Devil Staircase Dynamic in Arrays of Overdamped Josephson Junctions

Giovannella, Carlo; Ritort, Fèlix; Giannelli, A.

doi:10.1209/0295-5075/29/5/012

Cited by 7 publications

(6 citation statements)

References 25 publications

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“…The development of the SS can be well understood within the framework of the model describing the coupling between two oscillators. They mirror the existence of a locking between the external current and the intrinsic frequency of the system [4,5].…”

Section: Introductionmentioning

confidence: 73%

“…It may be caused, in fact, by the introduction of any type of disorder (coupling, positional, etc), by an inhomogeneous current polarization or, finally, by the presence of an external magnetic field. In this latter case, a devil's staircase structure with a 0953-8984/96/173057+12$19.50 c 1996 IOP Publishing Ltd fractal dimension D = 0.88 [5] has been observed. Under these conditions the array cannot be reduced any longer to a parallel arrangement of one-dimensional columns of oscillators, and the 2D cooperative behaviour comes into play.…”

Section: Introductionmentioning

confidence: 91%

“…Usually, the SSS are explained in terms of the formation and the coherent displacement of superarrays of vortices commensurate to the dimension of the array [8,9]. This interpretation, however, is somewhat contradicted by numerical simulations dealing with the dynamical behaviour of a single plaquette [10], of a ladder [11] and of small square arrays [5], which show locked states at fractional values of the normalized voltage that would correspond to commensurate arrays of vortices with a lattice period larger than that of the simulated SJA.…”

Section: Introductionmentioning

confidence: 99%

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On the locked dynamical states of an overdamped Josephson junction array

Ciria

Giovannella

1996

J. Phys.: Condens. Matter

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We study the dynamics of a 2D array of Josephson junctions biased with both dc and ac currents. Within certain ranges of the dc current intensity a locking between the natural oscillation frequency of the array and that of the ac forcing term occurs, giving rise to periodic solutions. As expected, a set of Shapiro steps appears in the V -I curve. We show that there is no one-to-one correspondence between the value of V on the Shapiro step and the dynamical state of the array. In particular for a frustration equal to 0.5, besides the well-known ground state, g.s., of the array (the checkerboard-like vortex configuration), there exist other dynamical states accessible to the system. These latter are characterized by the same average voltage of the g.s. but different average energies and vortex configurations, with one or more domain walls. These 'new' states are stable against small thermal fluctuations and phase perturbations. A better insight into the physical conditions needed to generate them has been obtained by studying the dynamical behaviour of a ladder as a function of its size and of its orientation with respect to the external bias current The relevance of our observations to the experimental studies of the array dynamics performed on a microscopical scale is briefly discussed.

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Section: Introductionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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On the locked dynamical states of an overdamped Josephson junction array

Ciria

Giovannella

1996

J. Phys.: Condens. Matter

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“…4 Fractional giant Shapiro steps at voltages V n,q = N n Ω/2eq, were observed experimentally 5,6 for strongly commensurate magnetic fields, f = p/q, with p, q integers, and extensively investigated in numerical simulations. 7,8,9,10,11 Also, subharmonic giant Shapiro steps at voltages V n,m = N n Ω/2em were observed experimentally 6 for zero magnetic field (f = 0), and attributed to the nucleation of complex collective dynamical states 12,13 induced by disorder or inductance effects. Shapiro-like phase-locking is also observed in the case of driven vortex lattices in bulk superconductors with two-dimensional periodic pinning arrays, as recently reported both experimentally 14 and theoretically.…”

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confidence: 96%

Transverse phase locking in fully frustrated Josephson junction arrays: A different type of fractional giant steps

et al. 2003

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We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied perpendicular to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudinal ac-drive. The critical current and the phase-locked current step width, increase quadratically with (small) amplitudes of the ac-drive. For larger amplitudes of the transverse ac-signal, we find windows where the critical current is hysteretic, and windows where phase locking is suppressed due to dynamical instabilities. We characterize the dynamical states around the phase-locking interference condition in the IV curve with voltage noise, Lyapunov exponents and Poincaré sections. We find that zero temperature phase-locking behavior in large fully frustrated arrays is well described by an effective four plaquette model.

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“…In fact, SSS have been found in systems with inhomogeneously injected current and/or disorder and frustration; in this last case, a devil staircase structure, with a fractal dimension D = 0.88 [10] has been observed. Aij is the circuitation of the vector potential between the points i and j.…”

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confidence: 96%