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Magnetic translation group for a finite system
Author(s) -
Wal A.
Publication year - 2005
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.200460030
Subject(s) - brillouin zone , square lattice , magnetic field , condensed matter physics , periodic boundary conditions , lattice (music) , physics , magnetic flux , translation (biology) , electron , crystal system , crystal structure , boundary value problem , mathematics , quantum mechanics , chemistry , biochemistry , messenger rna , acoustics , ising model , crystallography , gene
A magnetic translation group (MTG) for a finite system, with the Born‐Karman periodic boundary conditions, is introduced and its properties are described. We consider an itinerant electron, hopping to the nearest neighbours in a square lattice. Compatibility conditions for consistency of quantizations of the magnetic field with the periodic conditions impose severe restrictions for admissible distributions of quanta of magnetic flux. These restrictions are expressed in the structure of appropriate MTG, which defines the magnetic Brillouin zone. The energy band structure, analogous to the Landau levels for the free electron case, emerges from irreducible representations of MTG, their degeneracies and appropriate correlations with the crystal structure. An example of finite 4 × 4 crystal in quantized magnetic field is discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)