Regime Interpretation of Anomalous Vortex Dynamics in 2D Superconductors

Abstract

Low-frequency dynamic impedance $[{\ensuremath{\sigma}}^{\ensuremath{-}1}(\ensuremath{\omega},T)\ensuremath{\equiv}({\ensuremath{\sigma}}_{1}+i{\ensuremath{\sigma}}_{2}{)}^{\ensuremath{-}1}]$ measurements on Josephson junction arrays found that ${\ensuremath{\sigma}}_{1}\ensuremath{\sim}|\mathrm{ln}\ensuremath{\omega}|$, ${\ensuremath{\sigma}}_{2}\ensuremath{\sim}\mathrm{const}$. This implies anomalously sluggish vortex mobilities ${\ensuremath{\mu}}_{V}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\sigma}}_{1}^{\ensuremath{-}1}$, and is in conflict with general dynamical scaling expressions. We calculate (a) $\ensuremath{\sigma}(\ensuremath{\omega},T)$ by real-space vortex scaling and (b) ${\ensuremath{\mu}}_{V}(\ensuremath{\omega})$ using Mori's formalism for a screened Coulomb gas. We find, in addition to the usual critical (large-\ensuremath{\omega}) and hydrodynamic (low-\ensuremath{\omega}) regimes, a new intermediate-frequency scaling regime into which the experimental data fall. This resolves the above mentioned conflict and makes explicit predictions for the scaling form of $\ensuremath{\sigma}(\ensuremath{\omega},T)$.