Criticality as a Universal Thermodynamic Requirement for Perfect Intrinsic Superconducting Diodes

Superconducting diodes promise dissipation-less rectification, yet intrinsic platforms invariably have very low efficiencies. We reveal a fundamental thermodynamic origin of this behavior that is independent of microscopic details. Denoting $\epsilon = I_c^-/I_c^+$, where $I_c^\pm$ are critical current magnitudes in opposite directions with $I_c^+>I_c^-$ by convention, we show that $\epsilon=0$ is impossible without fine-tuning, while $\epsilon\to0$ can occur but only upon tuning to a critical point \emph{within} the superconducting state. Away from such internal instabilities, using general Landau theory, we derive a lower bound on $\epsilon$ that limits intrinsic diode performance. We illustrate these ideas in a minimal superconductor-Ising model, where the strong nonreciprocity can be seen explicitly. In particular, if the internal transition is continuous, we show that the scaling of $\epsilon$ near the transition is locked to known critical exponents.