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Overlap functions in planar crystals

Authors
Journal
Journal of Physics and Chemistry of Solids
0022-3697
Publisher
Elsevier
Publication Date
Volume
24
Issue
12
Identifiers
DOI: 10.1016/0022-3697(63)90089-1

Abstract

Abstract The overlap function F 2 = ¦∫ u ∗ k ( r) u k' ( r)d r¦ 2 is evaluated for several values of k and a wide mesh of points k', where u k is the modulating part of the Bloch wave function for a π-electron in the valence or conduction band, in planar boron nitride and graphite. It is found that for boron nitride, if u k and u k , are in the same band and ¦ k — k'¦ is less than a quarter of the radius of the Brillouin zone, then F 2 usually lies between 0.9 and 1. In graphite, however, F 2 behaves more erratically because the top of the valence band is degenerate with the bottom of the conduction band; a theoretical analysis of this behaviour is also presented.

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