  When an in-plane field is applied to a clean interface superconductor, a
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like phase is stabilized. This phase
has a $\mathrm{U}(1)\times\mathrm{U}(1)$ symmetry and, in principle, this
symmetry allows for flux carrying topological excitations different from
Abrikosov vortices (which are the simplest defects associated with $S^1 \to
S^1$ maps). However, in practice, largely due to electromagnetic and other
intercomponent interactions, such topological excitations are very rare in
superconducting systems. Here we demonstrate that a realistic microscopic
theory for interface superconductors, such as SrTiO$_3$/LaAlO$_3$, predicts an
unconventional magnetic response where the flux-carrying objects are skyrmions,
characterized by homotopy invariants of $S^2 \to S^2$ maps. Additionally, we
show that this microscopic theory predicts that stable fractional vortices form
near the boundary of these superconductors. It also predicts the appearance of
type-1.5 superconductivity for some range of parameters. Central to these
results is the assumption that the Rashba spin orbit coupling is much larger
than the superconducting gap.
