Finance

Combinatorics

Physics

Topology (electrical circuits)

Point reflection

Gapless playback

Symmetry (geometry)

Mathematics

Topological order

Topological insulator

Order (exchange)

Economics

Geometry

Condensed matter physics

Superconductivity

Quantum mechanics

Homogeneous space

Quantum

Physical review. B./Physical review. B

Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys.\ Rev.\ B {\bf 90}, 165114 (2014)], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all corresponding second-order topological insulators and superconductors. The classification also includes antiunitary symmetries and antisymmetries.

Second-order topological insulators and superconductors with an order-two crystalline symmetry