Abstract: Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Common lore says that these currents become nonreciprocal (i.e., they depend on the direction of the bias current) if both time-reversal and inversion symmetry are absent. This so-called Josephson diode effect is used to experimentally probe for spontaneous time-reversal symmetry breaking. Recently, however, a Josephson diode effect was observed in a time-reversal symmetric Josephson junction involving a single magnetic adatom . To resolve this apparent conflict, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric dissipative currents. These different origins also imply distinctly different symmetry requirements: current-phase asymmetry requires broken time-reversal symmetry, in contrast asymmetric dissipation stems from broken particle-hole symmetry. In the case of magnetic-atom Josephson junctions the latter may be traced back to Yu-Shiba-Rusinov subgap states. While our theory  was inspired by the experiment , it relies on general principles only, and may provide significant guidance in identifying the microscopic origin of nonreciprocities in any Josephson junction.
 Trahms et al. Nature 615 (2023)
 Steiner et al. PRL 130 (2023)