This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is

*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Berry Phase, pg. 6*3. Hall Conductance and Chern Numbers, pg. 15*4. Time-Reversal Symmetry, pg. 33*5. Magnetic Field on the Square Lattice, pg. 41*6. Hall Conductance and Edge Modes: The Bulk-Edge Correspondence, pg. 60*7. Graphene, pg. 70*8. Simple Models for the Chern Insulator, pg. 91*9. Time-Reversal-Invariant Topological Insulators, pg. 109*10. Z2 Invariants, pg. 123*11. Crossings in Different Dimensions, pg. 147*12. Time-Reversal Topological Insulators with Inversion Symmetry, pg. 158*13. Quantum Hall Effect and Chern Insulators in Higher Dimensions, pg. 164*14. Dimensional Reduction of 4-D Chern Insulators to 3-D Time-Reversal Insulators, pg. 177*15. Experimental Consequences of the Z2 Topological Invariant, pg. 186*16. Topological Superconductors in One and Two Dimensions, pg. 193*17. Time-Reversal-Invariant Topological Superconductors, pg. 214*18. Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces, pg. 226*APPENDIX. 3-D Topological Insulator in a Magnetic Field, pg. 237*References, pg. 241*Index, pg. 245

"This book presents an array of increasingly complicated problems centered around the idea of the topology of a band in k-space and the theorem that the Chern number determines the Hall effect. It will be invaluable to those who are in tune with the conceptual structure of modern band theory as reconfigured by Haldane and his fellow travelers."—Philip W. Anderson, Nobel Laureate in Physics

"One of the most exciting developments in condensed matter physics over the last seven or eight years has been the topic of topological insulators and superconductors. The present book, by one of the original pioneers in this area, is a very up-to-date and comprehensive introduction to the theory of these systems. It will be extremely useful to both graduate students and more senior researchers."—Anthony J. Leggett, University of Illinois, Urbana-Champaign

"An authoritative and sophisticated introduction to the mathematics of topological insulation."—Robert B. Laughlin, Stanford University

"This book gives the first comprehensive introduction to the theory of topological insulators and superconductors—an exciting new field in condensed matter physics. The authors contributed to the discovery of the first topological insulator HgTe, and now present a readable account accessible to most graduate students."—Shoucheng Zhang, Stanford University

"This excellent book introduces a relatively new topic in condensed matter physics. The material is well developed and sufficient detail is given for students to follow arguments and derivations. With a hands-on, no-nonsense approach, Topological Insulators and Topological Superconductors will be a mainstay in the field for years to come."—Marcel Franz, University of British Columbia

"Topological Insulators and Topological Superconductors deals with a very exciting subject that has become the focus of research in recent years. Bernevig and Hughes have made some of the most important theoretical contributions to this young field and this timely volume will have significant staying power. It will be of great interest to condensed matter physicists, high energy and string theorists, and mathematicians."—Eduardo Fradkin, University of Illinois, Urbana-Champaign