Strong influence of nonlocal nonequilibrium effects on the dynamics of the order parameter in a phase-slip center: Ring studies

Abstract

We study the influence of the inelastic relaxation time ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}$ of the quasiparticle distribution function $f(E)$ on the phase slip process in quasi-one-dimensional superconducting rings at a temperature close to the critical temperature ${T}_{c}$. We find that the initial time of growth of the order parameter $|\ensuremath{\Delta}|$ in the phase slip core after the phase slip is a nonmonotonic function of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}$ which has a maximum at ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}\ensuremath{\simeq}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{GL}=\ensuremath{\pi}\ensuremath{\hbar}/8{k}_{B}({T}_{c}\ensuremath{-}T)$ and has a tendency to saturate for large ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}⪢{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{GL}$. The effective ``heating'' of the electron subsystem due to the increase in $|\ensuremath{\Delta}|$ in the phase slip center together with the above effect result in a nonmonotonic dependence of the number of subsequent phase slips on ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}$ in rings of relatively large radius (in which each phase slip reduces the current density to a small fraction of its initial value). During the phase slip process the order parameter distribution has two peaks near the phase slip core due to the diffusion of the nonequilibrium quasiparticles from that region.