Wire Construction of Topological Crystalline Superconductors

Abstract

We present a unified framework to construct and classify topological crystalline superconductors (TCSCs). The building blocks are one-dimensional topological superconductors (TSCs) protected solely by onsite symmetries, which are arranged and glued by crystalline symmetries in real space. We call this real-space scheme "wire construction", and we show its procedure can be formulated mathematically. For illustration, we treat TCSCs of Altland-Zirnbauer (AZ) class[1] DIII protected by wallpaper group as well as layer group symmetries, with the resulting states by wire construction being TCSCs in two-dimension. We also discuss how these real-space TCSCs by wire construction are characterized by anomalous boundary states. Our method provides a real-space picture for TCSCs versus momentum-space pictures.