Interface currents and corner states in magnetic quarter-plane systems

TL;DR

This paper investigates quantized interface currents and topologically protected corner states in magnetic systems with a quarter-plane geometry, using tight-binding models and K-theory to establish their topological nature.

Contribution

It introduces a topological framework for understanding quantized interface currents and corner states in magnetic quarter-plane systems, linking them to bulk invariants.

Findings

Interface currents are quantized and determined by bulk topological invariants.

Necessary conditions for the existence of corner states are identified.

Corner states possess topologically protected asymptotic invariants.

Abstract

We study the propagation of currents along the interface of two $2$-$d$ magnetic systems, where one of them occupies the first quadrant of the plane. By considering the tight-binding approximation model and K-theory, we prove that, for an integer number that is given by the difference of two bulk topological invariants of each individual system, such interface currents are quantized. We further state the necessary conditions to produce corner states for these kinds of underlying systems, and we show that they have topologically protected asymptotic invariants.