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PRINTED BOOKS
Author Bernevig, B. Andrei, 1978- author.

Title Topological insulators and topological superconductors / B. Andrei Bernevig with Taylor L. Hughes.

Published Princeton, New Jersey : Princeton University Press, [2013]
©2013.

Copies

Location Call No. Status
 UniM ERC  530.413 BERN    AVAILABLE
Physical description ix, 247 pages : illustrations ; 26 cm
Bibliography Includes bibliographical references (pages [241]-243) and index.
Contents 1 Introduction 1 -- 2 Berry Phase 6 -- 2.1 General Formalism 6 -- 2.2 Gauge-Independent Computation of the Berry Phase 8 -- 2.3 Degeneracies and Level Crossing 10 -- 2.4 Spin in a Magnetic Field 13 -- 2.5 Can the Berry Phase Be Measured? 14 -- 2.6 Problems 14 -- 3 Hall Conductance and Chern Numbers 15 -- 3.1 Current Operators 15 -- 3.2 Linear Response to an Applied External Electric Field 18 -- 3.3 Current-Current Correlation Function and Electrical Conductivity 23 -- 3.4 Computing the Hall Conductance 24 -- 3.5 Alternative Form of the Hall Response 29 -- 3.6 Chern Number as an Obstruction to Stokes' Theorem over the Whole BZ 30 -- 3.7 Problems 32 -- 4 Time-Reversal Symmetry 33 -- 4.1 Time Reversal for Spinless Particles 33 -- 4.2 Time Reversal for Spinful Particles 35 -- 4.3 Kramers' Theorem 36 -- 4.4 Time-Reversal Symmetry in Crystals for Half-Integer Spin Particles 37 -- 4.5 Vanishing of Hall Conductance for T-Invariant Half-Integer Spin Particles 39 -- 4.6 Problems 40 -- 5 Magnetic Field on the Square Lattice 41 -- 5.1 Hamiltonian and Lattice Translations 41 -- 5.2 Diagonalization of the Hamiltonian of a 2-D Lattice in a Magnetic Field 44 -- 5.3 Hall Conductance 49 -- 5.4 Explicit Calculation of the Hall Conductance 51 -- 5.5 Problems 59 -- 6 Hall Conductance and Edge Modes: The Bulk-Edge Correspondence 60 -- 6.1 Laughlin's Gauge Argument 60 -- 6.2 Transfer Matrix Method 62 -- 6.3 Edge Modes 65 -- 6.4 Bulk Bands 65 -- 6.5 Problems 69 -- 7 Graphene 70 -- 7.1 Hexagonal Lattices 70 -- 7.2 Dirac Fermions 72 -- 7.3 Symmetries of a Graphene Sheet 72 -- 7.4 Global Stability of Dirac Points 76 -- 7.5 Edge Modes of the Graphene Layer 80 -- 7.6 Problems 90 -- 8 Simple Models for the Chern Insulator 91 -- 8.1 Dirac Fermions and the Breaking of Time-Reversal Symmetry 91 -- 8.2 Explicit Berry Potential of a Two-Level System 92 -- 8.3 Skyrmion Number and the Lattice Chern Insulator 95 -- 8.4 Determinant Formula for the Hall Conductance of a Generic Dirac Hamiltonian 99 -- 8.5 Behavior of the Vector Potential on the Lattice 99 -- 8.6 Problem of Choosing a Consistent Gauge in the Chern Insulator 100 -- 8.7 Chern Insulator in a Magnetic Field 102 -- 8.8 Edge Modes and the Dirac Equation 103 -- 8.9 Haldane's Graphene Model 104 -- 8.10 Problems 107 -- 9 Time-Reversal-Invariant Topological Insulators 109 -- 9.1 Kane and Mele Model: Continuum Version 109 -- 9.2 Kane and Mele Model: Lattice Version 113 -- 9.3 First Topological Insulator: Mercury Telluride Quantum Wells 117 -- 9.4 Experimental Detection of the Quantum Spin Hall State 120 -- 9.5 Problems 121 -- 10 Z₂ Invariants 123 -- 10.1 Z₂ Invariant as Zeros of the Pfaffian 123 -- 10.2 Theory of Charge Polarization in One Dimension 128 -- 10.3 Time-Reversal Polarization 130 -- 10.4 Z₂ Index for 3-D Topological Insulators 138 -- 10.5 Z₂ Number as an Obstruction 141 -- 10.6 Equivalence between Topological Insulator