Topological Aspects of Condensed Matter Physics : Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics. ## Abstract Topological condensed matter physics is a recent arrival among the disciplines of modern physics of a distinctive and substantive nature. Its roots reach far back, but much of its current importance derives from exciting developments in the last half-century. The field is advancing rapidly, growing explosively, and diversifying greatly. There is now a zoo of topological phenomena–the quantum spin Hall effect, topological insulators, Coulomb spin liquids, non-Abelian anyonic statistics and their potential application in topological quantum computing, to name but a few–as well as an increasingly sophisticated set of concepts and methods underpinning their understanding. The aim of this Les Houches Summer School was to present an overview of this field, along with a sense of its origins and its place on the map of advances in fundamental physics. The school comprised a set of basic lectures (Part I) aimed at a pedagogical introduction to the fundamental concepts, which was accompanied by more advanced lectures (Part II) covering individual topics at the forefront of today’s research in condensed matter physics. This work contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation This book contains lecture notes by world experts on topological quantum phenomena, which are being developed at unprecedented rates in novel material systems.