Nonlocal conductivity in type-II superconductors.

Multiterminal transport measurements on YBCO crystals in the vortex liquid regime have shown nonlocal conductivity on length scales up to 50 microns. Motivated by these results we explore the wavevector (k) dependence of the dc conductivity tensor, σμν(k), in the Meissner, vortex lattice, and disordered phases of a type-II superconductor. Our results are based on time-dependent Ginzburg-Landau (TDGL) theory and on phenomenological arguments. We find four qualitatively different types of behavior. First, in the Meissner phase, the conductivity is infinite at k = 0 and is a continuous function of k, monotonically decreasing with increasing k. Second, in the vortex lattice phase, in the absence of pinning, the conductivity is finite (due to flux flow) at k = 0; it is discontinuous there and remains qualitatively like the Meissner phase for k > 0. Third, in the vortex liquid regime in a magnetic field and at low temperature, the conductivity is finite, smooth and non-monotonic, first increasing with k at small k and then decreasing at larger k. This third behavior is expected to apply at temperatures just above the