Impact of spin-orbit interaction on the phase diagram and anisotropy of the in-plane critical magnetic field at the superconducting LaAlO3/SrTiO3 interface

The two-dimensional electron gas at the interface between ${\mathrm{LaAlO}}₃$ and ${\mathrm{SrTiO}}₃$ (LAO/STO) exhibits gate-tunable superconductivity with a characteristic domelike shape of the critical temperature (${T}_c$) in the phase diagram. As shown recently [Phys. Rev. B 102, 085420 (2020)], such an effect can be explained as a consequence of the extended $s\text{\ensuremath{-}}\mathrm{wave}$ symmetry of the gap within an intersite real space pairing scenario, leading to a good agreement between the experiment and theory. In this work, we turn to a detailed analysis of the influence of spin-orbit coupling on the LAO/STO phase diagram by considering separately the atomic component as well as the interorbital hopping induced by the broken inversion symmetry at the interface. In particular, we analyze the optimal carrier concentration for which the maximal ${T}_c$ is reached relative to the Lifshitz transition point. We find that the misalignment between the two can be significantly enhanced by the spin-orbit splitting of the bands, combined with the fact that superconductivity sets in when the Fermi level passes the anticrossing induced by the spin-orbital hybridization. In the presence of the external in-plane magnetic field, our calculations show fourfold anisotropy with the paramagnetic limit largely exceeded for ${B}_||$ directed along the high symmetry points [01] and [01]. The obtained electron concentration dependence of ${B}_c||$ reproduces the characteristic domelike shape reported in experiments and the estimated value of ${B}_c||$ corresponds to that measured experimentally.