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.

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.

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.

The idea that a long-lived form of spin order, namely singlet order, can be prepared from nuclear spin magnetisation first emerged in 2004. The unusual properties of singlet order–its long lifetime and the fact that it is NMR silent but interconvertible into other forms of NMR active order—make it a ‘smart tag’ that can be used to store information for a long time or through distant space points. It is not unexpected then, that since its first appearance, this idea has caught the attention of research groups interested in exploiting this form of order in different fields of research spanning from biology to materials science and from hyperpolarisation to quantum computing. This first book on the subject gives a thorough description of the various aspects that affect the development of the topic and details the interdisciplinary applications. The book starts with a section dedicated to the basic theories of long-lived spin order and then proceeds with a description of the state-of-the-art experimental techniques developed to manipulate singlet order. It then concludes by covering the generalization of the concept of singlet order by introducing and discussing other forms of long-lived spin order.

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.