Criticality as a Universal Thermodynamic Requirement for Perfect Intrinsic Superconducting Diodes

Abstract

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 $ε= I_c^-/I_c^+$, where $I_c^\pm$ are critical current magnitudes in opposite directions with $I_c^+>I_c^-$ by convention, we show that $ε=0$ is impossible without fine-tuning, while $ε\to0$ 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 $ε$ 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 $ε$ near the transition is locked to known critical exponents.

Figures (2)

• Figure 1: Top: schematic $F(q)$; bottom: corresponding $j(q)$. A perfect diode without fine-tuning ($\epsilon=0$, left) requires $j(q)\!\ge\!0$ and hence a discontinuity of $F(q)$, while physical systems allow only $\epsilon\!\ll\!1$ (right), where continuity of $F(q)$ enforces a small negative-current region and an internal non-analyticity.
• Figure 2: $F(q)$ (top) and $j(q)$ for the Ising-coupled superconductor. Blue curves show a generic finite-diode regime with parameters $F_0=1$, $K_+=1$, $K_-=0.7$, $\gamma_+=0.8$, $\gamma_-=0.35$, yielding $\epsilon=j_c^-/j_c^+\approx 0.41$. Orange curves show a near-perfect diode regime with $F_0=1$, $K_+=1$, $K_-=3\times10^{-3}$, $\gamma_+=\gamma_-=0.01$, yielding $\epsilon\approx 3\times10^{-3}$. Vertical dashed lines indicate the critical momenta $q_c^\pm$ at which superconductivity is destroyed, and horizontal dotted lines in the lower panel mark the corresponding critical currents $j_c^\pm$.