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An asymmetric triangular potential well provides the simplest model for theconfinement of mobile electrons at the interface between two insulating oxides,such as LaAlO_3 and SrTiO_3 (LAO/STO). These electrons have been recently shownto exhibit a large spin-orbit coupling of the Rashba type, i.e., linear in thein-plane momentum. In this paper we study the intrinsic spin Hall effect due toRashba coupling in an asymmetric triangular potential well. Besides splittingeach subband into two branches of opposite helicity, the spin-orbit interactioncauses the wave function in the direction perpendicular to the plane of thequantum well (the z direction) to depend on the in-plane wave vector k. Incontrast to the extreme asymmetric case, i.e., the wedge-shaped quantum well,for which the intrinsic spin Hall effect vanishes due to vertex corrections, wefind that the asymmetric well supports a non-vanishing intrinsic spin Hallconductivity, which increases in magnitude as the well becomes more symmetric.The spin Hall conductivity is found to be proportional to the square of thespin-orbit coupling constant and, in the limit of low carrier density, dependsonly on the effective mass renormalization associated with the k-dependence ofthe wave functions in the z direction. Its origin lies in the non-vanishingmatrix elements of the spin current between subbands corresponding to differentstates of quantized motion perpendicular to the plane of the well.

Intrinsic Spin Hall Effect at Oxide Interfaces: a Simple Model