Edge-following topological states

TL;DR

This paper proves that Chern insulators possess topologically protected edge states capable of navigating around corners and imperfections, demonstrating their robustness through the lens of index theory in operator algebras.

Contribution

It establishes a rigorous mathematical proof that topological edge states in Chern insulators can traverse complex boundary geometries, extending understanding of their robustness.

Findings

Edge states propagate unidirectionally along straight boundaries.

Edge states can navigate corners and imperfections without losing topological protection.

Mathematical proof uses index theory of semigroup operator algebras.

Abstract

We prove that Chern insulators have topologically protected edge states which not only propagate unidirectionally along a straight line boundary, but also swerve around arbitrary-angled corners and geometric imperfections of the material boundary. This is a physical manifestation of the index theory of certain semigroup operator algebras.