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A Short Course on Topological Insulators

Band Structure and Edge States in One and Two Dimensions

  • Book
  • © 2016

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Authors:
  1. János K. Asbóth

    1. Hungarian Academy of Sciences, Wigner Research Centre for Physics, Budapest, Hungary

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  2. László Oroszlány

    1. Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary

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  3. András Pályi

    1. Dept of Mat. Phy; Dept of Physics, Bud. Univ of Tech and Econ; Eotvos Loran, Budapest, Hungary

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  • Self-contained, course-based presentation
  • Authored by leading specialists in the field
  • Suitable both as advanced textbook and as self-study guide

Part of the book series: Lecture Notes in Physics (LNP, volume 919)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Su-Schrieffer-Heeger (SSH) Model

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 1-22

  3. Berry Phase, Chern Number

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 23-44

  4. Polarization and Berry Phase

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 45-53

  5. Adiabatic Charge Pumping, Rice-Mele Model

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 55-68

  6. Current Operator and Particle Pumping

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 69-83

  7. Two-Dimensional Chern Insulators: The Qi-Wu-Zhang Model

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 85-98

  8. Continuum Model of Localized States at a Domain Wall

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 99-117

  9. Time-Reversal Symmetric Two-Dimensional Topological Insulators: The Bernevig–Hughes–Zhang Model

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 119-138

  10. The \(\mathbb{Z}_{2}\) Invariant of Two-Dimensional Topological Insulators

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 139-152

  11. Electrical Conduction of Edge States

    • János K. Asbóth, László Oroszlány, András Pályi
    Pages 153-163

  12. Back Matter

    Pages 165-166
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Keywords

About this book

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 insulators.

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. 

The present approach uses 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 discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators.

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-containedtext, which is complemented by end-of-chapter problems.

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Authors and Affiliations

  • Hungarian Academy of Sciences, Wigner Research Centre for Physics, Budapest, Hungary

    János K. Asbóth

  • Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary

    László Oroszlány

  • Dept of Mat. Phy; Dept of Physics, Bud. Univ of Tech and Econ; Eotvos Loran, Budapest, Hungary

    András Pályi

About the authors

   

Bibliographic Information

  • Book Title: A Short Course on Topological Insulators

  • Book Subtitle: Band Structure and Edge States in One and Two Dimensions

  • Authors: János K. Asbóth, László Oroszlány, András Pályi

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/978-3-319-25607-8

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Softcover ISBN: 978-3-319-25605-4Published: 23 February 2016

  • eBook ISBN: 978-3-319-25607-8Published: 22 February 2016

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: XIII, 166

  • Number of Illustrations: 21 b/w illustrations, 23 illustrations in colour

  • Topics: Solid State Physics, Mathematical Methods in Physics, Magnetism, Magnetic Materials, Semiconductors

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