Vortex dynamics in classical underdamped junction arrays

Eikmans, H.; Himbergen, J. E. van

doi:10.1103/physrevb.45.10597

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…We construct a single vortex configuration with a method used previously in Ref. [8]. It allows for a direct calculation of the phase configuration in terms of the vorticities n(R) ∈ {−1, 0, 1} once a gauge choice for the A(r, r ′ ) and a choice for one of the phases θ(r) has been made.…”

Section: Calculational Approachmentioning

confidence: 99%

“…An example of this approach is given by the Bardeen-Stephens equation which has been successfully applied to conventional superconductors [1]. A similar approach has been attempted in the description of the transport properties in two-dimensional Josephson junction arrays (JJA) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. These arrays are 2D lattices of superconducting islands (sites) connected by Josephson junctions (bonds).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

Hagenaars¹,

Tiesinga²,

Himbergen³

et al. 1994

Phys. Rev. B

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When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a nonlinear viscous force of the form F D = η(ẏ)ẏ = A 1+Bẏẏ , whereẏ is the vortex velocity, η(ẏ) is the velocity dependent viscosity and A and B are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.

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Section: Calculational Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

Hagenaars¹,

Tiesinga²,

Himbergen³

et al. 1994

Phys. Rev. B

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“…For currents below the depinning current i dp the voltage is zero (see figure 2), when it is averaged over enough periods of the ac drive. The vortex deforms in response to the ac + dc drive, but stays in the same plaquette [23]. Or, for low enough frequency ν and large enough i ac , it can even oscillate back and forth over a finite number of plaquettes.…”

Section: The I -V Characteristicsmentioning

confidence: 99%

Single-vortex-induced voltage steps in Josephson-junction arrays

Tiesinga¹,

Hagenaars

Himbergen³

et al. 1997

J. Phys.: Condens. Matter

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We have numerically and analytically studied ac+dc driven Josephson-junction arrays with a single vortex or with a single vortex-antivortex pair present. We find single-vortex steps in the voltage versus current characteristics (I-V ) of the array. They correspond microscopically to a single vortex phaselocked to move a fixed number of plaquettes per period of the ac driving current. In underdamped arrays we find vortex motion period doubling on the steps. We observe subharmonic steps in both underdamped and overdamped arrays. We successfully compare these results with a phenomenological model of vortex motion with a nonlinear viscosity. The I-V of an array with a vortex-antivortex pair displays fractional voltage steps. A possible connection of these results to present day experiments is also discussed.

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“…where M = πβ c and η = π for a square array [9][10][11][12][13][14]23]. This equation describes the vortex as a point particle with mass M that, driven by a (Lorentz) force proportional to i b , moves through a sinusoidal pinning potential and experiences a viscous damping force with constant viscosity coefficient η.…”

Section: Model Equationsmentioning

confidence: 99%

“…(1) by currents through ohmic shunt resistors, give rise to a viscous force on a moving vortex. Furthermore, in capacitive arrays (β c > 0), the electromagnetic energy stored in the junction capacitors due to the vortex motion, can be interpreted as the kinetic energy of a massive vortex [9][10][11][12][13][14]23]. For an infinite array, and for infinite magnetic penetration depth, a coarse-grained model equation in terms of a single continuous vortex coordinate x reads:…”

Section: Model Equationsmentioning

confidence: 99%

Vortex reflection at boundaries of Josephson-junction arrays

Hagenaars¹,

Himbergen²,

José³

et al. 1996

Phys. Rev. B

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We study the propagation properties of a single vortex in square Josephson-junction arrays ͑JJA͒ with free boundaries and subjected to an applied dc current. We model the dynamics of the JJA by the resistively and capacitively shunted junction equations. For zero Stewart-McCumber parameter ␤ c we find that the vortex always escapes from the array when it gets to the boundary. For ␤ c у2.5 and for low currents we find that the vortex escapes, while for larger currents the vortex is reflected as an antivortex at one edge and the antivortex as a vortex at the other, leading to a stationary vortex oscillatory state and to a nonzero time-averaged voltage. The escape and the reflection of a vortex at the array edges is qualitatively explained in terms of a coarsegrained model of a vortex interacting logarithmically with its image. For ␤ c у50 we find that the reflection regime is split up in two disconnected regimes separated by a second vortex escape regime. When considering an explicit vortex-antivortex pair in an array with periodic boundaries, we find a solitonlike nondestructive collision in virtually the same current regimes as where we find reflection of a single vortex at a free boundary; outside these current regimes the pair annihilates. We also discuss the case when the free boundaries are at 45°with respect to the current direction, and thus the angle of incidence of the vortex to the boundaries is 45°. Finally, we study the effect of self-induced magnetic fields ͑for penetration depths ranging from 10 to 0.3 times the lattice spacing͒ by taking into account the full-range inductance matrix of the array and find qualitatively equivalent results. We also discuss possible consequences of these results to experimental systems.

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Vortex dynamics in classical underdamped junction arrays

Cited by 5 publications

References 7 publications

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

Single-vortex-induced voltage steps in Josephson-junction arrays

Vortex reflection at boundaries of Josephson-junction arrays

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