We consider a real periodic Schrödinger operator and a physically relevant family of m ≥ 1 Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension d ≤ 3, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

Construction of Real-Valued Localized Composite Wannier Functions for Insulators / Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - STAMPA. - 17:1(2016), pp. 63-97. [10.1007/s00023-015-0400-6]

Construction of Real-Valued Localized Composite Wannier Functions for Insulators

FIORENZA, DOMENICO;Domenico Monaco;PANATI, GIANLUCA
2016

Abstract

We consider a real periodic Schrödinger operator and a physically relevant family of m ≥ 1 Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension d ≤ 3, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.
electronic-structure; Bloch electrons; dynamics
01 Pubblicazione su rivista::01a Articolo in rivista
Construction of Real-Valued Localized Composite Wannier Functions for Insulators / Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - STAMPA. - 17:1(2016), pp. 63-97. [10.1007/s00023-015-0400-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/778319
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