Inhomogeneous superconductivity in (001), (110) and (111) KTaO${}_3$ two-dimensional electronic gas: $T_c$ driven from electronic confinement

We investigate superconductivity in KTaO${}_3$ (KTO)-based two-dimensional electron gases for the (001), (110), and (111) crystallographic orientations within a unified microscopic framework. Using a self-consistent tight-binding slab model, we determine the confinement potential, electronic structure, and orbital composition for each orientation, explicitly including inversion-symmetry-induced orbital Rashba couplings. Using a local spin-singlet s-wave pairing interaction, we find that the pronounced orientation dependence of the superconducting critical temperature primarily originates from differences in the spatial extent of the two-dimensional electron gas and the associated redistribution of the density of states at the Fermi level, rather than from changes in the pairing interaction. Our results provide a microscopic explanation for the experimentally observed orientation dependence of superconductivity at KTO-based interfaces.