Inhomogeneous superconductivity in (001), (110), and (111) KTaO${}_3$ two-dimensional electronic gases: effect of electronic confinement on the transition temperature

Abstract

Experimental observations on KTaO${}_3$ superconductivity report widely different critical temperatures with a clear hierarchy among different crystallographic orientations. Accounting for the first time for spatial confinement, we connect the inhomogeneous superconducting order parameter with the spatial extent of the two-dimensional electron gas. We reproduce the observed hierarchy within a unified framework, based on a self-consistent tight-binding slab model with local spin-singlet $s$-wave pairing. The methods developed here can readily be extended to include more general interaction models, while still consistently including the characteristic spatial structure of the electron gas.

21 pages, 11 figures