Energy Spectra and Spin Properties of Electrons in Spin-Orbit Superlattice Quantum Wires

We calculate the energy spectra of electrons in quantum wires with spatially uniform and modulated spin-orbit coupling. The effects of Rashba spin-orbit coupling arising from asymmetric confinement in perpendicular and lateral directions with respect to the plane containing the wire are considered. We investigate the resulting interplay of strong lateral confinement, a periodic one-dimensional superlattice potential, and spin-orbit coupling in two orthogonal directions. The implications for the spin-dependent properties of electrons confined within these quantum wires are discussed. A potential realization of such systems within narrow nanowires at the interface of LaAlO$_{3}$/SrTiO$_{3}$ heterostructures is also described.