Dynamical simulations of fractional giant Shapiro steps in two-dimensional Josephson arrays

Free, J. U.; Sp, Benz; Ms, Rzchowski; Tinkham, M.; Lobb, C. J.; Octavio, M.

doi:10.1103/physrevb.41.7267

Cited by 79 publications

(38 citation statements)

References 9 publications

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“…Numerical simulations 7,8 of large driven arrays suggest that this spatial periodicity is preserved when the dynamics is phase-locked to an external ac-perturbation applied in parallel to the dc force. We will show later, in section IV, that this is also a good approximation when the ac current is perpendicular to the dc current.…”

Section: Modelmentioning

confidence: 97%

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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Section: Modelmentioning

confidence: 97%

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

et al. 2003

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“…For q>l, these particular steps are namedfractional giant Shapiro steps (again, see Fig (Free et al, 1990. Curvesf=1/2 andf=0 are shifted from the origin along the current axis by successive 0.25 increments.…”

Section: Collective Effectsmentioning

confidence: 99%

“…Using the Josephson voltage relation [Josephson, 1962], we can relate vij to xj with he following, . We choose periodic boundaries perpendicular to the transport current direction in order to avoid boundary effects arising from simulating small-sized arrays [Free et al, 1990 andChung et al, 1990].…”

Section: Large Scalementioning

confidence: 99%

“…The behavior of [10]-oriented square-lattice proximity-effect Josephson-junction arrays has been described in terms of the driven motion of a superlattice of field-induced vortices commensurate with the underlying array lattice Free et al, 1990; K. H. ; and H. C. . For example, when f=1/2, the 2 x 2 vortex superlattice moves one array unit cell in a direction perpendicular to the trasport current after one rf cycle (see Figure 5.…”

Section: The Moving Vortex Modelmentioning

confidence: 99%

“…We take the phase differences, denoted as YA and ^B, of the junctions parallel to the external current to be equal to ±r14 (the array's ground state at f=112 [Teitel et a., 1983a]) at the beginning of the rcycle. When ¢ext is applied in the direction shown in the figure, it winds A and YB counterclockwise, YA by 37r/2 and 7 B by 7r/2 [Free et al, 1990], in one rf cycle (see Fig. 5.5c) such that the cell is now in the other f=1/2 ground state shown in Fig.…”

Section: The Moving Vortex Modelmentioning

confidence: 99%

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