Equilibrium currents in chiral systems with non-zero Chern number

TL;DR

This paper presents a simple quantum-mechanical method to calculate equilibrium edge currents in systems with non-zero Chern number, applicable to various topological and non-topological materials, without prior knowledge of their band topology.

Contribution

It introduces a unified approach to compute edge currents that treats topological and non-topological contributions equally, demonstrated on multiple physical systems.

Findings

Existence of topologically non-trivial edge currents in diverse systems

Method does not require prior band topology knowledge

Relation established between edge currents and orbital magnetization

Abstract

We describe simple quantum-mechanical approach to calculating equilibrium particle current along the edge of a system with non-trivial band spectrum topology. The approach does not require any a priori knowledge of the band topology and, as a matter of fact, treats topological and non-topological contributions to the edge currents on the same footing. We illustrate its usefulness by demonstrating the existence of `topologically non-trivial' particle currents along the edges of three different physical systems: two-dimensional electron gas with spin-orbit coupling and Zeeman magnetic field, surface state of a topological insulator, and kagome antiferromagnet with Dzyaloshinskii-Moriya interaction. We describe relation of our results to the notion of orbital magnetization.