Wire Construction of Topological Crystalline Superconductors

TL;DR

This paper introduces a real-space wire construction framework to classify and understand topological crystalline superconductors, linking real-space arrangements with boundary state phenomena.

Contribution

It develops a unified, mathematically formulated wire construction method for TCSCs, connecting real-space symmetry arrangements with topological classifications.

Findings

Constructed 2D TCSCs from 1D building blocks using crystalline symmetries.

Provided a real-space perspective complementing momentum-space approaches.

Characterized boundary states of TCSCs through the wire construction method.

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.