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arXiv:cond-mat/9808331 · Physical review. B, Condensed matter

Current-voltage scaling of chiral and gauge-glass models of two-dimensional superconductors

Enzo Granato

Published Nov 1, 1998• 43 citations
arXivHTMLPDF

Abstract

The scaling behavior of the current-voltage characteristics of chiral and gauge-glass models of disordered superconductors, are studied numerically, in two dimensions. For both models, the linear resistance is nonzero at finite temperatures and the scaling analysis of the nonlinear resistivity is consistent with a phase transition at $T=0$ temperature characterized by a diverging correlation length $\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}{\ensuremath{\nu}}_{T}}$ and thermal critical exponent ${\ensuremath{\nu}}_{T}.$ The values of ${\ensuremath{\nu}}_{T},$ however, are found to be different for the chiral and gauge-glass models, suggesting different universality classes, in contrast to the result obtained recently in three dimensions.

DOI
10.1103/physrevb.58.11161

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The scaling behavior of the current-voltage characteristics of chiral and gauge-glass models of disordered superconductors, are studied numerically, in two dimensions. For both models, the linear resistance is nonzero at finite temperatures and the scaling analysis of the nonlinear resistivity is consistent with a phase transition at T=0T=0T=0 temperature characterized by a diverging correlation length \ensuremathξ\ensuremath∝T\ensuremath−\ensuremathνT\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}{\ensuremath{\nu}}_{T}}\ensuremathξ\ensuremath∝T\ensuremath−\ensuremathνT​ and thermal critical exponent \ensuremathνT.{\ensuremath{\nu}}_{T}.\ensuremathνT​. The values of \ensuremathνT,{\ensuremath{\nu}}_{T},\ensuremathνT​, however, are found to be different for the chiral and gauge-glass models, suggesting different universality classes, in contrast to the result obtained recently in three dimensions.
Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration ppp are considered, where pc{p}_{c}pc​ is the percolation threshold. For p>pcp>{p}_{c}p>pc​ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At pc{p}_{c}pc​ and finite temperature T,T,T, the results show the scaling behavior of a T=0T=0T=0 superconducting transition. The resistance is linear but vanishes for decreasing TTT with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted XY\mathrm{XY}XY model at pc.{p}_{c}.pc​.
It has been suggested [Pierson et al., Phys. Rev. B 60, 1309 (1999); Ammirata et al., Physica C 313, 225 (1999)] that for two-dimensional (2D) superconductors there exists a phase transition with the dynamic critical exponent $z\ensuremath{\approx}5.6.$ We perform simulations for the 2D resistively-shunted-junction model and compare the results with the experimental data in Repaci et al. obtained for an ultrathin YBCO sample [Phys. Rev. B 54, R9674 (1996)]. We then use a different method of analyzing dynamic scaling than in Pierson et al., and conclude that both the simulations and the experiments are consistent with a conventional Kosterlitz Thouless (KT) transition in the thermodynamic limit for which z=2.z=2.z=2. For finite systems, however, we find both in simulations and experiments that the change in the current-voltage $(I\ensuremath{-}V)$ characteristics caused by the finite size shows a scaling property with an exponent $\ensuremath{\alpha}\ensuremath{\approx}1/6,$ seemingly suggesting a vanishing resistance at a temperature for which $z={\ensuremath{\alpha}}^{\ensuremath{-}1}.$ It is pointed out that the dynamic critical exponent found in Pierson et al. corresponds to the exponent ${\ensuremath{\alpha}}^{\ensuremath{-}1}.$ It is emphasized that this scaling property does not represent any true phase transition since in reality the resistance vanishes only at zero temperature. Nevertheless, the observed scaling behavior associated with $\ensuremath{\alpha}\ensuremath{\approx}1/6$ appears to be a common and intriguing feature for the finite size caused change in the $I\ensuremath{-}V$ characteristics around the KT transition.
We investigate the critical behavior of the gauge-glass model for the vortex-glass transition in three-dimensional superconductors, including screening of the interaction between vortices. A Monte Carlo study of the linear resistivity and a scaling analysis of current-voltage characteristics indicates that screening destroys the finite-temperature transition found earlier when screening was neglected. The correlation-length exponent at the resulting zero-temperature transition is found to be $\ensuremath{\nu}=1.05\ifmmode\pm\else\textpm\fi{}0.01$.
The resistivity behavior of inhomogeneous superconductors with random $\ensuremath{\pi}$ junctions, as in high-Tc{T}_{c}Tc​ materials with d-wave symmetry, is studied by numerical simulation of a three-dimensional XY\mathrm{XY}XY spin-glass model. Above a concentration threshold of antiferromagnetic couplings, a resistive transition is found in the chiral-glass phase at finite temperatures and the critical exponents are determined from dynamic scaling analysis. The power-law exponent for the nonlinear contribution found in recent resistivity measurements is determined by the dynamic critical exponent of this transition.
Numerical simulations based on Monte Carlo dynamics are used to investigate the resistivity behavior of granular superconductors containing a random distribution of pi junctions, as in superconducting materials with d-wave symmetry. The presence of pi junctions leads to quenched in circulating currents (chiralities) and to chiral glass behavior at low temperatures, even without an external magnetic field. An XY spin glass model in the phase representation is used to determine the current-voltage characteristics and critical exponents of the resistivity transition. In two dimensions, the linear resistivity is nonzero at finite temperatures and the dynamic scaling analysis of the nonlinear resistivity is consistent with a phase transition at zero temperature. In three dimensions, we find a transition at finite temperatures below which the linear resistivity vanishes and the corresponding critical exponents are determined from the scaling analysis. The results are in good agreement with Langevin simulations in the phase representation. The dynamic exponent z is significantly different from previous results obtained in the vortex representation.
We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.