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Wannier Functions from Landau Functions?
Author(s) -
Wannier G. H.
Publication year - 1984
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221210219
Subject(s) - wannier function , transformation (genetics) , landau quantization , physics , magnetic field , gauge (firearms) , mathematics , lattice (music) , wave function , square (algebra) , bloch wave , set (abstract data type) , square lattice , field (mathematics) , mathematical analysis , quantum mechanics , condensed matter physics , pure mathematics , computer science , geometry , history , biochemistry , chemistry , archaeology , acoustics , ising model , gene , programming language
It is well known that the set of functions in a Bloch band is equivalent to copies of a single function placed on a lattice. The possibility of establishing a similar relation in the presence of a magnetic field is investigated. Landau ground state wave functions for the symmetric gauge placed on a square net serve as trial objects. The result is equivocal. It is proved that the standard procedures of the Bloch—Wannier transformation are feasible for some fields, but impossible for other fields. Both sets of fields are infinite and all members of the second set are smaller than those on the first. The resulting situation is discussed.