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arXiv:cond-mat/9711127

Dynamic Scaling at the Zero-field 2D Superconducting Transition

S. M. Ammirata, Mark G. Friesen, Stephen W. Pierson, LeRoy A. Gorham, Jeffrey C. Hunnicutt, Matthew L. Trawick, C. D. Keener

Published Nov 13, 1997• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/9711127

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Zero-field current-voltage (I-V) characteristics of a thin ("two-dimensional") Bi2Sr2CaCu2O8+δBi_2Sr_2CaCu_2O_{8+δ}Bi2​Sr2​CaCu2​O8+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 III-VVV exponent ααα should be between z+1z+1z+1 and 1. A value of z≃5.6z \simeq 5.6z≃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.
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.
There has been ongoing debate over the critical behavior of two-dimensional superconductors; in particular for high Tc{T}_{c}Tc​ 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.
We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic fields. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below Tc{T}_{c}Tc​, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field, or system size is varied, and find a strong multiplicative logarithmic correction near Tc{T}_{c}Tc​, all of which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large-scale numerical simulations, and calculate the dynamic critical exponent zzz, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.
We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical behavior on the two-dimensional (2D) quantum superconductor-insulator (QSI) transition driven by the tuning parameter x. Concentrating on the sheet resistance R(x,T) BKT behavior implies: an explicit quantum scaling function for R(x,T) along the superconducting branch ending at the nonuniversal critical value Rc = R(xc); a BKT-transition line T(c)(x) [proportionality] (x - x(c))(zν[overline]), where z is the dynamic exponent and ν[overline] the exponent of the zero-temperature correlation length; independent estimates of zν[overline], z and ν[overline] from the x dependence of the nonuniversal parameters entering the BKT expression for the sheet resistance. To illustrate the potential and the implications of this scenario we analyze the data of Bollinger et al (2011 Nature 472 458) taken on gate voltage tuned epitaxial films of La2-xSrxCuO4 that are one unit cell in thickness. The resulting estimates, z ~/= 3.1 and ν[overline] ~/= 0.52, indicate a clean 2D-QSI critical point where hyperscaling, the proportionality between d/λ(2)(0) and Tc, and the correspondence between the quantum phase transitions in D dimensions and the classical ones in (D + z) dimensions are violated.
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)(z=2)(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 zzz of the Kosterlitz-Thouless-Berezinskii transition. By studying large system sizes (L=100L=100L=100), we show z=2.0±0.2z=2.0 \pm0.2z=2.0±0.2 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≃5.6z\simeq 5.6z≃5.6 using FFH scaling indicates that finite size effects are ubiquitous in 2D superconductors and Josephson Junction Arrays.