David VanderbiltCambridge University Press, 11/1/2018EAN 9781107157651, ISBN10: 110715765XHardcover, 394 pages, 25.4 x 17.8 x 1.9 cmLanguage: EnglishOriginally published in EnglishOver 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.PrefaceAcronymsIntroduction1. Invariance and quantization of charges and currents2. Review of electronic structure theory3. Berry phases and curvatures4. Electric polarization5. Topological insulators and semimetals6. Orbital magnetization and axion magnetoelectric couplingAppendix A. Fourier transform conventionsAppendix B. Optimal alignment and the singular value decompositionAppendix C. Gauge transformation of the Chern–Simons axion couplingAppendix D. The PythTB packageReferencesIndex.
