Exponential localization of Wannier functions in insulators

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.


Published in:
Physical Review Letters, 98, 4, 046402
Year:
2007
ISSN:
0031-9007
Keywords:
Laboratories:




 Record created 2012-06-29, last modified 2018-01-28


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