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arXiv · 1509.02295

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

János K. Asbóth·László Oroszlány·András Pályi
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Abstract

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.

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János K. Asbóth, László Oroszlány, András Pályi. 2015-09-08. A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions. https://doi.org/10.1007/978-3-319-25607-8

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