Higher-order topological insulators and superconductors protected by inversion symmetry

Here, higher-order topological insulators and superconductors protected by inversion symmetry are investigated. These phases are characterized by gapped bulk and surface with gapless modes confined to hinges or corners of the sample. Such surface states can be understood as topological defects that are globally stabilized by inversion. They can be built using a layer construction that embeds a standard topological insulator/superconductor into a higher dimension by symmetrically adding to it copies of itself. Using this procedure, a complete classification of such states in any dimension is obtained and several examples for possible physical realizations are provided.