Descriptions 144 -- 10.7 Problems 145 -- 11 Crossings in Different Dimensions 147 -- 11.1 Inversion-Asymmetric Systems 148 -- 11.2 Inversion-Symmetric Systems 151 -- 11.3 Mercury Telluride Hamiltonian 154 -- 11.4 Problems 156 -- 12 Time-Reversal Topological Insulators with Inversion Symmetry 158 -- 12.1 Both Inversion and Time-Reversal Invariance 159 -- 12.2 Role of Spin-Orbit Coupling 162 -- 12.3 Problems 163 -- 13 Quantum Hall Effect and Chern Insulators in Higher Dimensions 164 -- 13.1 Chern Insulator in Four Dimensions 164 -- 13.2 Proof That the Second Chern Number Is Topological 166 -- 13.3 Evaluation of the Second Chern Number: From a Green's Function Expression to the Non-Abelian Berry Curvature 167 -- 13.4 Physical Consequences of the Transport Law of the 4-D Chern Insulator 169 -- 13.5 Simple Example of Time-Reversal-Invariant Topological Insulators with Time-Reversal and Inversion Symmetry Based on Lattice Dirac Models 172 -- 13.6 Problems 175 -- 14 Dimensional Reduction of 4-D Chern Insulators to 3-D Time-Reversal Insulators 177 -- 14.1 Low-Energy Effective Action of (3 + 1)-D Insulators and the Magnetoelectric Polarization 177 -- 14.2 Magnetoelectric Polarization for a 3-D Insulator with Time-Reversal Symmetry 181 -- 14.3 Magnetoelectric Polarization for a 3-D Insulator with Inversion Symmetry 182 -- 14.4 3-D Hamiltonians with Time-Reversal Symmetry and/or Inversion Symmetry as Dimensional Reductions of 4-D Time-Reversal-Invariant Chern Insulators 184 -- 14.5 Problems 185 -- 15 Experimental Consequences of the Z₂ Topological Invariant 186 -- 15.1 Quantum Hall Effect on the Surface of a Topological Insulator 186 -- 15.2 Physical Properties of Time-Reversal Z₂-Nontrivial Insulators 187 -- 15.3 Half-Quantized Hall Conductance at the Surface of Topological Insulators with Ferromagnetic Hard Boundary 188 -- 15.4 Experimental Setup for Indirect Measurement of the Half-Quantized Hall Conductance on the Surface of a Topological Insulator 189 -- 15.5 Topological Magnetoelectric Effect 189 -- 15.6 Problems 191 -- 16 Topological Superconductors in One and Two Dimensions by Taylor L. Hughes 193 -- 16.1 Introducing the Bogoliubov-de-Gennes (BdG) Formalism for s-Wave Superconductors 193 -- 16.2 p-Wave Superconductors in One Dimension 196 -- 16.3 2-D Chiral p-Wave Superconductor 201 -- 16.4 Problems 211 -- 17 Time-Reversal-Invariant Topological Superconductors by Taylor L. Hughes 214 -- 17.1 Superconducting Pairing with Spin 214 -- 17.2 Time-Reversal-Invariant Superconductors in Two Dimensions 215 -- 17.3 Time-Reversal-Invariant Superconductors in Three Dimensions 219 -- 17.4 Finishing the Classification of Time-Reversal-Invariant Superconductors 222 -- 17.5 Problems 224 -- 18 Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces by Taylor L. Hughes 226 -- 18.1 Generating 1-D Topological Insulators and Superconductors on the Edge of the Quantum-Spin Hall Effect 226 -- 18.2 Constructing Topological States from Interfaces on the Boundary of Topological Insulators 228 -- 18.3 Problems 234.
Summary "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 ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field"--Publisher.
Other author Hughes, Taylor L., 1981- author.
Subject Energy-band theory of solids.
Superconductivity.
Solid state physics -- Mathematics.
Superconductors -- Mathematics.
ISBN 9780691151755 (hardback)
069115175X (hardback)