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

## TL;DR

This paper investigates how orbital selective confinement in oxide nanowires influences the emergence of topological superconductivity, revealing the importance of orbital effects and nanowire thickness on topological phase stability.

## Contribution

It introduces a microscopic three-band model considering orbital effects and confinement, providing new insights into the conditions for topological phases in oxide nanowires.

## Key findings

- Topological phases are pinned at specific electron fillings related to heavy band population.
- Nanowire thickness causes a transition from sparse to dense topological domain distribution.
- Orbital selective confinement critically influences the topological phase diagram.

## Abstract

We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with 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 LaAlO$_3$-SrTiO$_3$. 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 $t_{2g}$-states, we find that in the regime of strong confinement the onset of topological phases is pinned at electron filling where the quasi flat heavy bands start to get populated. The increase of the nanowire thickness leads to a changeover from sparse-to-dense distribution of topologically non-trivial domains which occurs at the cross-over associated to 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.