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- Cambridge University Press
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- 100 b/w illus.
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Berry Phases in Electronic Structure Theory
Electric Polarization, Orbital Magnetization and Topological Insulators
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'This book brings together almost forty years of progress in understanding how the wavefunctions of electrons in a crystal, and in particular their continuous evolution with momentum, determine important physical properties. David Vanderbilt is one of the creators of this field, and nearly every chapter includes topics where his contributions were decisive. In addition to its scope, one way in which this book differs from others on related topics is the clear path from physical insight, through theoretical understanding, to practical methods for specific materials. This book can be read profitably by those interested in the fundamental theory of topological phases as well as those seeking to understand modern electronic structure approaches.' Joel Moore, Chern-Simons Professor of Physics, University of California, Berkeley
'The geometric phase and related concepts provide a unified framework for describing many fundamental properties of electrons in solids, from electric polarization to quantized effects in topological materials. Readers wishing to become familiar with these notions will find David Vanderbilt's excellent book to be an invaluable resource.' Ivo Souza, University of the Basque Country, San Sebastin
'Berry phases and associated geometric and topological concepts have transformed our understanding of electronic properties. This book provides a much needed pedagogical exposition with computational instructions which will be very valuable for students and researchers in solid state physics and materials science.' Qian Niu, University of Texas
'David Vanderbilt explicates a new exciting frontier in solid state physics and materials theory, and does so in a clear and interesting to read way. Not only does he cover every nook and cranny of this new area, but in the process clearly explains the basics of electronic structure theory, such as density functional theory (DFT) and tight-binding, that will be extremely useful and important to any student of condensed matter theory. The subject of the book is how the phases of the wave functions, neglected for decades, affect important measurable properties of materials. He covers everything from the mathematical theory of geometric phases, applications to polarization and orbital magnetism, all the way to complex applications such as three-dimensional topological insulators and beyond. To be able to write about such seemingly esoteric matters in such a clear and gripping way is the mark of a great teacher. I look forward to my second reading of the book!' Ronald Cohen, Extreme Materials Initiative, Geophysical Laboratory, Carnegie Institution for Science
'For anyone who wants to learn about Berry phases in electronic structure and the exciting recent developments in topological insulators, I heartily recommend this book. David Vanderbilt is uniquely poised to present the concepts and practical developments in this field that has revolutionized our understanding of co...
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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.
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.