Title | Construction of Real-Valued Localized Composite Wannier Functions for Insulators |

Publication Type | Journal Article |

Year of Publication | 2016 |

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

Journal | Annales Henri Poincaré |

Volume | 17 |

Pagination | 63–97 |

Date Published | Jan |

ISSN | 1424-0661 |

Abstract | We consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type. |

URL | https://doi.org/10.1007/s00023-015-0400-6 |

DOI | 10.1007/s00023-015-0400-6 |

## Construction of Real-Valued Localized Composite Wannier Functions for Insulators

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