Quantization of edge currents along magnetic interfaces: A K-theory approach

TL;DR

This paper explores the mathematical properties of topological edge currents along magnetic interfaces in 2D materials using K-theory, providing foundational insights for future complex magnetic system studies.

Contribution

It introduces a K-theoretical framework for analyzing edge currents along magnetic interfaces, including detailed cases of localized and Iwatsuka magnetic fields.

Findings

K-theoretical duality between bulk and interface

Analysis of localized magnetic fields

Study of Iwatsuka magnetic field case

Abstract

The purpose of this paper is to investigate the propagation of topological currents along magnetic interfaces (also known as magnetic walls) of a two-dimensional material. We consider tight-binding magnetic models associated to generic magnetic multi-interfaces and describe the K-theoretical setting in which a bulk-interface duality can be derived. Then, the (trivial) case of a localized magnetic field and the (non trivial) case of the Iwatsuka magnetic field are considered in full detail. This is a pedagogical preparatory work that aims to anticipate the study of more complicated multi-interface magnetic systems.