2006/06/30 by Christian Brouder, Gianluca Panati, Matteo Calandra +2
Physics and Astronomy · Mathematics · #cond-mat.mtrl-sci #math-ph #math.MP
paper · pdf · doi:10.1103/physrevlett.98.046402
published as Physical Review Letters 98 (01/2007) 046402 · Four pages, two figures
arxiv created 2007/03/07 · arxiv updated 2009/12/01
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.