Footnote:
Description based upon print version of record
Description:
Topological Insulators; Preface; Contents; List of Abbreviations; Chapter 1: Introduction; 1.1 From the Hall Effect to Quantum Spin Hall Effect; 1.2 Topological Insulators as Generalization of Quantum Spin Hall Effect; 1.3 Topological Phases in Superconductors and Superfluids; 1.4 Dirac Equation and Topological Insulators; 1.5 Summary: The Confirmed Family Members; 1.6 Further Reading; References; Chapter 2: Starting from the Dirac Equation; 2.1 Dirac Equation; 2.2 Solutions of Bound States; 2.2.1 Jackiw-Rebbi Solution in One Dimension; 2.2.2 Two Dimensions; 2.2.3 Three and Higher Dimensions
2.3 Why Not the Dirac Equation2.4 Quadratic Correction to the Dirac Equation; 2.5 Bound State Solutions of the Modified Dirac Equation; 2.5.1 One Dimension: End States; 2.5.2 Two Dimensions: Helical Edge States; 2.5.3 Three Dimensions: Surface States; 2.5.4 Generalization to Higher-Dimensional Topological Insulators; 2.6 Summary; 2.7 Further Reading; References; Chapter 3: Minimal Lattice Model for Topological Insulator; 3.1 Tight Binding Approximation; 3.2 From Continuous to Lattice Model; 3.3 One-Dimensional Lattice Model; 3.4 Two-Dimensional Lattice Model; 3.4.1 Integer Quantum Hall Effect
3.4.2 Quantum Spin Hall Effect3.5 Three-Dimensional Lattice Model; 3.6 Parity at the Time Reversal Invariant Momenta; 3.6.1 One-Dimensional Lattice Model; 3.6.2 Two-Dimensional Lattice Model; 3.6.3 Three-Dimensional Lattice Model; 3.7 Summary; References; Chapter 4: Topological Invariants; 4.1 Bloch Theorem and Band Theory; 4.2 Berry Phase; 4.3 Quantum Hall Conductance and Chern Number; 4.4 Electric Polarization in a Cyclic Adiabatic Evolution; 4.5 Thouless Charge Pump; 4.6 Fu-Kane Spin Pump; 4.7 Integer Quantum Hall Effect: Laughlin Argument; 4.8 Time Reversal Symmetry and the Z2 Index
4.9 Generalization to Two and Three Dimensions4.10 Phase Diagram of Modified Dirac Equation; 4.11 Further Reading; References; Chapter 5: Topological Phases in One Dimension; 5.1 Su-Schrieffer-Heeger Model for Polyacetylene; 5.2 Ferromagnet with Spin-Orbit Coupling; 5.3 p-Wave Pairing Superconductor; 5.4 Ising Model in a Transverse Field; 5.5 One-Dimensional Maxwell's Equations in Media; 5.6 Summary; References; Chapter 6: Quantum Spin Hall Effect; 6.1 Two-Dimensional Dirac Model and the Chern Number; 6.2 From Haldane Model to Kane-Mele Model; 6.2.1 Haldane Model; 6.2.2 Kane-Mele Model
6.3 Transport of Edge States6.3.1 Landauer-Büttiker Formalism; 6.3.2 Transport of Edge States; 6.4 Stability of Edge States; 6.5 Realization of Quantum Spin Hall Effect in HgTe/CdTe Quantum Well; 6.5.1 Band Structure of HgTe/CdTe Quantum Well; 6.5.2 Exact Solution of Edge States; 6.5.3 Experimental Measurement; 6.6 Quantum Hall Effect and Quantum Spin Hall Effect: A Case Study; 6.7 Coherent Oscillation Due to the Edge States; 6.8 Further Reading; References; Chapter 7: Three-Dimensional Topological Insulators; 7.1 Family Members of Three-Dimensional Topological Insulators
7.1.1 Weak Topological Insulators: PbxSn1-xTe
Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these soluti