Abstract
An eight-band k\ensuremath{\cdot}p model of the electronic states near the \ensuremath{\Gamma} point of a strained zinc-blende semiconductor is renormalized using L\"owdin perturbation theory. The renormalization leads to matrices of reduced dimensionality, 2\ifmmode\times\else\texttimes\fi{}2, 4\ifmmode\times\else\texttimes\fi{}4, and 2\ifmmode\times\else\texttimes\fi{}2, for the conduction, light- and heavy-hole, and spin-orbit split-off bands, respectively. The reduced dimensionality of these matrices allows us to obtain analytic dispersion relations in the presence of small but arbitrary strains. Comparison of the analytic dispersion relations is made to those obtained by numerically diagonalizing the eight-band model for the case of biaxially strained and unstrained GaAs.
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