Geometric Rashba Control of Polar Pairing at LaAlO${}_3$/KTaO${}_3$ Interfaces

At LaAlO${}_3$/KTaO${}_3$ interfaces, the superconducting $T_c$ exhibits a striking quasi-linear dependence on crystallographic orientation, coexisting with switchable polar nanoregions (PNRs). We propose an effective minimal Eliashberg framework in which overdamped PNR fluctuations provide the pairing glue, while geometric Rashba coupling controls its angular dependence. Within a reduced isotropic helicity-band description, the dynamic Rashba vertex scales as $\sin (\theta )$, yielding a pairing strength $\lambda (\theta )={\lambda }_0+C{\sin }^2(\theta )$. Exact Matsubara-Eliashberg numerical solutions show that this non-linear mapping naturally yields the same qualitative quasi-linear $T_c(\theta )$ dependence within the reduced model. Because the Rashba-activated polar channel is amplified by the large atomic spin-orbit coupling of Ta $5d$ orbitals, the same framework also rationalizes why KTaO${}_3$ interfaces exhibit both a much stronger orientational dependence and a substantially higher $T_c$ scale than their SrTiO${}_3$ counterparts.