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arXiv:cond-mat/0404179 · Physical Review B

Effect of columnar disorder on the superconducting transition of a type-II superconductor in zero applied magnetic field

Anders Vestergren, Mats Wallin, Stephen Teitel, Hans Werner Weber

Published Aug 10, 2004• 6 citations
arXivHTMLPDF

Abstract

We investigate the effect of random columnar disorder on the superconducting phase transition of a type-II superconductor in zero applied magnetic field using numerical simulations of three dimensional $XY$ and vortex loop models. We consider both an unscreened model, in which the bare magnetic penetration length is approximated as infinite, and a strongly screened model, in which the magnetic penetration length is of order the vortex core radius. We consider both equilibrium and dynamic critical exponents. We show that, as in the disorder free case, the equilibrium transitions of the unscreened and strongly screened models lie in the same universality class, however scaling is now anisotropic. We find for the correlation length exponent $\ensuremath{\nu}=1.2\ifmmode\pm\else\textpm\fi{}0.1$, and for the anisotropy exponent $\ensuremath{\zeta}=1.3\ifmmode\pm\else\textpm\fi{}0.1$. We find different dynamic critical exponents for the unscreened and strongly screened models.

DOI
10.1103/physrevb.70.054508

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We present a finite temperature Monte Carlo study of the XY\mathrm{XY}XY model in the vortex representation and study its dynamical critical behavior in two limits. The first neglects magnetic-field fluctuations, corresponding to the absence of screening, which should be a good approximation in high-Tc{T}_{c}Tc​ superconductors $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ except extremely close to the critical point. Here, from finite-size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be $z\ensuremath{\approx}1.5$. The second limit includes magnetic-field fluctuations in the strong screening limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}0)$ corresponding to the true asymptotic inverted XY\mathrm{XY}XY critical regime, where we find the unexpectedly large value $z\ensuremath{\approx}2.7.$ We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin-wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.
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