ac response of the flux-line liquid in the high-Tc superconductors

We use a hydrodynamics theory to discuss the response of a viscous flux-line liquid to an ac perturbation applied at the surface of the sample. The theory incorporates viscoelastic effects and describes the crossover between liquidlike and solidlike response of the vortex array as the frequency of the perturbation increases. A large viscosity from flux-line interactions and entanglement leads to viscous screening of surface fields. As a result, two frequency-dependent length scales are needed to describe the penetration of an ac field. For large viscosities the imaginary part of the ac permeability can exhibit, in addition to the well-known peak associated with flux diffusion across the sample, a low-frequency peak corresponding to the transition from solidlike to liquidlike behavior.