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Acta Physico-Chimica Sinica

Non-equilibrium Phase Transition of Two-dimensional Fully-frustrated Josephson Junction Arrays

Ying Guo

Published Jan 1, 2007• 0 citations
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Abstract

The non-equilibrium phase transition, Ising-like phase transition of two-dimensional fully-frustrated Josephson junction arrays driven by external current was studied in the framework of the short-time dynamic scaling method. Within the resistively shunted junction (RSJ) dynamics, besides the critical temperature TC, the static critical exponents 2β/ν and ν, and dynamic critical exponent z were obtained.

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The non-equilibrium phase transition, Ising-like phase transition of two-dimensional fully-frustrated Josephson junction arrays driven by external current was studied in the framework of the short-time dynamic scaling method. Within the resistively shunted junction (RSJ) dynamics, besides the critical temperature TC, the static critical exponents 2β/ν and ν, and dynamic critical exponent z were obtained.
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.
Short-time dynamic behaviour of two-dimensional fully frustrated XY model near the Ising-like phase-transition temperature is studied with resistively shunted junction dynamics. The transition temperature T c and the dynamic and static critical exponents z , 2β/ν and ν are estimated under both a periodic boundary condition (PBC) and a fluctuating twist boundary condition (FTBC) using the short-time dynamic scaling analysis. The results show that T c , 2β/ν and ν are almost independent of the boundary conditions, whereas z depends on the boundary condition. The value of z = 2.18(5) of the PBC is roughly equal to that of the FF XY model with Monte Carlo dynamics under the PBC, while z = 2.05(4) of the FTBC is in agreement with that of the Coulomb gas model.
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​.
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.