Theory of an infinitely anisotropic phase of a two-dimensional superconductor

We propose a simple model of a two-dimensional ``locally smectic superconductor’’ that exhibits power-law non-linear I-V characteristics with different powers for current applied in two orthogonal directions. We discuss the potential relevance of this model to recent experimental findings on interfacial superconductivity in EuO/KTaO${}_3$(110) (Nat. Phys. 20, 957 (2024)), where the apparent critical temperature ($T_c$) has been shown experimentally to depend on the current direction.