern marker defined on physical grounds -- as the local cross-conductivity around a chosen point in the bulk of the system. The formulation can be related to several other proposed local measures but has the advantage that it constitutes a physical observable of the system. Examples are probed, showing that it is quantized when calculated sufficiently far from the boundary and resistant against disorder.

Topics & Concepts