| Summary: | Motivated by the discovery of superconductivity in KTaO _3 -based heterostructures, we study a pairing mechanism based on spin-orbit assisted coupling between the conduction electrons and the ferroelectric (FE) modes present in the material. We use ab initio frozen-phonon computations to show a linear-in-momentum Rashba-like coupling with a strong angular dependence in momentum for the lower $j = 3/2$ manifold, deviating from the conventional isotropic Rashba model. This implies the Rashba-like interaction with the polar modes has substantial L = 3 cubic harmonic corrections, which we quantify for each electronic band. The strong anisotropy of the Rashba interaction is captured by a microscopic toy model for the $t_{2g}$ electrons. We find its origin to be the angular dependence in electronic momentum imposed by the kinetic term on the degenerate $j = 3/2$ manifold. A comparison between the toy model and ab initio results indicates that additional symmetry allowed terms beyond odd-parity spin-conserving inter-orbital hopping processes are needed to describe the Rashba-like polar interaction between the electrons and the soft FE mode.
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