Superconductivity with Rashba spin-orbit coupling and magnetic field.

Two-dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin-orbit coupling, which is tunable by a transverse electric field. Ferromagnetism near the interface can simultaneously induce strong local magnetic fields. This combination of spin-orbit coupling and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both the Bardeen-Cooper-Schrieffer superconductor with inter-band pairing and a mixed parity state with finite-momentum intra-band pairing. We present a phase diagram for the superconducting groundstates and analyze the density of states, the spectra, and the momentum distribution functions of the different phases. The results are discussed in the context of superconductivity and ferromagnetism at LaAlO3-SrTiO3 interfaces and superconductors with broken inversion symmetry.