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We study the homogeneous interacting hole gas in $p$-doped bulk III-Vsemiconductors. The structure of the valence band is modelled by Luttinger'sHamiltonian in the spherical approximation, giving rise to heavy and light holedispersion branches, and the Coulomb repulsion is taken into account via aself-consistent Hartree-Fock treatment. As a nontrivial feature of the model,the self-consistent solutions of the Hartree-Fock equations can be found in analmost purely analytical fashion, which is not the case for other types ofeffective spin-orbit coupling terms. In particular, the Coulomb interactionrenormalizes the Fermi wave numbers for heavy and light holes. As aconsequence, the ground state energy found in the self-consistent Hartree-Fockapproach and the result from lowest-order perturbation theory do not agree. Wediscuss the consequences of our observations for ferromagnetic semiconductors,and for the possible observation of the spin-Hall effect in bulk $p$-dopedsemiconductors. Finally, we also investigate elementary properties of thedielectric function in such systems.Comment: 9 pages, 5 figures, title slightly changed in the course of editorial  process, a few references added, version to appear in Phys. Rev.

physical review. b, condensed matter and materials physics

Theoretical study of interacting hole gas in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-doped bulk III-V semiconductors

Theoretical study of interacting hole gas inp-doped bulk III-V semiconductors