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Symmetry 2015, 7(2), 561-598; https://doi.org/10.3390/sym7020561

Group Theory of Wannier Functions Providing the Basis for a Deeper Understanding of Magnetism and Superconductivity

Institut für Materialwissenschaft, Materialphysik, Universität Stuttgart, D-70569 Stuttgart, Germany
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Academic Editor: Gervais Chapuis
Received: 6 January 2015 / Revised: 27 April 2015 / Accepted: 27 April 2015 / Published: 5 May 2015
(This article belongs to the Special Issue Crystal Symmetry and Structure)
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Abstract

The paper presents the group theory of optimally-localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all of the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into optimally-localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M or to a subgroup of G or M. In this context, the paper considers usual, as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors (Ekkehard Krüger) in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the optimally-localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly-correlated localized electrons makes clear predictions of whether or not the system can possess superconducting or magnetic eigenstates. View Full-Text
Keywords: Wannier functions; spin-dependent Wannier functions; magnetism; superconductivity; group theory Wannier functions; spin-dependent Wannier functions; magnetism; superconductivity; group theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Krüger, E.; Strunk, H.P. Group Theory of Wannier Functions Providing the Basis for a Deeper Understanding of Magnetism and Superconductivity. Symmetry 2015, 7, 561-598.

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