AC RESPONSE OF ABRIKOSOV VORTICES IN LAYERED SUPERCONDUCTORS

In a layered high-T(c) superconductor an Abrikosov vortex line perpendicular to the layers can be considered as a stack of coupled two-dimensional ''pancake'' vortices (2DV) with cores residing inside the superconducting layers. When the in-plane penetration length lambda(ab) = lambda is smaller than the Josephson length lambda(J) = lambda(c)d/lambda (d: layer period) the interaction between 2DV is via a magnetic pair force which is complicated but exactly known. We calculate linear and nonlinear ac responses for this model including randomly distributed pinning centers, In detail, the thermally averaged shift S(n)(t) of a 2DV in layer n under the influence of a finite external ac current in the frequency range up to 1 GHz is computed from coupled Fokker-Planck equations for the distribution functions of 2DV positions. In the adiabatic approximation, the Fokker-Planck equations can be cast into a nonlinear differential equation for a continuous shift function S(z, t) using a gradient expansion. The constitutive equation for S(z, t) is solved perturbatively for the linear ac response and for the mixing current at frequency 2omega1 - omega2 from two external currents at frequencies omega2 and omega2 almost-equal-to 2omega1 due to a third order process. This pseudo-harmonic mixing probes the nonlinearity of the intervortex force and its interplay with pinning. Explicit results for the film geometry are given for the surface impedance Z(s) and the mixing current amplitude deltaj(3) as functions of external frequencies, crossover frequency omega(c) is-proportional-to n(i)domega(D) (measuring the pinning), and diffusion frequency omega(D) of free 2DV.