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arXiv:0805.2428 · Physical Review B

Phase transition in site-diluted Josephson junction arrays: A numerical study

Jian-Ping Lv, Huan Liu, Qing‐Hu Chen

Published Mar 16, 2009• 17 citations
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Abstract

We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied; evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings but also shed some light on the relevant phase transitions.

DOI
10.1103/physrevb.79.104512

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We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied; evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings but also shed some light on the relevant phase transitions.
We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson-junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that, with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied, evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings, but also shed some light on the relevant phase transitions.
Measurements of the IV characteristics of site-diluted Josephson-junction arrays have revealed intriguing effects of percolative disorder on the phase transition and the vortex dynamics in a two-dimensional XY system. Different from other types of phase transitions, the Kosterlitz-Thouless transition was eliminated with the introduction of percolative disorder far below the percolation threshold. Even after the Kosterlitz-Thouless order had been removed, the system remained superconducting at low temperatures by establishing a different type of order. Near the percolation threshold, evidence was found that, as a consequence of the underlying fractal structure, the critical dynamics of the phase degrees of freedom persisted down to zero temperature.
Using resistivity-shunted-junction dynamics, we model bond dilutions in Josephson junction arrays. The current-voltage characteristics are obtained by large-scale numerical simulations. By dynamic scaling analysis to the finite-temperature phase transition, we provide clear evidence for the existence of non-Kosterlitz–Thouless-type phase transition, as described by Kosterlitz et al. [J. Phys. C 6, 1181 (1973); J. Phys. C 7, 1046 (1974)] in a wide range of disorder strengths. Critical temperature and exponents of the phase transitions are estimated, which are further confirmed by the finite-size scaling analysis at the transition temperature.
We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of EJ∕kB{E}_{J}∕{k}_{B}EJ​∕kB​ with the Josephson coupling strength EJ{E}_{J}EJ​), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent z=2.0z=2.0z=2.0 in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.
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​.
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.