Subject: Topology in Electronic Structures
Topological insulators (TI) are a novel quantum state of matter that reveals the coexisting bulk bandgap and conducting surface states. As a tutorial for TI, this lecture consists of two parts with a general introduction. First, we introduce tight-binding models for a 1-dimensional chain and 2-dimensional honeycomb lattice to understand the basic electronic band structure. For the second part, two representative examples of topologically non-trivial insulators are presented based on the tight-binding models. The 1-dimensional chain and 2-dimensional honeycomb lattice are links to the Su-Schrieffer-Heeger model and Kane-Mele model, respectively, which host various exotic topological phases.