Note: Cover -- Title -- Copyright -- Contents -- 1 Introduction -- 2 Berry Phase -- 2.1 General Formalism -- 2.2 Gauge-Independent Computation of the Berry Phase -- 2.3 Degeneracies and Level Crossing -- 2.3.1 Two-Level System Using the Berry Curvature -- 2.3.2 Two-Level System Using the Hamiltonian Approach -- 2.4 Spin in a Magnetic Field -- 2.5 Can the Berry Phase Be Measured? -- 2.6 Problems -- 3 Hall Conductance and Chern Numbers -- 3.1 Current Operators -- 3.1.1 Current Operators from the Continuity Equation -- 3.1.2 Current Operators from Peierls Substitution -- 3.2 Linear Response to an Applied External Electric Field -- 3.2.1 The Fluctuation Dissipation Theorem -- 3.2.2 Finite-Temperature Green's Function -- 3.3 Current-Current Correlation Function and Electrical Conductivity -- 3.4 Computing the Hall Conductance -- 3.4.1 Diagonalizing the Hamiltonian and the Flat-Band Basis -- 3.5 Alternative Form of the Hall Response -- 3.6 Chern Number as an Obstruction to Stokes' Theorem over the Whole BZ -- 3.7 Problems -- 4 Time-Reversal Symmetry -- 4.1 Time Reversal for Spinless Particles -- 4.1.1 Time Reversal in Crystals for Spinless Particles -- 4.1.2 Vanishing of Hall Conductance for T-Invariant Spinless Fermions -- 4.2 Time Reversal for Spinful Particles -- 4.3 Kramers' Theorem -- 4.4 Time-Reversal Symmetry in Crystals for Half-Integer Spin Par -- 4.5 Vanishing of Hall Conductance for T-Invariant Half-Integer Spin Particles -- 4.6 Problems -- 5 Magnetic Field on the Square Lattice -- 5.1 Hamiltonian and Lattice Translations -- 5.2 Diagonalization of the Hamiltonian of a 2-D Lattice in a Magnetic Field -- 5.2.1 Dependence on ky -- 5.2.2 Dirac Fermions in the Magnetic Field on the Lattice -- 5.3 Hall Conductance -- 5.3.1 Diophantine Equation and Streda Formula Method -- 5.4 Explicit Calculation of the Hall Conductance -- 5.5 Problems. , 6 Hall Conductance and Edge Modes: The Bulk-Edge Correspondence -- 6.1 Laughlin's Gauge Argument -- 6.2 The Transfer Matrix Method -- 6.3 Edge Modes -- 6.4 Bulk Bands -- 6.5 Problems -- 7 Graphene -- 7.1 Hexagonal Lattices -- 7.2 Dirac Fermions -- 7.3 Symmetries of a Graphene Sheet -- 7.3.1 Time Reversal -- 7.3.2 Inversion Symmetry -- 7.3.3 Local Stability of Dirac Points with Inversion and Time Reversal -- 7.4 Global Stability of Dirac Points -- 7.4.1 C3 Symmetry and the Position of the Dirac Nodes -- 7.4.2 Breaking of C3 Symmetry -- 7.5 Edge Modes of the Graphene Layer -- 7.5.1 Chains with Even Number of Sites -- 7.5.2 Chains with Odd Number of Sites -- 7.5.3 Influence of Different Mass Terms on the Graphene Edge Modes -- 7.6 Problems -- 8 Simple Models for the Chern Insulator -- 8.1 Dirac Fermions and the Breaking of Time-Reversal Symmetry -- 8.1.1 When the Matrices r Correspond to Real Spin -- 8.1.2 When the Matrices r Correspond to Isospin -- 8.2 Explicit Berry Potential of a Two-Level System -- 8.2.1 Berry Phase of a Continuum Dirac Hamiltonian -- 8.2.2 The Berry Phase for a Generic Dirac Hamiltonian in Two Dimensions -- 8.2.3 Hall Conductivity of a Dirac Fermion in the Continuum -- 8.3 Skyrmion Number and the Lattice Chern Insulator -- 8.3.1 M > -- 0 Phase and M < -- −4 Phase -- 8.3.2 The −2 < -- M < -- 0 Phase -- 8.3.3 The −4 < -- M < -- −2 Phase -- 8.3.4 Back to the Trivial State for M < -- −4 -- 8.4 Determinant Formula for the Hall Conductance of a Generic Dirac Hamiltonian -- 8.5 Behavior of the Vector Potential on the Lattice -- 8.6 The Problem of Choosing a Consistent Gauge in the Chern Insulator -- 8.7 Chern Insulator in a Magnetic Field -- 8.8 Edge Modes and the Dirac Equation -- 8.9 Haldane's Graphene Model -- 8.9.1 Symmetry Properties of the Haldane Hamiltonian -- 8.9.2 Phase Diagram of the Haldane Hamiltonian. , 8.10 Problems -- 9 Time-Reversal-Invariant Topological Insulators -- 9.1 The Kane and Mele Model: Continuum Version -- 9.1.1 Adding Spin -- 9.1.2 Spin ↑ and Spin ↓ -- 9.1.3 Rashba Term -- 9.2 The Kane and Mele Model: Lattice Version -- 9.3 First Topological Insulator: Mercury Telluride Quantum Wells -- 9.3.1 Inverted Quantum Wells -- 9.4 Experimental Detection of the Quantum Spin Hall State -- 9.5 Problems -- 10 Z2 Invariants -- 10.1 Z2 Invariant as Zeros of the Pfaffian -- 10.1.1 Pfaffian in the Even Subspace -- 10.1.2 The Odd Subspace -- 10.1.3 Example of an Odd Subspace: da = 0 Subspace -- 10.1.4 Zeros of the Pfaffian -- 10.1.5 Explicit Example for the Kane and Mele Model -- 10.2 Theory of Charge Polarization in One Dimension -- 10.3 Time-Reversal Polarization -- 10.3.1 Non-Abelian Berry Potentials at k, −k -- 10.3.2 Proof of the Unitarity of the Sewing Matrix B -- 10.3.3 A New Pfaffian Z2 Index -- 10.4 Z2 Index for 3-D Topological Insulators -- 10.5 Z2 Number as an Obstruction -- 10.6 Equivalence between Topological Insulator Descriptions -- 10.7 Problems -- 11 Crossings in Different Dimensions -- 11.1 Inversion-Asymmetric Systems -- 11.1.1 Two Dimensions -- 11.1.2 Three Dimensions -- 11.2 Inversion-Symmetric Systems -- 11.2.1 na = nb -- 11.2.2 na = −nb -- 11.3 Mercury Telluride Hamiltonian -- 11.4 Problems -- 12 Time-Reversal Topological Insulators with Inversion Symmetry -- 12.1 Both Inversion and Time-Reversal Invariance -- 12.2 Role of Spin-Orbit Coupling -- 12.3 Problems -- 13 Quantum Hall Effect and Chern Insulators in Higher Dimensions -- 13.1 Chern Insulator in Four Dimensions -- 13.2 Proof That the Second Chern Number Is Topological -- 13.3 Evaluation of the Second Chern Number: From a Green's Function Expression to the Non-Abelian Berry Curvature -- 13.4 Physical Consequences of the Transport Law of the 4-D Chern Insulator. , 13.5 Simple Example of Time-Reversal-Invariant Topological Insulators with Time-Reversal and Inversion Symmetry Based on Lattice Dirac Models -- 13.6 Problems -- 14 Dimensional Reduction of 4-D Chern Insulators to 3-D Time-Reversal Insulators -- 14.1 Low-Energy Effective Action of (3 + 1)-D Insulators and the Magnetoelectric Polarization -- 14.2 Magnetoelectric Polarization for a 3-D Insulator with Time-Reversal Symmetry -- 14.3 Magnetoelectric Polarization for a 3-D Insulator with Inversion Symmetry -- 14.4 3-D Hamiltonians with Time-Reversal Symmetry and/or Inversion Symmetry as Dimensional Reductions of 4-D Time-Reversal-Invariant Chern Insulators -- 14.5 Problems -- 15 Experimental Consequences of the Z2 Topological Invariant -- 15.1 Quantum Hall Effect on the Surface of a Topological Insulator -- 15.2 Physical Properties of Time-Reversal Z2-Nontrivial Insulators -- 15.3 Half-Quantized Hall Conductance at the Surface of Topological Insulators with Ferromagnetic Hard Boundary -- 15.4 Experimental Setup for Indirect Measurement of the Half-Quantized Hall Conductance on the Surface of a Topological Insulator -- 15.5 Topological Magnetoelectric Effect -- 15.6 Problems -- 16 Topological Superconductors in One and Two Dimensions -- 16.1 Introducing the Bogoliubov-de-Gennes (BdG) Formalism for s-Wave Superconductors -- 16.2 p-Wave Superconductors in One Dimension -- 16.2.1 1-D p-Wave Wire -- 16.2.2 Lattice p-Wave Wire and Majorana Fermions -- 16.3 2-D Chiral p-Wave Superconductor -- 16.3.1 Bound States on Vortices in 2-D Chiral p-wave Superconductors -- 16.4 Problems -- 17 Time-Reversal-Invariant Topological Superconductors by Taylor L. Hughes -- 17.1 Superconducting Pairing with Spin -- 17.2 Time-Reversal-Invariant Superconductors in Two Dimensions -- 17.2.1 Vortices in 2-D Time-Reversal-Invariant Superconductors. , 17.3 Time-Reversal-Invariant Superconductors in Three Dimensions -- 17.4 Finishing the Classification of Time-Reversal-Invariant Superconductors -- 17.5 Problems -- 18 Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces -- 18.1 Generating 1-D Topological Insulators and Superconductors on the Edge of the Quantum-Spin Hall Effect -- 18.2 Constructing Topological States from Interfaces on the Boundary of Topological Insulators -- 18.3 Problems -- APPENDIX: 3-D Topological Insulator in a Magnetic Field -- References -- Index.

Note: 162 Advances in Polymer Science -- Radiation Effects on Polymers for Biological Use -- Copyright -- Volume Editor -- Preface -- Advances in Polymer Science Available Electronically -- Contents -- Engineering and Characterization of Polymer Surfaces for Biomedical Applications -- Plasma and Radiation-Induced Graft Modification of Polymers for Biomedical Applications -- The Effects of Radiation on the Structural and Mechanical Properties of Medical Polymers -- Effects of Ion Radiation on Cells and Tissues -- Author Index Volumes 101-162 -- Subject Index.