Higher-order bulk-boundary correspondence for topological crystalline phases

Understand

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.