Abstract This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene insulators. Amusingly, many these have connection contributions high-energy physics by Dirac. The review starts presentation Dirac magnetic monopole, goes on with Berry phase two-level system geometrical/topological for Bloch electrons cry...

Hermitian topological materials are characterized by the nontrivial relation between numbers and edge modes, i.e. bulk-boundary correspondence. In non-Hermitian systems, conventional correspondence breaks down. Instead, in Su-Schrieffer-Heeger model, non-Bloch correspondence, which is winding number skin effect, proposed S. Yao Z. Wang. We introduce polarization as a quantity to detect effect. ...