A Short Course on Topological Insulators: Band structure topology and edge states in one and two dimensions
This course based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk boundary correspondence with as simple mathematical tools as possible. We use noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one dimensional case (the Su Schrieffer Heeger model for polyacetylene) to two dimensional time reversal invariant topological insulators (the Bernevig Hughes Zhang model for HgTe) In each case the model is introduced first and then its properties are discussed and subsequently generalized. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self contained text, which is complemented by end of chapter problems.