Topological band theory
Zhixiong Li, Yunshan Cao, Peng Yan · 2023
In this chapter, we give a brief introduction to topological band theory. First, we present detailed derivation about several typical topological invariants, such as Berry phase and Chern number, which are useful to describe the first-order topological insulating phases. Then we give the definition of bulk polarization and ZN Berry phase which represent the important topological invariants for characterizing higher-order topological insulators. Finally, we focus on the pedagogical topological models including the Su–Schrieffer–Heeger model and the Haldane model. In these two models, the band structure, the wave-function distribution, and topological stability of edge states are discussed.