Frequency dependence of Shapiro steps in Josephson-junction arrays

Rzchowski, M. S.; Sohn, Lydia L.; Tinkham, M.

doi:10.1103/physrevb.43.8682

Cited by 45 publications

(27 citation statements)

References 11 publications

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“…If we maintain this assumption of periodicity, the equations of Ref. [19] are readily extended to to the case of currents applied at an angle to the plaquette edges. The resulting equations take the form…”

Section: A Four-plaquette Unit Cellmentioning

confidence: 99%

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Dynamical phase transition in a fully frustrated Josephson array on a square lattice

1999

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We study dynamical phase transitions at temperature T = 0 in a fully frustrated square Josephson junction array subject to a driving current density which has nonzero components ix, iy parallel to both axes of the lattice. Our numerical results show clear evidence for three dynamical phases: a pinned vortex lattice characterized by zero time-averaged voltages vx t and vy t, a "plastic" phase in which both vx t and vy t are nonzero, and a moving lattice phase in which only one of the timeaverage voltage components is nonzero. The last of these has a finite transverse critical current: if a current is applied in the x direction, a nonzero transverse current density iy is required before vy t becomes nonzero. The voltage traces in the moving lattice phase are periodic in time. By contrast, the voltages in the plastic phase have continuous power spectra which are weakly dependent on frequency. This phase diagram is found numerically to be qualitatively unchanged by the presence of weak disorder. We also describe two simple analytical models which recover some, but not all, the characteristics of the three dynamical phases, and of the phase diagram calculated numerically. 74.60.Ge,74.50.+r,74.60.Jg

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Section: A Four-plaquette Unit Cellmentioning

confidence: 99%

“…1 of Ref. [19]), t ′ = t/τ is a dimensionless time, and I tot,x and I tot,y are the total bias currents in the x and y directions per 2 × 2 superlattice cell (in units of the single-junction critical current).…”

Section: A Four-plaquette Unit Cellmentioning

confidence: 99%

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

1999

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“…33 The same model was later used in Ref. 9 to study the (longitudinal) Shapiro steps. Since the analysis done in the work of Refs.…”

Section: Modelmentioning

confidence: 99%

“…The presence of a magnetic field (f = 0) breaks the axial symmetry in the direction of the bias current, and 2D-cooperative behavior may come into play. This leads to the well-known fractional giant Shapiro steps 5,6,7,8,9,10,11 induced by a longitudinal ac current. It also, as we will demonstrate in this paper, allows for transverse phase locking when the ac current is perpendicular to the dc current, since the two directions of motion become coupled.…”

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confidence: 99%

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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“…Their properties and some interesting phenomena have been studied recently in the dc+ac driven Frenkel-Kontorova (FK) model [3][4][5][6]. Those works have been stimulated by theoretical and experimental studies of the Shapiro steps in physical systems such as charge-density or spin-density wave conductors [7][8][9][10][11][12][13], vortex lattices [14], Josephson-junction arrays biased by external currents [15][16][17][18][19][20], and superconducting nanowires.…”

Section: Introductionmentioning

confidence: 99%

Friction phenomena in the overdamped three-layer model

et al. 2015

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An overdamped three-layer model consisting of two harmonic chains of interacting particles, representing the upper and the middle layers, which move over the substrate potential, is studied in the present paper. A dc+ac force is applied only on the upper harmonic chain, and dynamics of both layers are investigated. The results show that the dynamical mode locking and Shapiro steps appear not only in the upper layer but also in the middle one. It is noted that the motion of particles in the upper layer corresponds to the standard Frenkel-Kontorova model. The dependence of the Shapiro steps of the middle layer on the system parameters are determined. It is shown that the height of the first Shapiro step of the upper layer is unrelated to the interaction parameters of the particles of both the upper and the middle layers, while the height of the first Shapiro step of the middle layer depend only on the interaction parameters of the particles of the middle layers. Two critical forces which transfer from locked state to the sliding one of both the upper and the middle layers are also studied. They depend on the amplitude and the frequency of the external ac driving force.

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Frequency dependence of Shapiro steps in Josephson-junction arrays

Cited by 45 publications

References 11 publications

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

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

Friction phenomena in the overdamped three-layer model

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