COLLECTIVE FLUX CREEP IN HIGH-TC SUPERCONDUCTORS

We develop a scaling approach to flux-line pinning in high-T(c) superconductors. Our main result is a nonlinear relation V(j(ex)) approximately exp(-Cj(ex)-mu) between the voltage V and the external current density j(ex), where the exponent-mu is related to the roughness exponent and has been estimated in an earlier paper [T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990)]. For the low-frequency ac resistivity we find two contributions rho-1(omega) approximately omega-2[1-(T/T*)ln-omega-tau-0]4/psi and rho-2(omega) approximately omega[1-(T/T*)ln-omega-tau-0]2/psi, where psi almost-equal-to 1 in three dimensions, and where T* is a characteristic temperature. Similar power laws are obtained for the dynamic susceptibility chi"(omega), whereas the magnetization due to the change of the applied field varies in time as (lnt)-1/mu.