Title | Z2 Invariants of Topological Insulators as Geometric Obstructions |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | Fiorenza, D, Monaco, D, Panati, G |

Journal | Communications in Mathematical Physics |

Volume | 343 |

Pagination | 1115–1157 |

Date Published | May |

ISSN | 1432-0916 |

Abstract | We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones. |

URL | https://doi.org/10.1007/s00220-015-2552-0 |

DOI | 10.1007/s00220-015-2552-0 |

## Z2 Invariants of Topological Insulators as Geometric Obstructions

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