Superconductivity has been observed for the 2D electron gas (2DEG) at the interface of ${\mathrm{KTaO}}_3$ with other oxides, with a transition temperature about an order of magnitude higher than its $3d$ cousin ${\mathrm{SrTiO}}_3$. The superconducting transition temperature is strongly dependent on the orientation of the interface. Motivated by this observation, we study pairing due to the exchange of the soft transverse optic phonon mode characteristic of quantum paraelectrics and use the resulting theory to comment on the nature of superconductivity of this 2DEG. We find (1) an orientation dependence consistent with experiment along with an anisotropic gap function, but (2) a BCS coupling constant that is smaller than needed and so must be augmented by contributions from other phonons to be consistent with the observed values of $T_c$.

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• Electron-phonon coupling
• Pairing mechanisms
• Superconductivity
• Heterostructures
• Oxides
• Perovskites
• BCS theory