Relation between the interband dipole and momentum matrix elements in semiconductors
It is shown that a frequently used relation between the interband momentum and dipole matrix elements (shortened to the "p-r relation") in semiconductors acquires an additional correction term if applied to finite-volume crystals treated with periodic boundary conditions. The correction te...
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Veröffentlicht in: | Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2013-03, Vol.87 (12), Article 125301 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | It is shown that a frequently used relation between the interband momentum and dipole matrix elements (shortened to the "p-r relation") in semiconductors acquires an additional correction term if applied to finite-volume crystals treated with periodic boundary conditions. The correction term, which is a generalization of the one obtained by Yafet for infinite crystals, does not vanish in the limit of infinite volume. We illustrate this with numerical examples for bulk GaAs and GaAs superlattices. Finally, we discuss the p-r relation for nanostructures in the envelope function approximation and show that the cell-envelope factorization of the nanostructure dipole matrix element into a cell-matrix element and an envelope overlap integral involves the cell gradient rather than the cell dipole matrix element. |
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ISSN: | 1098-0121 1550-235X |
DOI: | 10.1103/PhysRevB.87.125301 |