Numerical construction of Wannier functions through homotopy

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Date
2019
Link to item file
https://hal.archives-ouvertes.fr/hal-01955842
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Wannier functions; Kane-Mele model
Journal issue
Journal of Mathematical Physics
Volume
60
Number
3
Publication date
2019
Publisher
American Institute of Physics
DOI
http://dx.doi.org/10.1063/1.5085753
URI
https://basepub.dauphine.fr/handle/123456789/18673
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Author
Gontier, David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Levitt, Antoine
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Siraj-Dine, Sami
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Type
Article accepté pour publication ou publié
Abstract (EN)
We provide a mathematically proven, simple and efficient algorithm to build localised Wannier functions, with the only requirement that the system has vanishing Chern numbers. Our algorithm is able to build localised Wannier for topological insulators such as the Kane-Mele model. It is based on an explicit and constructive proof of homotopies for the unitary group. We provide numerical tests validating the methods for several systems, including the Kane-Mele model.