Geometric Control of Pairing: Universal Scaling of Superconductivity at KTaO3 Interfaces

The superconducting transition temperature Tc at KTaO3-based oxide interfaces exhibits a dramatic dependence on crystallographic orientation, yet a unifying principle has remained elusive. Here, we discover a universal linear scaling between Tc and a single geometric parameter - the angle {\theta} between the (hkl) plane and the (100) plane - across ten different orientations of LaAlO3/KTaO3 interfaces. With the exception of (100), all orientations exhibit two dimensional superconductivity, with transition temperatures Tc ranging from ~ 0.12 K to 1.9 K. This linear {\theta}-Tc scaling is robust against variations in growth temperature, device geometry, and transport configuration. By establishing geometric orientation as a direct control knob for pairing strength, our results impose a critical benchmark for microscopic theories of superconductivity in KTaO3-based systems.