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.
An introduction to the role of Berry phases in our modern understanding of the physics of electrons in solids.
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.
'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 Sebastián
'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
condensed matter. He has made some of the most important advances
in electronic structure theory in the last twenty years, including
the original work that has made Berry phases a central part the
field, and he is known for lucid presentations. In this book
Vanderbilt introduces the concepts in a way that is accessible to a
nonexpert, with clear explanations and instructive examples, and
yet he presents the material in the depth that it deserves. I
recommend this book for anyone who wants to be a part of condensed
matter theory in the twenty-first century or just to appreciate the
basic ideas and phenomena of this exciting field.' Richard M.
Martin, University of Illinois, Urbana Champaign
'This is a well-structured book which will serve admirably as a
text for advanced students as well as a means for more mature
readers to gain an appreciation of the recent developments in this
area of activity.' K. Alan Shore, Contemporary Physics
'Its author, Rutgers University physicist David Vanderbilt, is
eminently qualified for the task: he is the senior author of a
large part of the research at the book's core. That literature is
now fundamental knowledge for any scientist working on modern
electronic structure. … The book's presentation combines
mathematical rigor with illuminating discussions and examples … the
ideal textbook for any special-topics course that broadly covers
geometry and topology in electronic structure.' Physics Today
'… 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
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