Higher-order bulk-boundary correspondence for topological crystalline phases

TL;DR

This paper develops a comprehensive framework for understanding the bulk-boundary correspondence in topological crystalline phases, including higher-order topological phases, using subgroup sequences of classifying groups.

Contribution

It introduces a novel formulation of bulk-boundary correspondence that accounts for higher-order phases and symmetries, expanding the classification of topological states.

Findings

Complete classification of higher-order topological phases with order-two symmetries

Unified description of boundary states and bulk topological invariants

Inclusion of phases without protected boundary states

Abstract

We study the bulk-boundary correspondence for topological crystalline phases, where the crystalline symmetry is an order-two (anti)symmetry, unitary or antiunitary. We obtain a formulation of the bulk-boundary correspondence in terms of a subgroup sequence of the bulk classifying groups, which uniquely determines the topological classification of the boundary states. This formulation naturally includes higher-order topological phases as well as topologically nontrivial bulk systems without topologically protected boundary states. The complete bulk and boundary classification of higher-order topological phases with an additional order-two symmetry or antisymmetry is contained in this work.