Evolution of topological superconductivity by orbital-selective confinement in oxide nanowires

We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with a finite lateral width in the presence of an in-plane external magnetic field. We employ a microscopic description that is based on a three-band electronic model including both the atomic spin-orbit coupling and the inversion asymmetric potential at the interface between oxide band-gap insulators. We consider amplitudes of the pairing gap, spin-orbit interactions, and electronic parameters that are directly applicable to nanowires of LaAlO3-SrTiO3. The lateral confinement introduces a splitting of the d orbitals that alters the orbital energy hierarchy and significantly affects the electron filling dependence of the topological phase diagram. Due to the orbital directionality of the t2g states, we find that in the regime of strong confinement the onset of topological phases is pinned at electron filling where the quasiflat heavy bands start to get populated. The increase of the nanowire thickness leads to a changeover from a sparse-to-dense distribution of topologically nontrivial domains which occurs at the crossover associated with the orbital population inversion. These findings are corroborated by a detailed analysis of the most favorable topological superconducting phases in the electron doping-magnetic field plane highlighting the role of orbital-selective confinement.