The study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.

Topological Phases of Matter are an exceptionally dynamic field of research: several of the most exciting recent experimental discoveries and conceptual advances in modern physics have originated in this field. These have generated new, topological, notions of order, interactions and excitations. This text provides an accessible, unified and comprehensive introduction to the phenomena surrounding topological matter, with detailed expositions of the underlying theoretical tools and conceptual framework, alongside accounts of the central experimental breakthroughs. Among the systems covered are topological insulators, magnets, semimetals, and superconductors. The emergence of new particles with remarkable properties such as fractional charge and statistics is discussed alongside possible applications such as fault-tolerant topological quantum computing. Suitable as a textbook for graduate or advanced undergraduate students, or as a reference for more experienced researchers, the book assumes little prior background, providing self-contained introductions to topics as varied as phase transitions, superconductivity, and localisation.

This book presents a comprehensive theory on glide-symmetric topological crystalline insulators. Beginning with developing a theory of topological phase transitions between a topological and trivial phase, it derives a formula for topological invariance in a glide-symmetric topological phase when inversion symmetry is added into a system. It also shows that the addition of inversion symmetry drastically simplifies the formula, providing insights into this topological phase, and proposes potential implementations. Lastly, based on the above results, the author establishes a way to design topological photonic crystals. Allowing readers to gain a comprehensive understanding of the glide-symmetric topological crystalline insulators, the book offers a way to produce such a topological phase in various physical systems, such as electronic and photonic systems, in the future.

Most textbooks in the field are either too advanced for students or don’t adequately cover current research topics. Bridging this gap, Electronic Structure of Materials helps advanced undergraduate and graduate students understand electronic structure methods and enables them to use these techniques in their work. Developed from the author’s lecture notes, this classroom-tested book takes a microscopic view of materials as composed of interacting electrons and nuclei. It explains all the properties of materials in terms of basic quantities of electrons and nuclei, such as electronic charge, mass, and atomic number. Based on quantum mechanics, this first-principles approach does not have any adjustable parameters. The first half of the text presents the fundamentals and methods of electronic structure. Using numerous examples, the second half illustrates applications of the methods to various materials, including crystalline solids, disordered substitutional alloys, amorphous solids, nanoclusters, nanowires, graphene, topological insulators, battery materials, spintronic materials, and materials under extreme conditions. Every chapter starts at a basic level and gradually moves to more complex topics, preparing students for more advanced work in the field. End-of-chapter exercises also help students get a sense of numbers and visualize the physical picture associated with the problem. Students are encouraged to practice with the electronic structure calculations via user-friendly software packages.

The fourth volume of the Collected Works is devoted to Wigners contribution to physical chemistry, statistical mechanics and solid-state physics. One corner stone was his introduction of what is now called the Wigner function, while his paper on adiabatic perturbations foreshadowed later work on Berry phases. Although few in number, Wigners articles on solid-state physics laid the foundations for the modern theory of the electronic structure of metals.

We present first-principles methods for calculating two distinct types of physical quantities within the framework of density functional theory: the response properties of an insulator to finite electric fields, and the anomalous Hall conductivity of a ferromagnet. Both of the methods are closely related to the same ingredient, namely the Berry phase, a geometric phase acquired by a quantum system transporting in parameter space. We develop gauge-invariant formulations in which the random phases of Bloch functions produced by numerical subroutines are irrelevant. First, we provide linear-response methods for calculating phonon frequencies, Born effective charge tensors and dielectric tensors for insulators in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded with respect to both small atomic displacements and electric fields within the framework of density-functional perturbation theory. The linear responses of field-polarized Bloch functions to atomic displacements and electric fields are obtained by minimizing the second-order derivatives of the total-energy functional. The desired second-order tensors are then constructed from these optimized first-order field-polarized Bloch functions. Next, an efficient first-principles approach for computing the anomalous Hall conductivity is described. The intrinsic anomalous Hall conductivity in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent {it ab-initio} studies found that it was necessary to sample the Brillouin zone at millions of k-points to converge the calculation. We start out by performing a conventional electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse k-point mesh. From the resulting Bloch states, maximally localized Wannier functions are constructed which reproduce the {it ab-initio} states up to the Fermi level. With inexpensive Fourier and unitary transformations the quantities of interest are interpolated onto a dense k-point mesh and used to evaluate the anomalous Hall conductivity as a Brillouin-zone integral. The present scheme, which also avoids the cumbersome summation over all unoccupied states in the Kubo formula, is applied to bcc Fe, giving excellent agreement with conventional, less efficient first-principles calculations. Finally, we consider another {it ab-initio} approach for computing the anomalous Hall conductivity based on Haldane's Fermi-surface formulation. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi surface sheets with theslice by standard contour methods, organize these into a set of closed loops, and compute the Berry phase of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices.

T. Ziegler: A Chronicle About the Development of Electronic Structure Theories for Transition Metal Complexes.- J. Linderberg: Orbital Models and Electronic Structure Theory.- J.S. and J.E. Avery: Sturmians and Generalized Sturmians in Quantum Theory.- B.T Sutcliffe: Chemistry as a “Manifestation of Quantum Phenomena” and the Born–Oppenheimer Approximation?- A.J. McCaffery: From Ligand Field Theory to Molecular Collision Dynamics: A Common Thread of Angular Momentum.- M. Atanasov, D. Ganyushin, K. Sivalingam and F. Neese: A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions.- R.S. Berry and B.M. Smirnov: The Phase Rule: Beyond Myopia to Understanding.

These are the proceedings of the 2nd International Conference on Key Engineering Materials (ICKEM 2012), held on 26-28th February 2012 in Singapore. The objective was to provide a forum for the discussion of new developments, recent progress and innovations in the field of key engineering materials. All aspects of design methodology were addressed and emphasis was placed on current and future challenges to research and development in both academia and industry.

Computer simulations of materials are rapidly moving from the level of fundamental studies into the domain of industrial research and development tools. Papers in this book provide an extensive review of advances in materials theory and modeling by addressing new frontiers for theoretical and computational research on real materials, identifying crucial areas where experimental studies have or can be complemented by theory and simulation, and establishing a blueprint for further development of multiscale methods in computational materials science. A number of algorithms for boosting the simulation of time scale of atomistic systems have been introduced but they do not quite answer the need for a solid and widely applicable method. Topics include: mechanical properties, fracture and plasticity; radiation-matter interactions; polymers and macromolecules; multiresolution and multiscale methods - microstructural evolution; new methods for materials simulation; multi-time-scale methods and applications and large-scale ab initio calculations.