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Register a new userDynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder
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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 an 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 %by Yun {it et al.} in cond-mat/0509151 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 $E_J/k_B$ with the Josephson coupling strength $E_J$), the correlation length critical exponent $ u=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.
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The boundary effects on the current-voltage characteristics in two-dimensional arrays of resistively shunted Josephson junctions are examined. In particular, we consider both the conventional boundary conditions (CBC) and the fluctuating twist boundary conditions (FTBC), and make comparison of the obtained results. It is observed that the CBC, which have been widely adopted in existing simulations, may give a problem in scaling, arising from rather large boundary effects; the FTBC in general turn out to be effective in reducing the finite-size effects, yielding results with good scaling behavior. To resolve the discrepancy between the two boundary conditions, we propose that the proper scaling in the CBC should be performed with the boundary data discarded: This is shown to give results which indeed scale well and are the same as those from the FTBC.
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W. A. C. Passos
, F. M. Araujo-Moreira
, W. A. Ortiz (Grupo den Supercondutividade e Magnetismo
1999
In this work we study the magnetic remanence exhibited by Josephson junction arrays in response to an excitation with an AC magnetic field. The effect, predicted by numerical simulations to occur in a range of temperatures, is clearly seen in our tridimensional disordered arrays. We also discuss the influence of the critical current distribution on the temperature interval within which the array develops a magnetic remanence. This effect can be used to determine the critical current distribution of an array.
As the size of a Josephson junction is reduced, charging effects become important and the superconducting phase across the link turns into a periodic quantum variable. Isolated Josephson junction arrays are described in terms of such periodic quantum variables and thus exhibit pronounced quantum interference effects arising from paths with different winding numbers (Aharonov-Casher effects). These interference effects have strong implications for the excitation spectrum of the array which are relevant in applications of superconducting junction arrays for quantum computing. The interference effects are most pronounced in arrays composed of identical junctions and possessing geometric symmetries; they may be controlled by either external gate potentials or by adding/removing charge to/from the array. Here we consider a loop of N identical junctions encircling one half superconducting quantum of magnetic flux. In this system, the ground state is found to be non-degenerate if the total number of Cooper pairs on the array is divisible by N, and doubly degenerate otherwise (after the stray charges are compensated by the gate voltages).
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W. A. C. Passos
, U. R. de Oliveira
, W. A. Ortiz (Grupo den Supercondutividade e Magnetismo
2000
In this contribution we present a simple and effective procedure to determine the average critical current of a tridimensional disordered Josephson junction array (3D-DJJA). Using a contactless configuration we evaluate the average critical current and the typical width of the distribution through the analysis of the isothermal susceptibility response to the excitation field amplitude, chiAC(h). A 3D-DJJA fabricated from granular Nb is used to illustrate the method.
We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction (RCSJ) model, including full capacitance-matrix effects}. We define and study three different models of the capacitance matrix $C_{vec{r},vec{r}}$: Model A includes only mutual capacitances; Model B includes mutual and self capacitances, leading to exponential screening of the electrostatic fields; Model C includes a dense matrix $C_{vec{r},vec{r}}$ that is constructed approximately from superposition of an exact analytic solution for the capacitance between two disks of finite radius and thickness. In the latter case the electrostatic fields decay algebraically. For comparison, we have also evaluated the full capacitance matrix using the MIT fastcap algorithm, good for small lattices, as well as a corresponding continuum effective-medium analytic evaluation of a finite voltage disk inside a zero-potential plane. In all cases the effective $C_{vec{r},vec{r}}$ decays algebraically with distance, with different powers. We have then calculated current voltage characteristics for DC+AC currents for all models. We find that there are novel giant capacitive fractional steps in the I-Vs for Models B and C, strongly dependent on the amount of screening involved. We find that these fractional steps are quantized in units inversely proportional to the lattice sizes and depend on the properties of $C_{vec{r},vec{r}}$. We also show that the capacitive steps are not related to vortex oscillations but to localized screened phase-locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed.
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