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Brazilian Journal of Physics

Numerical study of resistivity scaling in pi junction granular superconductors

Enzo Granato

Published Dec 1, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1590/s0103-97332003000400005

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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.
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.
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 $\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}{\ensuremath{\nu}}_{T}}$ 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.
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​.
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.
We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to fff flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of fff. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation. For a square-lattice array, the critical exponents obtained near f=1/2f=1/2f=1/2 are consistent with the experimental observations. The same scaling behavior is observed near f=1/3f=1/3f=1/3. For a honeycomb array, although similar results are obtained for f=1/3f=1/3f=1/3, the transition is absent for f=1/2f=1/2f=1/2, consistent with an incommensurate vortex phase.
We study the dynamic vortex Mott transition in two-dimensional superconducting arrays in a magnetic field with fff flux quantum per plaquette. The transition is induced by external driving current and thermal fluctuations near rational vortex densities set by the value of fff and has been observed experimentally from the scaling behavior of the differential resistivity. Recently, numerical simulations of interacting vortex models have demonstrated this behavior only near fractional fff. A fine-grid vortex model is introduced, which allows us to consider both the cases of fractional and integer fff. The critical behavior is determined from a scaling analysis of the current-voltage relation and voltage correlations near the transition and by Monte Carlo simulations. The critical exponents for the transition near f=1/2f=1/2f=1/2 are consistent with the experimental observations and previous numerical results from a standard vortex model. The same scaling behavior is obtained for f=1f=1f=1, in agreement with experiments. However, the estimated correlation-length exponent indicates that even at integer fff, the critical behavior is not of mean-field type.