Topological Euler insulators and metals on triangular lattices

Abstract The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied. Differently from two-band Chern insulators, a topological Euler insulator is a kind of three-band model, described by the Euler number not the Chern number. The spin textures of a topological Euler insulator in the momentum space is like a Néel-type skyrmion. It is found that the topological edge states exist in the band gap of the topological Euler insulator, and the topological Euler insulator can be transformed into a topological metal without the topological phase transition.