Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0312506 · Physical Review B

Scaling determination of the nonlinear I−V characteristics for two-dimensional superconducting networks

Petter Minnhagen, Beom Jun Kim, Andreas Grönlund

Published Feb 27, 2004• 2 citations
arXivHTMLPDF

Abstract

It is shown from computer simulations that the current-voltage $(I\ensuremath{-}V)$ characteristics for the two-dimensional XY model with resistively shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear $I\ensuremath{-}V$ exponent a can be determined to good precision. This determination supports the conclusion $a=z+1,$ where z is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B 67, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. 78, 4324 (1997)].

DOI
10.1103/physrevb.69.064515

Related papers

Analysis of current-voltage characteristics of two-dimensional superconductors: Finite-size scaling behavior in the vicinity of the Kosterlitz-Thouless transition

Kateryna Medvedyeva, Beom Jun Kim, Petter Minnhagen

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/0009291•Physical review. B, Condensed matter•Dec 1, 2000•41 citations

Current-voltage characteristics of the two-dimensional XY model with Monte Carlo dynamics

Beom Jun Kim

Current-voltage characteristics and the linear resistance of the two-dimensional $\mathrm{XY}$ model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent z at various temperatures. From the comparison with the resistively shunted junction dynamics, it is concluded that z is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.

arXiv:cond-mat/0010121•Physical review. B, Condensed matter•Dec 13, 2000•10 citations

Current-voltage characteristics of diluted Josephson-junction arrays: Scaling behavior at current and percolation threshold

Enzo Granato, Daniel Domı́nguez

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 $p$ are considered, where ${p}_{c}$ is the percolation threshold. For $p>{p}_{c}$ 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 ${p}_{c}$ and finite temperature $T,$ the results show the scaling behavior of a $T=0$ superconducting transition. The resistance is linear but vanishes for decreasing $T$ 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 $\mathrm{XY}$ model at ${p}_{c}.$

arXiv:cond-mat/9709012•Physical review. B, Condensed matter•Dec 1, 1997•15 citations

Scaling, finite size effects, and crossovers of the resistivity and current-voltage characteristics in two-dimensional superconductors

Andreas Andersson, Jack Lidmar

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 ${T}_{c}$, 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 ${T}_{c}$, 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 $z$, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.

arXiv:1203.5317•Physical Review B•Jun 17, 2013•8 citations

Dynamic critical exponent of two-, three-, and four-dimensional XY models with relaxational and resistively shunted junction dynamics

Lars Melwyn Jensen, Beom Jun Kim, Petter Minnhagen

The dynamic critical exponent z is determined numerically for the d-dimensional $\mathrm{XY}$ model $(d=2,$ 3, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of z are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the same boundary condition do not always give the same value of z. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of z consistent with expectations for superfluids and superconductors: $z=2,$ 3/2, and 2 for $d=2,$ 3, and 4, respectively.

arXiv:cond-mat/0003447•Physical review. B, Condensed matter•Jun 1, 2000•44 citations

Dynamic critical behaviors of three-dimensional XY models related to superconductors/superfluids

L. M Jensen, B. J Kim, Petter Minnhagen

The dynamic critical exponent z is determined from numerical simulations for the three-dimensional XY model subject to two types of dynamics, i.e. , relaxational dynamics and resistively shunted junction (RSJ) dynamics, as well as for two different treatments of the boundary, i.e. , periodic boundary condition (PBC) and fluctuating twist boundary condition (FTBC). In case of relaxational dynamics, finite-size scaling at the critical temperature gives z ≈ 2 for PBC and 1.5 for FTBC, while for RSJ dynamics z ≈ 1.5 is obtained in both cases. The results are discussed in the context of superfluid/superconductors and vortex dynamics, and are compared with what has been found for other related models.

arXiv:cond-mat/9912325•Europhysics Letters (EPL)•Mar 1, 2000•14 citations
It is shown from computer simulations that the current-voltage (I\ensuremath−V)(I\ensuremath{-}V)(I\ensuremath−V) characteristics for the two-dimensional XY model with resistively shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear I\ensuremath−VI\ensuremath{-}VI\ensuremath−V exponent a can be determined to good precision. This determination supports the conclusion a=z+1,a=z+1,a=z+1, where z is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B 67, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. 78, 4324 (1997)].
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.
Current-voltage characteristics and the linear resistance of the two-dimensional XY\mathrm{XY}XY model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent z at various temperatures. From the comparison with the resistively shunted junction dynamics, it is concluded that z is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.
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 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.
The dynamic critical exponent z is determined numerically for the d-dimensional XY\mathrm{XY}XY model (d=2,(d=2,(d=2, 3, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of z are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the same boundary condition do not always give the same value of z. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of z consistent with expectations for superfluids and superconductors: z=2,z=2,z=2, 3/2, and 2 for d=2,d=2,d=2, 3, and 4, respectively.
The dynamic critical exponent z is determined from numerical simulations for the three-dimensional XY model subject to two types of dynamics, i.e. , relaxational dynamics and resistively shunted junction (RSJ) dynamics, as well as for two different treatments of the boundary, i.e. , periodic boundary condition (PBC) and fluctuating twist boundary condition (FTBC). In case of relaxational dynamics, finite-size scaling at the critical temperature gives z ≈ 2 for PBC and 1.5 for FTBC, while for RSJ dynamics z ≈ 1.5 is obtained in both cases. The results are discussed in the context of superfluid/superconductors and vortex dynamics, and are compared with what has been found for other related models.