Exponential localization of Wannier functions in insulators

Details Exponential localization of Wannier functions in insulators Exponential localization of Wannier functions in insulators

2006-06-28

arxiv.org/abs/cond-mat/0606726v2

Physical Review Letters 98 (01/2007) 046402

Physics

Condensed Matter

Materials Science

Four pages, two figures

Scientific paper

10.1103/PhysRevLett.98.046402

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.

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