Topological insulators : Dirac equation in condensed matter /: Dirac equation in condensed matter. (2017)

• Record Type: Book
• Further Information: Note: Shun-Qing Shen.
• Authors: Shen, Shun-Qing
• Contents: Preface to the Second Edition; Preface to the First Edition; Contents; 1 Introduction; 1.1 From the Hall Effect to the Quantum Spin Hall Effect; 1.2 Topological Insulators as a Generalization of the Quantum Spin Hall Systems; 1.3 Beyond Band Insulators: Disorder and Interaction; 1.4 Topological Phases in Superconductors and Superfluids; 1.5 Topological Dirac and Weyl Semimetals; 1.6 Dirac Equation and Topological Insulators; 1.7 Topological Insulators and Landau Theory of Phase Transition; 1.8 Summary; 1.9 Further Reading; References; 2 Starting from the Dirac Equation; 2.1 Dirac Equation. 2.2 Solutions of Bound States2.2.1 Jackiw-Rebbi Solution in One Dimension; 2.2.2 Two Dimensions; 2.2.3 Three and Higher Dimensions; 2.3 Why not the Dirac Equation?; 2.4 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; 3 Minimal Lattice Model for Topological Insulators; 3.1 Tight Binding Approximation. 3.2 Mapping from a Continuous Model to a Lattice Model3.3 One-Dimensional Lattice Model; 3.4 Two-Dimensional Lattice Model; 3.4.1 Integer Quantum Hall Effect; 3.4.2 Quantum Spin Hall Effect; 3.5 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; 4 Topological Invariants; 4.1 Bloch's Theorem and Band Theory; 4.2 Berry Phase; 4.3 Quantum Hall Conductance and the Chern Number. 4.4 Electric Polarization in a Cyclic Adiabatic Evolution4.5 Thouless Charge Pump; 4.6 Fu -- Kane Spin Pump; 4.7 Integer Quantum Hall Effect: The Laughlin Argument; 4.8 Time Reversal Symmetry and the Z2 Index; 4.9 Generalization to Two and Three Dimensions; 4.10 Phase Diagram of the Modified Dirac Equation; 4.11 Further Reading; References; 5 Topological Phases in One Dimension; 5.1 Su -- Schrieffer -- Heeger Model for Polyacetylene; 5.2 Topological Ferromagnet; 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.
• Edition: Second edition
• Publisher Details: Singapore : Springer
• Publication Date: 2017
• Extent: 1 online resource (xiii, 266 pages), illustrations (some color)
• Subjects: 621.319/37; Electric insulators and insulation; Dirac equation; Condensed matter; TECHNOLOGY & ENGINEERING -- Mechanical; Condensed matter; Dirac equation; Electric insulators and insulation; Physics; Semiconductors; Solid State Physics; Optical and Electronic Materials; Electronic books; Electronic book
• Languages: English
• ISBNs: 9789811046063; 9811046069
• Related ISBNs: 9789811046056; 9811046050
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 24, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.