Abstract
We have calculated an accurate exchange-correlation energy of a hole gas, including the complexities related to the valence band coupling as occurring in semiconductors like GaAs, but excluding the band warping. A parametrization for the dependence on the density and the ratio between light- and heavy-hole masses is given. We apply our results to a hole gas in an ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}$As quantum well and calculate the two-dimensional band structure and the band-gap renormalization. The inclusion of the valence band coupling in the calculation of the exchange-correlation potentials for holes and electrons leads to a much better agreement between theoretical and experimental data than when it is omitted.
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