Dielectric function of the semiconductor hole gas

The semiconductor hole gas can be viewed as the companion of the classic interacting electron gas with a more complicated band structure and plays a crucial role in the understanding of ferromagnetic semiconductors. Here we study the dielectric function of a homogeneous hole gas in zinc blende III–V bulk semiconductors within random phase approximation with the valence band being modeled by Luttinger’s Hamiltonian in the spherical approximation. In the static limit we find a beating of Friedel oscillations between the two Fermi momenta for heavy and light holes, while at large frequencies dramatic corrections to the plasmon dispersion occur. Copyright c © EPLA, 2010 The interacting electron gas, combined with a homogeneous neutralizing background, is one of the paradigmatic systems of many-body physics [1–3]. Although it is obviously a grossly simplified model of a solid-state system, its predictions provide a good description of important properties of three-dimensional bulk metals and, in the regime of lower carrier densities, of n-doped semiconductors where the electrons reside in the s-type conduction band. On the other hand, in a p-doped zinc blende III–V semiconductor such as GaAs, the defect electrons or holes occupy the p-type valence band whose more complex band structure can be expected to significantly modify the electronic properties. Moreover, the most intensively studied ferromagnetic semiconductors such as Mn-doped GaAs are in fact p-doped with the holes playing a key role in the occurrence of carrier-mediated ferromagnetism among the localized Mn magnetic moments [4]. Thus, such p-doped bulk semiconductor systems lie at the very heart of the still growing field of spintronics [5], and therefore it appears highly desirable to gain a deeper understanding of their many-body physics. Following the above motivations, we investigate in the present letter the dielectric function of the homogeneous hole gas in p-doped zinc blende III–V bulk semiconductors within random phase approximation (RPA) [1–3]. The single-particle band structure of the valence band is modeled by Luttinger’s Hamiltonian in the spherical approximation [6]. In previous work we have studied the same system using the Hartree-Fock (HF) approximation [7]. (a)E-mail: [email protected] A key result here is the observation that in a fully self-consistent solution of the HF equations the Coulomb repulsion among holes modifies the Fermi momenta compared to the non-interacting situation. In particular, the self-consistent solution of the HF equations is not equivalent to first-order perturbation theory as it the case for the ordinary electron gas [1–3]. Moreover, we mention recent studies of the dielectric function in two-dimensional electron systems with spin-orbit coupling [8,9] and twodimensional hole systems [10]. Other recent related studies have dealt with the dielectric function of planar graphene sheets where an effective spin is incorporated by the sublattice degree of freedom [11,12]. Luttinger’s Hamiltonian describing heavyand lighthole states around the Γ in III–V zinc blende semiconductors reads [6] H= 1 2m0 (( γ1 + 5 2 γ2 ) p 2 − 2γ2( p · S ) )