Spin-Orbit Coupling Effects in Strongly-Confined Electron Systems

We investigate theoretically spin-orbit coupling effects in low-dimensional electron systems. The consequences of introducing Rashba spin-orbit coupling into a two-dimensional electron system in the presence of additional strong lateral confinement and an external magnetic field are explored. The nature of the spin-orbital states in these systems and the resulting Berry phase effects are studied as a function of confinement geometry. The implications of these results are discussed in the context of recent experimental measurements of the properties of electrostatically-defined nanostructures in LaAlO$_{3}$/SrTiO$_{3}$ systems.