Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators

To fully appreciate this text, understanding the PythTB programming package is necessary (it is relatively short compared to other computational chemistry and physics packages). Here is a summary of most of its functions:- The tb_model object is initialized by defining the lattice vectors, the position of orbitals, and specifying which index of the lattice data structure.- The diagonal elements of the hamiltonian are the self energies of each lattice site, which is defined using set_onsite.- For the tight binding method, non-diagonal elements have hopping terms between each lattice site that are specified as a list of vectors containing amplitude and lattice shift information, which is created in the set_hop function.- A hamiltonian has to be constructed for each momentum integer or vector. Each hopping amplitude has been multiplied by euler’s number to the power of the dot product between the basis reciprocal lattice vector and the sum of each perspective orbital lattice location and stored lattice shift.- Different functions are made to give the option of solving for the eigenvalues and eigenvectors quickly for a list of momentum number vectors.- Wfs initializes a data structure that could hold the eigenvectors at different momentum values, even in a three dimensional periodic system. Solve_on_grid actually carries out the computation.- A data structure whose dimensions are the number of momentum vectors along a chosen direction, the number of occupied orbitals (bands) and the number of orbitals within a system is used for input for a calculation where each eigenvector of a specific momentum vector and band is dotted with the conjugate of another eigenvector with all other bands but a different adjacent momentum vector. This calculation is critical to the construction of berry phases and curvatures.Going through the pythtb.py file really helps solidify the intuition behind the many programs the text introduces to apply the concepts and equations derived.

Professor David Vanderbilt has a remarkable ability to explain complex and abstract concepts in a clear and accessible manner. If you have completed coursework in quantum mechanics, E&M, and solid-state physics, and are starting your research, this book is excellent for bridging the gap between first-year graduate courses and research.While this edition contains a few typos, a list of errata is available on his webpage.The combination of PyTHTB code and lectures is another outstanding feature of this book. Based on my personal experience, I have a recommendation for readers intending to use PyTHTB for research: find an example that is similar to your problem, run the example to understand both the code and the underlying physics, and then adapt the code accordingly.

A very concise and hands-on presentation of the physics and math behind Berry phases in electronic structure. Even though the subject is inherently mathematically technical, David Vanderbilt has the ability to make the ideas intuitive. Except for presenting rigorous proofs when it is needed, he cleverly uses approaches, such as pictorial proofs, physical intuition, and computational examples not just to make clear arguments but to make his proposition inevitable.Recommended to anyone interested in condensed matter physics!

This book seems to be good, but the equations are tiny. Do not buy this book on kindle!!!

I'm sure the book is great, but the e-version is unreadable.