Observation of Linear Scaling of Superconductivity with Crystal Orientation at a-LaAlO_{3}/KTaO_{3} Interfaces

The superconducting transition temperature T_{c} at KTaO_{3}-based oxide interfaces exhibits a dramatic dependence on crystallographic orientation, yet a unifying mechanism remains elusive. Here, we report a linear scaling between T_{c} and a single geometric parameter-the angle θ between the (hkl) plane and the (100) plane-across ten different orientations of amorphous-LaAlO_{3}/KTaO_{3} interfaces. Except for (100), all orientations exhibit two-dimensional superconductivity, with transition temperatures T_{c} ranging from ∼0.12 to 2.1 K. This linear θ-T_{c} scaling is robust against variations in growth temperature, device geometry, and transport configuration. By establishing the geometric orientation angle as a robust empirical scaling parameter for the superconducting transition, our results set a critical phenomenological benchmark for future microscopic theories of superconductivity in KTaO_{3}-based systems.