Dynamic scaling of I-V data for the neutral 2D Coulomb gas

Stephen W. Pierson, Mark G. Friesen

Published Jan 1, 2000• 1 citation

Abstract

The value of the dynamic critical exponent z has been studied for experimental two-dimensional superconducting and Josephson junction array systems in zero magnetic "eld via the Fisher}Fisher}Huse dynamic scaling analysis. We found zK5.6$0.3, a relatively large value indicative of non-di!usive dynamics. We extend this work here to simulational I}< curves that are also found to be characterized by the same large value of z. # 2000 Elsevier Science B.V. All rights reserved.

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Dynamic scaling of I-V data for the neutral 2D Coulomb gas

Stephen W. Pierson, Mark G. Friesen

Published Jan 1, 2000• 1 citation

OpenAlex

Abstract

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Stephen W. Pierson, Mark G. Friesen, S. M. Ammirata +2 more

The value of the dynamic critical exponent z is studied for two-dimensional superconducting, superfluid, and Josephson junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find $z\ensuremath{\simeq}5.6\ifmmode\pm\else\textpm\fi{}0.3$, a relatively large value indicative of nondiffusive dynamics. Universality of the scaling function is tested and confirmed for the thinnest samples. We discuss the validity of the dynamic scaling analysis as well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition in these systems, the results of which seem to be consistent with simple diffusion $(z=2)$ . Further studies are discussed and encouraged.The value of the dynamic critical exponent z is studied for two-dimensional superconducting, superfluid, and Josephson junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find $z\ensuremath{\simeq}5.6\ifmmode\pm\else\textpm\fi{}0.3$, a relatively large value indicative of nondiffusive dynamics. Universality of the scaling function is tested and confirmed for the thinnest samples. We discuss the validity of the dynamic scaling analysis as well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition in these systems, the results of which seem to be consistent with simple diffusion $(z=2)$. Further studies are discussed and encouraged.

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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 $z=2.$ 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.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 $z=2.$ 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.

arXiv:cond-mat/0009291Physical review. B, Condensed matterDec 1, 200041 citations

(z=2)

. Further studies are discussed and encouraged.

A numerical study of the neutral two-dimensional (2D) lattice Coulomb gas is performed to examine dynamic scaling, finite size effects, and the dynamic critical exponent

z

of the Kosterlitz-Thouless-Berezinskii transition. By studying large system sizes (

L=100

), we show

z=2.0 \pm0.2

using Fisher-Fisher-Huse (FFH) scaling. We also present evidence that the vortex correlation length is finite below the transition temperature, in contrast to conventional wisdom. Finally, we conclude that previous findings for a variety of experimental systems that

z\simeq 5.6

using FFH scaling indicates that finite size effects are ubiquitous in 2D superconductors and Josephson Junction Arrays.

{T}_{c}

, the static and dynamic critical exponents $2\ensuremath{\beta}∕\ensuremath{\nu}$, $\ensuremath{\nu}$, and

z

are obtained. The resulting values of

{T}_{c}

are consistent with previous steady-state simulations and decrease with the increase of currents. It is found that the values of the exponent $\ensuremath{\nu}$ are not sensitive to external currents, while the values of $2\ensuremath{\beta}∕\ensuremath{\nu}$ and

z

are strongly current dependent.

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.