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Manetoelectronic Denisty of States for a Model Crystal
Author(s) -
Wannier G. H.,
Obermair G. M.,
Ray R.
Publication year - 1979
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.2220930139
Subject(s) - eigenvalues and eigenvectors , density of states , magnetic field , landau quantization , quantum , physics , condensed matter physics , quantum mechanics , simple (philosophy) , quantum state , state (computer science) , field (mathematics) , wave function , statistical physics , mathematics , pure mathematics , philosophy , epistemology , algorithm
As shown previously, a first principles calculation of the quantum states of a crystalline electron in a magnetic field leads to a difference equation. The splitting of one Landau level by a particularly simple crystalline potential has been extensively studied. This paper proceeds further for this model case: All quantum numbers characterizing each individual state are exhaustively defined. One of them is discrete and the other two are contionous phases. It is shown that are ene gy eigenvalues depend only on the sum of the cosines of these phases. These properties permit the calculation of the density of states, which still shows as a function of the magnetic field the well known erratic behaviour. Physically understandable rusults are obtained, however, for the integrated density of states: at two magnetic fields which are numerically nearly equal, the intergrated densities of states of states are numerically almost indistinguishable although very different analytically.