We theoretically study the superconducting properties of multiband two-dimensional transition metal oxide superconductors by analyzing not only the role played by conventional singlet pairings, but also by the triplet order parameters, favored by the spin-orbit couplings present in these materials. In particular, we focus on the two-dimensional electron gas at the (001) interface between ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ band insulators where the low electron densities and the sizable spin-orbit couplings affect the superconducting features. Our theoretical study is based on an extended superconducting mean-field analysis of the typical multiband tight-binding Hamiltonian, as well as on a parallel analysis of the effective electronic bands in the low-momentum limit, including static on-site and intersite intraband attractive potentials under applied magnetic fields. The presence of triplet pairings is able to strongly reduce the singlet order parameters which, as a result, are no longer a monotonic function of the charge density. The interplay between the singlet and the triplet pairings affects the dispersion of quasiparticle excitations in the Brillouin zone and also induces anisotropy in the superconducting behavior under the action of an in-plane and of an out-of-plane magnetic fields. Finally, nontrivial topological superconducting states become stable as a function of the charge density, as well as of the magnitude and of the orientation of the magnetic field. In addition to the chiral, time-reversal breaking, topological superconducting phase, favored by the linear Rashba couplings and by the on-site attractive potentials in the presence of an out-of-plane magnetic field, we find that a time-reversal invariant topological helical superconducting phase is promoted by nonlinear spin-orbit couplings and by the intersite attractive interactions in the absence of magnetic field.

• Received 2 July 2021
• Revised 29 September 2021
• Accepted 30 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.134509