Higher‐Order Topological Band Structures

The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these “higher‐order” boundary states comes from topology, with constraints imposed by symmetry. Herein, the bulk–boundary correspondence of topological crystalline band structures, which relates the topology of the bulk band structure to the pattern of the boundary states, is reviewed. Furthermore, recent advances in the K‐theoretic classification of topological crystalline band structures are discussed.