Geometric Rashba Control of Polar Pairing at a-LaAlO$_3$/KTaO$_3$ Interfaces

Abstract

At amorphous-LaAlO$_3$/KTaO$_3$ interfaces, superconductivity coexists with switchable polar nanoregions (PNRs), and $T_c$ depends quasi-linearly on crystallographic orientation. We propose a minimal theoretical framework in which overdamped PNR fluctuations mediate pairing, while geometric Rashba coupling controls its angular dependence. Within a reduced isotropic helicity-band description, the leading dynamic Rashba vertex scales as $\sin\theta$, where $\theta$ is the angle between the interface normal and the $[100]$ axis, yielding $\lambda(\theta)=\lambda_0+C\sin^2\theta$. Numerical Matsubara--Eliashberg solutions show that this nonlinear mapping reproduces the observed quasi-linear $T_c(\theta)$. Because the Rashba-activated polar channel is amplified by the large atomic spin-orbit coupling of Ta $5d$ orbitals, the framework also offers a parametric---not yet quantitative---rationale for why KTaO$_3$ interfaces are both more orientation-sensitive and higher-$T_c$ than their SrTiO$_3$ counterparts.