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 approximate to 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 normal -superconducting junctions between a normal metal and a helical superconductor and comment on related models with spin -orbit interactions and magnetic Zeeman fields.