## Topological Insulators and Topological SuperconductorsThis 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. |

### What people are saying - Write a review

### Contents

Introduction | 1 |

Contents | 2 |

Z2 Invariants | 10 |

Hall Conductance and Chern Numbers | 15 |

TimeReversal Symmetry | 33 |

TimeReversal Topological Insulators with Inversion Symmetry | 40 |

Magnetic Field on the Square Lattice | 41 |

Contents | 51 |

Simple Models for the Chern Insulator | 91 |

Contents | 169 |

Dimensional Reduction of 4D Chern Insulators to 3D TimeReversal | 177 |

Experimental Consequences of the Z2 Topological Invariant | 186 |

Topological Superconductors in One and Two Dimensions | 193 |

TimeReversalInvariant Topological Superconductors by Taylor L Hughes | 214 |

Contents ix | 226 |

3D Topological Insulator in a Magnetic Field | 237 |