Superconducting diode effect in Ising superconductors

We study the superconducting diode effect (SDE) in an Ising superconductor with broken basal mirror symmetry in a parallel magnetic field. We show that in the presence of a small Rashba spin splitting, $\Delta_R$, the dominant Ising spin-orbit coupling ($\Delta_I >> \Delta_R$) dramatically enhances the SDE efficiency compared to a Rashba superconductor with $\Delta_I = 0$ and the same $\Delta_R$. The suppression of the SDE for $\Delta_I = 0$ at $\Delta_R$ much larger than the critical temperature ($T_c$) is accidental. At $\Delta_R << T_c$, the SDE efficiency is small because, to linear order, $\Delta_R$ can be removed by a gauge transformation. These two factors -- the accidental suppression of the SDE at large $\Delta_R$ and the systematic suppression at small $\Delta_R$ -- are eliminated by Ising spin-orbit coupling. As a result, SDE efficiency is substantially enhanced for $\Delta_I >> \Delta_R \neq 0$.