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arXiv:cond-mat/9611208 · Physical Review Letters

1/ω Flux Noise and Dynamical Critical Properties of Two-DimensionalXYModels

Paul H. E. Tiesinga, Thomas J. Hagenaars, Johannes E. Van Himbergen, Jorge V. José

Published Jan 20, 1997• 29 citations
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Abstract

We have numerically studied the dynamic correlation functions in thermodynamic equilibrium of two-dimensional O(2) symmetry models with either bond [resistively shunted Josephson (RSJ)] or site [time-dependent Ginsburg-Landau (TDGL)] dissipation as a function of temperature $T$. We find that above the critical temperature the frequency dependent flux noise ${S}_{\ensuremath{\Phi}}(\ensuremath{\omega})\ensuremath{\sim}|1+(\ensuremath{\omega}/\ensuremath{\Omega}{)}^{2}{|}^{\ensuremath{-}\ensuremath{\alpha}(T)/2}$, with $0.85\ensuremath{\le}\ensuremath{\alpha}(\mathrm{TDGL})(T)\ensuremath{\le}0.95$ and $1.17\ensuremath{\le}\ensuremath{\alpha}(\mathrm{RSJ})(T)\ensuremath{\le}1.27$, while the dynamic critical exponents $z(\mathrm{TDGL})\ensuremath{\sim}2.0$ and $z(\mathrm{RSJ})\ensuremath{\sim}0.9$. Contrary to expectation the TDGL results are in closer agreement with the experiments in Josephson-junction arrays by Shaw et al. [Phys. Rev. Lett. 76, 2551 (1996)] than those from the RSJ model.

DOI
10.1103/physrevlett.78.519

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Two-dimensional XY\mathrm{XY}XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent z in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature TCG{T}^{\mathrm{CG}}TCG and the vortex renormalization given by the dielectric constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}) z=1/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}{T}^{\mathrm{CG}}\ensuremath{-}2>~2$ both for RSJ and TDGL and that the nonlinear IV\mathrm{IV}IV exponent a is given by a=z+1a=z+1a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.
The nonequilibrium phase transition of two-dimensional fully frustrated Josephson junction arrays driven by external currents is studied in the framework of the short-time dynamic scaling approach. Within the resistively shunted junction dynamics, besides the critical temperature Tc{T}_{c}Tc​, the static and dynamic critical exponents $2\ensuremath{\beta}∕\ensuremath{\nu}$, $\ensuremath{\nu}$, and zzz are obtained. The resulting values of Tc{T}_{c}Tc​ 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 zzz are strongly current dependent.
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 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.
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