title: Exponential localization of Wannier functions in insulators.
abstract: The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.
authors.affiliation: Institut de Minéralogie et de Physique des Milieux Condensés, CNRS UMR 7590, Universités Paris 6 et 7, IPGP, 140 rue de Lourmel, 75015 Paris, France.
authors.forename: Christian
authors.initials: C
authors.lastname: Brouder
authors.forename: Gianluca
authors.initials: G
authors.lastname: Panati
authors.forename: Matteo
authors.initials: M
authors.lastname: Calandra
authors.forename: Christophe
authors.initials: C
authors.lastname: Mourougane
authors.forename: Nicola
authors.initials: N
authors.lastname: Marzari