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, ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}$, the dominant Ising spin-orbit coupling (${\mathrm{\ensuremath{\Delta}}}_{\text{I}}\ensuremath{\gg}{\mathrm{\ensuremath{\Delta}}}_{\text{R}}$) dramatically enhances the SDE efficiency compared to a Rashba superconductor with ${\mathrm{\ensuremath{\Delta}}}_{\text{I}}=0$ and the same ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}$. The suppression of the SDE for ${\mathrm{\ensuremath{\Delta}}}_{\text{I}}=0$ at ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}$ much larger than the critical temperature (${T}_{\text{c}}$) is accidental. At ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}\ensuremath{\ll}{T}_{\text{c}}$, the SDE efficiency is small because, to linear order, ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}$ can be removed by a gauge transformation. These two factors---the accidental suppression of the SDE at large ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}$ and the systematic suppression at small ${\mathrm{\ensuremath{\Delta}}}_{\text{R}}$---are eliminated by Ising spin-orbit coupling. As a result, SDE efficiency is substantially enhanced for ${\mathrm{\ensuremath{\Delta}}}_{\text{I}}\ensuremath{\gg}{\mathrm{\ensuremath{\Delta}}}_{\text{R}}\ensuremath{\ne}0$.