Sliding Abrikosov vortex lattice in the presence of a regular array of columnar pinning centers: Ac conductivity and criticality near the transition to a pinned state

The dynamics of the flux lattice in the mixed state of strongly type-II superconductor near the upper critical field Hc2 (T) subjected to ac field and interacting with a periodic array of short-range pinning centers (nanosolid) is considered. The superconductor in a magnetic field in the absence of thermal fluctuations on the mesoscopic scale is described by the time-dependent Ginzburg-Landau equations. An exact expression for the ac resistivity in the case of a δ -function model for the pinning centers in which the nanosolid is commensurate with the Abrikosov lattice (vortices outnumber pinning centers) is obtained. It is found that below a certain critical pinning strength uc and sufficiently low frequencies there exists a sliding Abrikosov lattice, which moves nearly uniformly despite interactions with the pinning centers. At small frequencies the conductivity diverges as (u- uc) -1, whereas the ac conductivity on the depinning line diverges as i ω-1. This sliding lattice behavior, which does not exists in the single vortex-pinning regime, becomes possible due to strong interactions between vortices when they outnumber the columnar defects. Physically it is caused by "liberation" of the temporarily trapped vortices by their freely moving neighbors.