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.
Highlights
The picture of strongly-correlated localized or nearly-localized electrons is the basis of a successful theoretical description of both high-temperature superconductivity and magnetism
The physical power of this natural method of producing closed complexes of energy bands in suitable band structures is corroborated by two observations: (i) Materials possessing a magnetic structure with the magnetic group M possess a closed, narrow and roughly half-filled complex of energy bands in their band structure whose Bloch functions can be unitarily transformed into optimally-localized Wannier functions that are symmetry-adapted to the magnetic group M
(ii) Both normal and high-temperature superconductors possess a closed, narrow and roughly half-filled complex of energy bands in their band structure whose Bloch spinors can be unitarily transformed into optimally-localized spin-dependent Wannier functions that are symmetry-adapted to the space group G of the material
Summary
The picture of strongly-correlated localized or nearly-localized electrons is the basis of a successful theoretical description of both high-temperature superconductivity and magnetism (see, e.g., [1,2,3] and the citations given there). (i) Materials possessing a magnetic structure with the magnetic group M possess a closed, narrow and roughly half-filled complex of energy bands in their band structure whose Bloch functions can be unitarily transformed into optimally-localized Wannier functions that are symmetry-adapted to the magnetic group M. (ii) Both normal and high-temperature superconductors (and only superconductors) possess a closed, narrow and roughly half-filled complex of energy bands in their band structure whose Bloch spinors can be unitarily transformed into optimally-localized spin-dependent Wannier functions that are symmetry-adapted to the (full) space group G of the material. These energy bands form a “superconducting band”; see Definition 22. Though we shall define the two terms “magnetic” and “superconducting” band (Definitions 16 and 22, respectively), which are related to the nonadiabatic Heisenberg model, the presented group theory is independent of any physical model of magnetism or superconductivity
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
