A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
By János K. Asbóth, L. Oroszl'any, A. P'alyi. 2015
1,158 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/6be38738fef09b171eff85b107a4b6f19ce37fb6
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Quantum Electrodynamics in a Topological Waveguide (2020, methodology): “For a finite system, it is well known that edge states localized on the boundary of the waveguide at a ω 1⁄4 ω0 only appear in the case of δ < 0, the so-called topological phase [3,9].”
- Topological characterization of chiral models through their long time dynamics (2017, background): “, acting only within a single unit cell), unitary and Hermitian operator Γ (so that Γ(2) = I) which anticommutes with the Hamiltonian [2, 34], ΓHΓ = −H.”