  We investigate the impact of impurity scattering on superconductivity in an
anisotropic multi-orbital model with spin-orbit coupling which describes the
electron fluid at two-dimensional oxide interfaces. As the pairing mechanism is
under debate, both conventional and unconventional superconducting states are
analyzed. We consider magnetic and nonmagnetic spin-dependent intra- and
interorbital scattering and discuss possible microscopic realizations leading
to these processes. It is found that, for magnetic disorder, the unconventional
superconductor is protected against interband scattering and, thus, more robust
than the conventional condensate. In case of nonmagnetic impurities, the
conventional superconductor is protected as expected from the Anderson theorem
and the critical scattering rate of the unconventional state is enhanced by a
factor of four due to the spin-orbit coupling and anisotropic masses in oxide
interfaces.
