Dissipation in Superfluid 3He Weak Links

We suggest a new interpretation of the Berkeley data on the dissipation of superflow in Josephson junctions in superfluid ³He-B. The measurements are well described by the following relation between the current through a junction and the pressure head applied to it (current-pressure relation or CPR): $I = G_1 P + G_2 sqrt P $ . The Berkeley group has proposed an explanation based on 1) ballistic removal of quasiparticles from the junction; 2) dissipative motion of the anisotropy axis of the order parameter inside the junction. We argue that part 1) of the model, which is responsible for the G ₂ part of the CPR, is invalid, since it presumes the existence, in the bulk, of quasiparticles with energies inside the superfluid gap. Part 2) which is responsible for the G ₁ term implies that the anisotropy axis of the order parameter strongly depends on the phase difference across the junction. Our agternative model is based on mechanisms well known in superconductors: dissipation due to time lag of inequilibrium order parameter and/or Andreev reflection of quasiparticles trapped inside the junction. For the parameters of the Berkeley experiment these models give the same order of magnitude for the G ₁ in the CPR, and are in rough agreement with the experiment. The nature of the G ₂ term remains mysterious. It could arise due to saturation of the current of Andreev-scattered quasiparticles if the quasiparticle relaxation time in the junction is considerably longer than in normal Fermi liquid.