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Half Title; Editor; Title; Copyright; Contents; Contributors; Series Preface; Volume Preface; Part I: Theoretical Foundations; 1 Topological Band Theory and the Z2 Invariant; 1 Introduction; 2 Topology and Band Theory; 2.1 Topology; 2.2 Band Theory; 2.3 Topological Band Theory and the Bulk-Boundary Correspondence; 2.4 Berry Phase, and the Chern Invariant; 3 Illustrative Example: Polarization and Topology in One Dimension; 3.1 Polarization as a Berry Phase; 3.2 Su, Schrieffer, Heeger Model; 3.3 Domain Wall States and the Jackiw Rebbi Model; 3.4 Thouless Charge Pump, and the Chern Invariant.

4 Integer Quantum Hall Effect4.1 Laughlin Argument, and the TKNN Invariant; 4.2 Haldane Model; 4.3 Chiral Edge States, and the Bulk Boundary Correspondence; 5 Z2 Topological Insulators; 5.1 Quantum Spin Hall Insulator in Graphene; 5.2 Z2 Topological Invariant; 5.2.1 Time Reversal Symmetry; 5.2.2 Bulk Boundary Correspondence; 5.2.3 Physical Meaning of the Invariant; 5.2.4 Formulas for the Z2 Invariant; 5.3 Topological Insulators in Three Dimensions; 5.3.1 Weak Topological Insulator; 5.3.2 Strong Topological Insulator; 6 Related Topics; 6.1 Topological Crystalline Insulators.

6.2 Topological Nodal Semimetals6.3 Topological Superconductivity; 6.4 Topological Defects; Acknowledgments; References; 2 Theory of Three-Dimensional Topological Insulators; 1 Introduction; 2 Topological Properties of Band Structures; 2.1 Building the 3D Topological Insulator from 2D; 2.2 Materials Considerations; 2.3 Berry Phases of Bloch Electrons and Chern-Simons Form of Z2 Invariant; 2.4 Time-Reversal Breaking, Surface Hall Effect, and Magnetoelectric Response; 3 Transport in Topological Surface States and Real-Space Geometry; 4 Consequences of Strong Electronic Interactions.

4.1 Defining the 3D Topological Insulator with Interactions4.2 Superconducting Proximity Effect; 4.3 Fractional Topological Insulators; 4.4 Related States in Three Dimensions; Acknowledgments; References; 3 Models and Materials for Topological Insulators; 1 Introduction; 2 HgTe Quantum Wells and the Bernevig-Hughes-Zhang Model; 3 Effective Model of the Three-Dimensional Topological Insulator; 4 Helical Edge/Surface State of 2D/3D Topological Insulators; 5 Physical Properties of Topological Edge/Surface States.

Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old.

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