Topological Phases of Matter

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.

Preface; Acknowledgements; 1. Introduction; 2. Basic concepts of topology and condensed matter; 3. Integer topological phases; 4. Geometry and topology of wavefunctions in crystals; 5. Hydrogen atoms for fractionalisation; 6. Gauge and topological field theories; 7. Topology in gapless matter; 8. Disorder and defects in topological phases; 9. Topological quantum computation via non-Abelian statistics; 10. Topology out of equilibrium; 11. Symmetry, topology, and information; Appendix; References; Index.

Roderich Moessner is director at the Max Planck Institute for the Physics of Complex Systems in Dresden. His theoretical discoveries include classical and quantum spin liquids, emergent magnetic monopoles, and non-equilibrium spatiotemporal ordering phenomena. He is recipient of the Leibniz Prize and of the Europhysics Prize, Honorary Fellow of Hertford College, Oxford, and member of the Executive Board of the German Physical Society.
Joel E. Moore is Chern-Simons Professor of Physics at the University of California, Berkeley and Senior Faculty Scientist at Lawrence Berkeley National Laboratory. His research interests include topological insulators, semimetals, and semiconductors, along with the application of quantum information concepts to many-body physics. He is a Simons Investigator, a Fellow and former elected Member-at-Large of the American Physical Society, and Chair of the Advisory Board of the Kavli Institute for Theoretical Physics.