Traveling edge states in massive Dirac equations along slowly varying edges

TL;DR

This paper analyzes edge states in massive Dirac equations with slowly varying edges, providing asymptotic solutions for traveling edge states along curved edges, highlighting their localized and unidirectional properties.

Contribution

It introduces a novel analytical approach to characterize traveling edge states along curved edges in Dirac equations with domain wall masses.

Findings

Asymptotic solutions for edge states along circular and curved edges

Edge states exhibit localized, unidirectional propagation

Curvature effects are quantitatively characterized

Abstract

Topologically protected wave motion has attracted considerable interest due to its novel properties and potential applications in many different fields. In this work, we study edge modes and traveling edge states via the linear Dirac equations with so-called domain wall masses. The unidirectional edge state provides a heuristic approach to more general traveling edge states through the localized behavior along slowly varying edges. We show the leading asymptotic solutions of two typical edge states that follow the circular and curved edges with small curvature by analytic and quantitative arguments.