Edge states for second order elliptic operators

Abstract

We present a general framework to study edge states for second order elliptic operators. We associate an integer valued index to some bulk materials, and we prove that for any junction between two such materials, localised states must appear at the boundary whenever the indices differ.

Spectral properties of periodic systems cut at an angle

“…It turns out that the essential spectrum of H ♯ k (t) is independent of t ∈ R, see e.g. [HK11b,Gon21]. This comes from the fact that the essential spectrum describes modes that escape to infinity, and that, far from the boundary, these modes only feel the bulk operator.…”