Topological insulators /

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"Version: 20190401"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references and index.1. Symmetries and effective Hamiltonians -- 1.1. Crash course on symmetry transformations -- 1.2. Effective Hamiltonians for bulk III-V semiconductors -- 1.3. Hands-on : symmetry analysis of a triple quantum dot2. Electron-coupling to external fields and transport theory -- 2.1. Electromagnetic potentials, fields and currents -- 2.2. Minimal coupling and electric charge conservation law -- 2.3. Charge current in lattice systems -- 2.4. Linear response and current-current correlation functions -- 2.5. Matsubara technique and thermal Green functions -- 2.6. Matsubara formulation of linear response -- 2.7. Charge conductivity of an electron gas -- 2.8. Thermoelectric and thermal transport -- 2.9. Hands-on : magnetoconductivity tensor of a triangular triple quantum dot -- 2.10. Hands-on : Boltzmann transport equation3. Jackiw-Rebbi model and Goldstone-Wilczek formula -- 3.1. Helical electrons in nanowires : emergent Jackiw-Rebbi model -- 3.2. Zero-energy solutions in the Jackiw-Rebbi model -- 3.3. The Jackiw-Rebbi model in condensed matter physics -- 3.4. Goldstone-Wilczek formula and dissipationless current -- 3.5. Hands-on : derivation of the Goldstone-Wilczek formula for a sliding charge density wave conductor4. Topological insulators in 1+1 dimensions -- 4.1. Prototypical topological-insulator model in 1+1 dimensions -- 4.2. Lattice topological-insulator model and higher winding numbers -- 4.3. Adiabatic transport : Thouless pump and Berry curvature -- 4.4. Berry phase -- 4.5. Hands-on : winding number in a 3+1d model -- 4.6. Hands-on : current and electric polarisation formula -- 4.7. Hands-on : violation of chiral symmetry and electric polarisation5. Chern insulators--fundamentals -- 5.1. Jackiw-Rebbi model and Dirac physics in 2 + 1d -- 5.2. Chern insulator in 2 + 1d -- 5.3. Quantised Hall conductance and Chern number--bulk approach -- 5.4. Chern insulators in higher dimensions -- 5.5. Dimensional reduction : chiral anomaly -- 5.6. Hands-on : Chern-Simons action -- 5.7. Hands-on : Chern number for interacting systems -- 5.8. Hands-on : second Chern number6. Chern insulators--applications -- 6.1. Dynamical anomalous Hall response and polar Kerr effect -- 6.2. Chern insulators in an external magnetic field -- 6.3. Anomalous thermoelectric and thermal Hall transport -- 6.4. Hands-on : magnetic-field-induced Chern systems -- 6.5. Hands-on : thermoelectric transport in the Haldane model7. Z2 topological insulators -- 7.1. Z2 topological insulators in 2 + 1 dimensions -- 7.2. Z2 topological insulators in 3 + 1 dimensions -- 7.3. Dimensional reduction from a 4 + 1d Chern insulator and magnetoelectric coupling -- 7.4. Hands-on : quasiparticle interference on the topological surface -- 7.5. Hands-on : topological Kondo insulator8. Topological classification of insulators and beyond -- 8.1. Generalised antinunitary symmetries and symmetry classes -- 8.2. The art of topological classification -- 8.3. Topological classification of gapless systems -- 8.4. Topological classification of insulators and defects -- 8.5. Topological superconductors and Majorana fermions -- 8.6. Further topics and outlook -- 8.7. Hands-on : Berry magnetic monopoles in hole-like semiconductors -- 8.8. Hands-on : Floquet topological insulator.This book provides an introduction to topological matter with a focus on insulating bulk systems. A number of prerequisite concepts and tools are first laid out, including the notion of symmetry transformations, the band theory of semiconductors and aspects of electronic transport. The main part of the book discusses realistic models for both time-reversal-preserving and -violating topological insulators, as well as their characteristic responses to external perturbations. Special emphasis is given to the study of the anomalous electric, thermal, and thermoelectric transport properties, the theory of orbital magnetisation, and the polar Kerr effect. The topological models studied throughout this book become unified and generalised by means of the tenfold topological-classification framework and the respective systematic construction of topological invariants. This approach is further extended to topological superconductors and topological semimetals. This book covers a wide range of topics and aims at the transparent presentation of the technical aspects involved. For this purpose, homework problems are also provided in dedicated Hands-on sections. Given its structure and the required background level of the reader, this book is particularly recommended for graduate students or researchers who are new to the field.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Dr. Panagiotis Kotetes recently started as an Associate Professor at the Institute of Theoretical Physics of the Chinese Academy of Sciences in Beijing. During 2015-2018 he was a postdoctoral researcher at the Niels Bohr Institute of the University of Copenhagen. Right before that, he carried out a five-year-long postdoctoral appointment at the Karlsruhe Institute of Technology. Panagiotis completed his Diploma, Masters and PhD studies at the National Technical University of Athens in Greece. His research interests and activity cover topics such as topological systems, unconventional superconductivity, exotic magnetism, and quantum computing.Title from PDF title page (viewed on May 6, 2019).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9781681745176

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530.4/1

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Subject(s)

SCIENCE / Nanoscience.
Nanotechnology.
Energy-band theory of solids.
Superconductivity.
Topological dynamics.

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Panagiotis Kotetes.

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