A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions

Understand

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.