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Topological insulators and topological superconductors

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...

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Bibliographic Details
Main Author: Bernevig, B. Andrei
Other Authors: Hughes, Taylor L.
Format: eBook
Language:English
Published: Princeton, New Jersey ; Oxford Princeton University Press 2013, ©2013
Subjects:
Energy-band Theory Of Solids
Superconductivity
Solid State Physics > mathematics
Superconductors > mathematics
Online Access:
Collection: DeGruyter MPG Collection - Collection details see MPG.ReNa
Table of Contents:
  • 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

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