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

Abstract

The dynamics of the flux lattice in the mixed state of strongly type-II superconductor near the upper critical field ${H}_{c2}(T)$ 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 $\ensuremath{\delta}$-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 ${u}_{c}$ 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 ${(u\ensuremath{-}{u}_{c})}^{\ensuremath{-}1}$, whereas the ac conductivity on the depinning line diverges as $i{\ensuremath{\omega}}^{\ensuremath{-}1}$. 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.