arXiv:cond-mat/9901295 · Physical review. B, Condensed matter

Dynamic scaling for two-dimensional superconductors, Josephson-junction arrays, and superfluids

Stephen W. Pierson, Mark G. Friesen, S. M. Ammirata, Jeffrey C. Hunnicutt, LeRoy A. Gorham

Published Jul 1, 1999• 49 citations

Abstract

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.

DOI: 10.1103/physrevb.60.1309

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

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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.

Jan 1, 20001 citation

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arXiv:cond-mat/9901295 · Physical review. B, Condensed matter

Dynamic scaling for two-dimensional superconductors, Josephson-junction arrays, and superfluids

Stephen W. Pierson, Mark G. Friesen, S. M. Ammirata, Jeffrey C. Hunnicutt, LeRoy A. Gorham

Published Jul 1, 1999• 49 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physrevb.60.1309

Related papers

Dynamic scaling theory of the Kosterlitz-Thouless-Berezinskii transition: ubiquitous finite size effects

Louis Colonna-Romano, Stephen W. Pierson, Mark G. Friesen

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.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.

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Finite-size effects and dynamical scaling in two-dimensional Josephson junction arrays

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In recent years many groups have used Fisher, Fisher and Huse (FFH) dynamical scaling to investigate and demonstrate details of the superconducting phase transition. Some attention has been focused on two dimensions where the phase transition is of the Kosterlitz-Thouless-Berezinskii (KTB) type. Pierson et al. used FFH dynamical scaling almost exclusively to suggest that the dynamics of the two-dimensional superconducting phase transition may be other than KTB-like. In this work we investigate the ability of scaling behavior by itself to yield useful information on the nature of the transition. We simulate current-voltage (IV) curves for two-dimensional Josephson junction arrays with and without finite-size-induced resistive tails. We find that, for the finite-size effect data, the values of the scaling parameters, specifically the transition temperature and the dynamical scaling exponent z, depend critically on the magnitude of the contribution that the resistive tails make to the IV curves. In effect, the values of the scaling parameters depend on the noise floor of the measuring system.In recent years many groups have used Fisher, Fisher and Huse (FFH) dynamical scaling to investigate and demonstrate details of the superconducting phase transition. Some attention has been focused on two dimensions where the phase transition is of the Kosterlitz-Thouless-Berezinskii (KTB) type. Pierson et al. used FFH dynamical scaling almost exclusively to suggest that the dynamics of the two-dimensional superconducting phase transition may be other than KTB-like. In this work we investigate the ability of scaling behavior by itself to yield useful information on the nature of the transition. We simulate current-voltage (IV) curves for two-dimensional Josephson junction arrays with and without finite-size-induced resistive tails. We find that, for the finite-size effect data, the values of the scaling parameters, specifically the transition temperature and the dynamical scaling exponent z, depend critically on the magnitude of the contribution that the resistive tails make to the IV curves. In effect, the values of the scaling parameters depend on the noise floor of the measuring system.

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Jan 1, 20001 citation

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Jaegon Um, Beom Jun Kim, Petter Minnhagen +2 more

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S. M. Ammirata, Mark G. Friesen, Stephen W. Pierson +4 more

Zero-field current-voltage (I-V) characteristics of a thin ("two-dimensional") $Bi_2Sr_2CaCu_2O_{8+δ}$ crystal are reported and analyzed in two ways. The "conventional" approach yields ambiguous results while a dynamical scaling analysis offers new insights into the Kosterlitz-Thouless-Berezinskii transition. The scaling theory predicts that the universal jump of the $I$ - $V$ exponent $α$ should be between $z+1$ and 1. A value of $z \simeq 5.6$ is obtained for the dynamical critical exponent, and is corroborated by data from other 2D superconductors. A simple dynamical model is presented to account for the results.Zero-field current-voltage (I-V) characteristics of a thin ("two-dimensional") $Bi_2Sr_2CaCu_2O_{8+δ}$ crystal are reported and analyzed in two ways. The "conventional" approach yields ambiguous results while a dynamical scaling analysis offers new insights into the Kosterlitz-Thouless-Berezinskii transition. The scaling theory predicts that the universal jump of the $I$-$V$ exponent $α$ should be between $z+1$ and 1. A value of $z \simeq 5.6$ is obtained for the dynamical critical exponent, and is corroborated by data from other 2D superconductors. A simple dynamical model is presented to account for the results.

arXiv:cond-mat/9711127Nov 13, 19970 citations

z\ensuremath{\simeq}5.6\ifmmode\pm\else\textpm\fi{}0.3

(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.

There has been ongoing debate over the critical behavior of two-dimensional superconductors; in particular for high

{T}_{c}

superconductors. The conventional view is that a Kosterlitz-Thouless-Berezinskii transition occurs as long as finite size effects do not obscure the transition. However, there have been recent suggestions that a different transition actually occurs which incorporates aspects of both the dynamic scaling theory of Fisher, Fisher, and Huse and the Kosterlitz-Thouless-Berezinskii transition. Of general interest is that this modified transition apparently has a universal dynamic critical exponent. Some have countered that this apparent universal behavior is rooted in a newly proposed finite-size scaling theory; one that also incorporates scaling and conventional two-dimensional theory. To investigate these issues we study dc voltage versus current data of a 12-\AA{}-thick ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ film. We find that the newly proposed scaling theories have intrinsic flexibility that is relevant to the analysis of the experiments. In particular, the data scale according to the modified transition for arbitrarily defined critical temperatures between 0 and 19.5 K, and the temperature range of a successful scaling collapse is related directly to the sensitivity of the measurement. This implies that the apparent universal exponent is due to the intrinsic flexibility rather than some real physical property. To address this intrinsic flexibility, we propose a criterion which would give conclusive evidence for phase transitions in two-dimensional superconductors. We conclude by reviewing results to see if our criterion is satisfied.

{E}_{J}∕{k}_{B}

with the Josephson coupling strength

{E}_{J}

), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent

z=2.0

in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.

Zero-field current-voltage (I-V) characteristics of a thin ("two-dimensional")

Bi_2Sr_2CaCu_2O_{8+δ}

crystal are reported and analyzed in two ways. The "conventional" approach yields ambiguous results while a dynamical scaling analysis offers new insights into the Kosterlitz-Thouless-Berezinskii transition. The scaling theory predicts that the universal jump of the

I

V

exponent

α

should be between

z+1

and 1. A value of

z \simeq 5.6

is obtained for the dynamical critical exponent, and is corroborated by data from other 2D superconductors. A simple dynamical model is presented to account for the results.