Collective excitations in symmetric p-type ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells

We present a calculation of the collective plasmon excitations in p-type ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells that is based on the random-phase approximation and, within the $\mathbf{k}\cdot \mathbf{p}$ model takes exactly into account band-structure effects and the strong dependence of the subband wave functions on the in-plane wave vector. For symmetrically modulation-doped wells, the subband structure in the Hartree approximation, plasmon dispersions, single-particle excitations, and energy-loss spectra at zero temperature are consistently calculated. In contrast to the corresponding n-type quantum wells, a multisubband approximation yields a strong coupling of the intra- and intersubband plasmons, even in symmetrical wells, and predicts the existence of an additional intersubband plasmon at finite wave vectors. These drastic differences between electron and hole quantum wells are attributed to the finite overlap between eigenfunctions belonging to different subbands and different in-plane wave vectors, which exists in hole but not in electron systems.