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Berry Phases in Electronic Structure Theory

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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.

Online resources include a PythTB code package which is used for computational examples and exercises

Explores in detail the methods that lie at the heart of modern notions about topological insulators

The self-contained approach enables less experienced students to learn the essential concepts

Author: Vanderbilt David
Publisher: CAMBRIDGE UNIVERSITY PRESS
Pages: 394
ISBN: 9781107157651
Cover: Hardback
Edition Number: 1
Release Year: 2018

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.

David Vanderbilt is Board of Governors Professor of Physics at Rutgers University, New Jersey, where he has made significant contributions to computational condensed matter physics. He is a Fellow of the American Physical Society and a member of the National Academy of Sciences, and was awarded the prestigious Rahman Prize in Computational Physics of the American Physical Society in 2006.

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