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We compute the spin-Hall conductance in a multiband model describing thetwo-dimensional electron gas formed at a LaAlO3/SrTiO3 interface in thepresence of a finite concentration of impurities. Combining linear responsetheory with a systematic calculation of the impurity contributions to theself-energy, as well as to the vertex corrections of the relevant diagrams, werecover the full spin-Hall vs. sheet conductance dependence of LaAlO3/SrTiO3 asreported in Trier et al. [Nano Lett. 20, 395 (2020)], finding a very goodagreement with the experimental data below and above the Lifshitz transition.In particular, we demonstrate that the multiband electronic structure leads toonly a partial, instead of a complete, screening of the spin-Hall conductance,which decreases with increasing the carrier density. Our method can begeneralized to other two-dimensional systems characterized by a brokeninversion symmetry and multiband physics.

Spin-Hall Current and Nonlocal Transport in Ferromagnet-Free Multi-band models for SrTiO3-Based Nanodevices in the presence of impurities