Collective Excitations and Exchange Instabilities in Semiconductor Quantum Wells

Calculations of far-infrared optical absorption for Al_{x}Ga_ {1-x}As perturbed parabolic quantum wells (PQW) with a magnetic field in the plane of the electron slab are presented within the linear response theory. We study two different types of samples. The first type consists of PQWs with controlled delta-planar perturbations. These samples were recently used in an experimental study aimed at measuring the magneto-roton dispersion relation of a three dimensional electron gas. We construct a magneto-plasmon dispersion relation and critically discuss whether the experimental results are consistent with the bulk magneto-roton picture originally invoked to understand the data. The second system is an asymmetric parabolic well; we study the absorption spectra as function of the areal density and compare them with recent experimental results. We also study, employing the time-dependent local -density approximation (TDLDA), the elementary excitation energies and the associated inelastic light scattering spectra of a strongly coupled two-component plasma in a double quantum well system. We find, consistent with the results of a recent experimental Raman scattering study, that the intersubband spin density excitations tend to merge with the single particle excitations (i.e. the excitonic shift decreases monotonically) as the Fermi energy increases beyond the symmetric-antisymmetric energy gap. On the other hand, we predict that exchange-correlation induced many-body excitonic vertex correction may lead to an instability in the normal ground state of this system by suppressing the symmetric-antisymmetric gap at low but accessible ( {~}0.7 times 10^{11} cm^ {-2}) electron densities. We predict as a consequence a novel electronic phase transition to, possibly, a new many-body triplet excitonic liquid ground state. Finally, we study the ferromagnetic transition in quasi-two-dimensional electron systems, employing the local-spin density (LSD) formalism. We conclude that the intersubband spin-density instability reported before in this dissertation does not correspond to the ferromagnetic transition. We also apply the LSD formalism to single square quantum wells and determine the dependence of the critical areal density on the well width.