Analysis of Topological Material Surfaces

Abstract

We provide a systematic analysis of the boundary condition for the edge state, which is a ubiquitous feature in topological phases of matter. We show how to characterize the boundary condition, and how the edge state spectrum depends on it, with several exam- ples, including 2d topological insulator and 3d Weyl semimetal. We also demonstrate the edge-of-edge state localized at the intersection of boundaries.