Quasi-two-dimensional (2D) systems, such as an electron gas confined in a quantum well, are important model systems for many-body theories, and we are interested in studying collective excitations in such systems using a linear-response approach based on time-dependent density-functional theory. In the second chapter, we consider a non-spin-polarized electron gas confined in a quantum well, and we study three- to two-dimensional crossover in time-dependent density-functional theory. Earlier studies of the crossover from 3D to 2D in groundstate density-functional theory showed that local and semilocal exchange-correlation functionals which are based on the 3D electron gas are appropriate for wide quantum wells, but eventually break down as the 2D limit is approached. We now consider the dynamical case and study the performance of various linear-response exchange kernels in time-dependent density-functional theory. We compare approximate local, semilocal, and orbital-dependent exchange kernels, and analyze their performance for inter- and intrasubband plasmons as the quantum wells approach the 2D limit. 3D (semi)local exchange functionals are found to fail for quantum well widths comparable to the 2D Wigner-Seitz radius r[superscript s 2D], which implies in practice that 3D local exchange remains valid in the quasi-2D dynamical regime for typical quantum well parameters, except for very low densities. In the third chapter, we consider a partially spin-polarized electron gas in a semiconductor quantum well in the presence of Rashba and Dresselhaus spin-orbit coupling. Larmor's theorem holds for magnetic systems that are invariant under spin rotation. In the presence of spin-orbit coupling this invariance is lost and Larmor's theorem is broken: for systems of interacting electrons, this gives rise to a subtle interplay between the spin-orbit coupling acting on individual single-particle states and Coulomb many-body effects. Using a linear-response approach based on time-dependent density-functional theory in our system, we calculate the dispersions of spin-flip waves. We obtain analytic results for small wave vectors and up to second order in the Rashba and Dresselhaus coupling strengths [alpha] and [beta]. Comparison with experimental data from inelastic light scattering allows us to extract [alpha] and [beta] as well as the spin-wave stiffness very accurately. We find significant deviations from the local density approximation for spin-dependent electron systems. In the last chapter, we consider a two-dimensional electron gas (2DEG) with equal-strength Rashba and Dresselhaus spin-orbit coupling. This system sustains persistent helical spin-wave states, which have remarkably long lifetimes. In the presence of an in-plane magnetic field, there exist single-particle excitations that have the character of propagating helical spin waves. For magnon-like collective excitations, the spin-helix texture reemerges as a robust feature, giving rise to a decoupling of spin-orbit and electronic many-body effects. We prove that the resulting spin-flip wave dispersion is the same as in a magnetized 2DEG without spin-orbit coupling, apart from a shift by the spin-helix wave vector. The precessional mode about the persistent spin-helix state is shown to have an energy given by the bare Zeeman splitting, in analogy with Larmor's theorem. We also discuss ways to observe the spin-helix Larmor mode experimentally.
Quasi-Low-Dimensional Electron Gas with One Populated Band as a Testing Ground for Time-Dependent Density-Functional Theory of Mesoscopic Systems
