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. © 2007 The American Physical Society.

Exponential localization of Wannier functions in insulators / Brouder, C.; Panati, G.; Calandra, M.; Mourougane, C.; Marzari, N.. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 98:4(2007). [10.1103/PhysRevLett.98.046402]

Exponential localization of Wannier functions in insulators

Calandra M.;
2007-01-01

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. © 2007 The American Physical Society.
2007
4
Brouder, C.; Panati, G.; Calandra, M.; Mourougane, C.; Marzari, N.
Exponential localization of Wannier functions in insulators / Brouder, C.; Panati, G.; Calandra, M.; Mourougane, C.; Marzari, N.. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 98:4(2007). [10.1103/PhysRevLett.98.046402]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/261391
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