Nonlinear Electrodynamics of Randomly Inhomogeneous Superconductors

We investigate the effect of macroscopic inhomogeneities on nonlinear transport properties of type-II superconductors and develop an effective medium theory to derive general relations between the global and local currents and electric fields. We show that even weak inhomogeneities with 〈δJc²〉Jc² can qualitatively change nonlinear transport characteristics (here δJc denotes fluctuations of the critical current density Jc), causing a nonmonotonic magnetic field dependence of the global averaged J̄c(B), even if the local Jc(B) decreases with B. We predict a superconducting Gunn effect, for which inhomogeneities can give rise to negative differential conductivity, bistability, and electric field domains.