Berry Phases in Electronic Structure Theory
Electric Polarization, Orbital Magnetization and Topological Insulators

An introduction to the role of Berry phases in our modern understanding of the physics of electrons in solids.

David Vanderbilt (Author)

9781107157651, Cambridge University Press

Hardback, published 1 November 2018

394 pages, 100 b/w illus.
25.4 x 17.8 x 2.3 cm, 0.95 kg

'… I would like to recommend this book to crystallographers, and more generally to condensed-matter physicists who wish to learn about the physics of Berry phases. The pedagogical presentation used throughout will allow careful readers to start working on the more detailed literature with a solid basis and a clear view of recent results.' Laurent Chaput, Acta Crystallographica

Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.

Preface
Acronyms
Introduction
1. Invariance and quantization of charges and currents
2. Review of electronic structure theory
3. Berry phases and curvatures
4. Electric polarization
5. Topological insulators and semimetals
6. Orbital magnetization and axion magnetoelectric coupling
Appendix A. Fourier transform conventions
Appendix B. Optimal alignment and the singular value decomposition
Appendix C. Gauge transformation of the Chern–Simons axion coupling
Appendix D. The PythTB package
References
Index.

Subject Areas: Mathematical physics [PHU], Condensed matter physics [liquid state & solid state physics PHFC], Physics [PH]