Classification of topological invariants related to corner states

TL;DR

This paper develops a periodic table of topological invariants for corner states in higher-order topological insulators, linking bulk properties to corner phenomena through mathematical and computational methods.

Contribution

It introduces a systematic classification framework for topological invariants associated with corner states, including definitions, proofs, computations, and explicit examples.

Findings

Established a periodic table for topological invariants

Proved the relation between invariants and corner states

Constructed explicit models demonstrating the invariants

Abstract

We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four things: (1) the definition of topological invariants, (2) a proof of their relation with corner states (3) computations of K-groups and (4) a construction of explicit examples.