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.
Author(s): David Vanderbilt
Edition: 1
Publisher: Cambridge University Press
Year: 2018
Language: English
Pages: 395
Cover......Page 1
Front Matter
......Page 2
BERRY PHASES IN ELECTRONIC
STRUCTURE THEORY......Page 4
Copyright
......Page 5
Contents
......Page 6
Preface......Page 8
Acronyms......Page 11
Introduction......Page 12
1 Invariance and Quantization of Charges
and Currents......Page 16
2 Review of Electronic Structure Theory......Page 49
3 Berry Phases and Curvatures......Page 86
4 Electric Polarization......Page 152
5 Topological Insulators and Semimetals......Page 212
6 Orbital Magnetization and Axion Coupling......Page 287
Appendix A. Fourier Transform Conventions
......Page 327
Appendix B.
Optimal Alignment and the Singular Value
Decomposition......Page 330
Appendix C.
Gauge Transformation of the Chern–Simons
Axion Coupling......Page 332
Appendix D.
The PythTB Package......Page 338
References
......Page 374
Index......Page 385
