Diode Effects in Current-Biased Josephson Junctions

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, 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 quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.

Figure 1

RCSJ model for weakly damped Josephson junctions. (a) Hysteretic dependence of time-averaged voltage on bias current ($T=0$: red, dashed; $T\ne 0$: green) and characteristic currents. Trace generated for asymmetric current-phase relation $I_0(\phi )$ (left inset) and dissipative current $I_d(V)$ (right inset). Dotted traces in insets show corresponding curves used in the conventional RCSJ model. (b) Equivalent circuit of the RCSJ model. (c) Phase-space diagram of the deterministic junction dynamics with coexisting trapped (orange) and running (green) solutions. Parameters: [28].

Figure 2

Histograms of retrapping ($i_{\mathbf{re},\pm }$) and switching ($i_{\mathbf{sw},\pm }$) currents for bias currents $i_b$ of both signs ($\pm$). (a) Conventional RCSJ model. (b) Asymmetric current-phase relation $I_0(\phi )$ and symmetric dissipative current $I_d(\phi )$. (c) Symmetric $I_0(\phi )$ and asymmetric $I_d(\phi )$. Parameters: [28].

Figure 3

Microscopic model of Josephson junction with magnetic impurity. (a) $I\text{−}V$ characteristics of quasiparticle current due to YSR state associated with magnetic impurity for different potential scatterings $\mathcal{K}$. (b)–(d) Histograms of switching and retrapping currents corresponding to $I\text{−}V$ characteristics in (a) (note color-coded box), emphasizing the importance of particle-hole symmetry. Parameters: [28].