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Best Localized Symmetry‐Adapted Wannier Functions of the Diamond Structure
Author(s) -
Teichler H.
Publication year - 1971
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.2220430132
Subject(s) - wannier function , wave function , bloch wave , lattice (music) , orthogonality , symmetry (geometry) , unitary state , tetrahedron , physics , quantum mechanics , matrix (chemical analysis) , mathematics , mathematical physics , chemistry , geometry , chromatography , political science , acoustics , law
By application of proper unitary matrices the four Bloch functions of each bandgroup with equal wave vector k are transformed into modified Bloch functions in such a way that the resulting four sets of Wannier functions are adapted to the tetrahedral symmetry of the lattice. The Wannier functions behave like the “equivalent MO's” of the tight‐binding approximation (but with vanishing non‐orthogonality integrals). Furthermore, we give explicitely those phases of the Bloch functions that lead to best localized Wannier functions. Values of energy matrix elements between these functions are determined for Ge and Si.