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The intrinsic spin Hall conductivity of a two-dimensional gas confined toSrTiO$_3$, such as occurs at an LaAlO$_3$/SrTiO$_3$ interface, is calculatedfrom the Kubo formula. The effect of strain in the [001] (normal to the quantumwell direction) and the [111] direction is incorporated into a fulltight-binding Hamiltonian. We show that the spin-charge conversion ratio can besignificantly altered through strain and gate voltage by tuning the chemicalpotential. Strain direction is also a significant factor in the spin Hallresponse as this direction affects the alignment of the conduction bands.

Strain Engineering of the Intrinsic Spin Hall Conductivity in a SrTiO$_3$ Quantum Well