Nonreciprocal charge transport and subharmonic structure in voltage-biased Josephson diodes

We study charge transport in voltage-biased single-channel junctions involving helical superconductors with finite Cooper pair momentum. For a Josephson junction, the equilibrium current-phase relation shows a superconducting diode effect: the critical current depends on the propagation direction. We formulate a scattering theory for voltage-biased Josephson diodes and show that multiple Andreev reflection processes cause a rich subharmonic structure in the DC current-voltage curve at low temperatures and small voltages due to Doppler shifts of the spectral gap. In the current-biased case, the diode efficiency has maximal rectification efficiency $\eta_0\approx 0.4$ for this model. In the voltage-biased case, however, the rectification efficiency can reach the ideal value $\eta=1$. We also discuss charge transport for NS junctions between a normal metal and a helical superconductor and comment on related models with spin-orbit interactions and magnetic Zeeman fields.