Conformal maps and edge mode attenuation on imperfect boundaries

TL;DR

This paper introduces a conformal mapping method to analyze how edge modes decay along imperfect boundaries, providing insights into their robustness and potential applications in 2+1 dimensional systems.

Contribution

The authors develop a conformal map technique to study edge mode attenuation on imperfect boundaries, offering a new analytical approach for such problems.

Findings

Conformal maps can straighten boundaries, simplifying edge mode analysis.

Edge modes can be robust against damping under certain conditions.

The method applies to 2+1 dimensional edge-mode problems.

Abstract

We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the boundary, simplifying the boundary conditions. Using the example of edge modes in a simple field-theoretical model, we examined scattering into the bulk and identified conditions that ensure the robustness of edge modes against damping. This technique has the potential to be applied to other edge-mode problems in 2+1 dimensions.