A theory of the thermal depinning transition in type-2 superconductors

It is pointed out theoretically that the electric field, E, vs. current density, J, characteristic of the vortex glass state is different from that predicted by M.P.A. Fisher; that is, the electric resistivity, ρ = E/J has a finite value even at J → 0, while the Fisher theory predicts ρ → 0 with J → 0. It is also pointed out that the vortex glass-liquid transition is merely a kind of the bifurcation transition in the mixed state of type-2 superconductors containing pinning centers, which may be called the thermal depinning transition between the pinning state and the depinning state of fluxoids resulting from the thermal agitation on fluxoids. Furthermore, it is shown theoretically that only the flux flow resistivity obeys the scaling law near the thermal depinning transition temperature, T_dp, while the flux creep resistivity approaches a finite value as J is decreased to zero, even in the pinning state below T_dp. When ρ is measured down to a very small level of E, therefore, the noticeable deviation from the scaling law of ρ against J that was predicted by Fisher is expected to appear due to the above-mentioned behavior of the flux creep resistivity. The above theoretical conclusion that is contrary to the theoretical prediction by Fisher, however, seems to be supported by the recently observed data over a very wide range of the electric field, E provided by Kodama et al., because the present theoretical expression for the E vs. J, characteristics agrees quantitatively with these observed data.