Phase transitions in Josephson-junction arrays with long-range interaction

Ll, Sohn; Ms, Rzchowski; Free, J. U.; Tinkham, M.

doi:10.1103/physrevb.47.967

Cited by 22 publications

(16 citation statements)

References 16 publications

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“…The critical current is linear in N for small N, but saturates at a finite value for large N. The saturation value varies as the inverse square root of wire inductance per unit length. This is in excellent agreement with a simple model suggested by Sohn et al, 3,4 and the occurrence of saturation is also confirmed experimentally. 3,4 We also find that our numerical current-voltage (IV) characteristics are hysteretic, even though the array, in our model, is composed entirely of nonhysteretic elements.…”

Section: Introductionsupporting

confidence: 91%

“…For this reason, such arrays are sometimes said to have long-range interactions. Arrays of this kind were, to the best of our knowledge, first studied theoretically by Vinokur et al 2 They have since been fabricated and studied both experimentally and theoretically by Sohn et al 3,4 In the presence of a magnetic field, it has been predicted that such long-range interactions, even in periodic arrays, will give rise to glassy behavior. 2,5,6 Other types of hybrid arrays can readily be imagined.…”

Section: Introductionmentioning

confidence: 99%

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Josephson-junction arrays with long-range interactions

Harbaugh

Stroud

1997

Phys. Rev. B

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We calculate the current-voltage (IV) characteristics of a Josephson-junction array with long-range interactions. The array consists of two sets of equally spaced parallel superconducting wires placed at right angles. A Josephson junction is formed at every point wherever the wires cross. We treat each such junction as an overdamped resistively shunted junction, and each wire segment between two junctions as a similar resistively shunted junction with a much higher critical current. The IV characteristics are obtained by solving the coupled Josephson equations numerically. We find that, for a sufficiently large number of wires, the critical current saturates at a finite value because of the wire inductance, in excellent agreement with experiment. The calculated IV characteristics also show a striking hysteresis, even though each of the individual junctions is nonhysteretic. The hysteresis results from a global redistribution of current flow on the upper and lower voltage branches, and is also in excellent agreement with experiment.

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Section: Introductionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Josephson-junction arrays with long-range interactions

Harbaugh

Stroud

1997

Phys. Rev. B

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“…Although such arrays had been fabricated by Sohn et al [2], the samples used in the present Letter for the first time have low enough critical currents and hence low enough screening to be in the regime well described by existing theoretical models [3,4].…”

Section: Department Of Physics and Division Of Engineering And Appliementioning

confidence: 91%

“…For an ordered array with long-range interaction in the limit of negligible screening, Sohn et al [3] have performed a mean-field analysis and computed the transition temperature T MF c ͑ f͒ as a function of the applied field and array size. Because each wire has a large number of nearest neighbors, a mean-field theory using the phase of each wire as a classical thermodynamic variable should provide a good description of this system.…”

Section: Department Of Physics and Division Of Engineering And Appliementioning

confidence: 99%

Transition Temperature of Josephson Junction Arrays with Long-Range Interaction

Shea

Tinkham

1997

Phys. Rev. Lett.

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We report measurements of the dependence on magnetic field and array size of the resistive transition of Josephson junction arrays with long-range interaction. Because every wire in these arrays has a large number of nearest neighbors (9 or 18 in our case), a mean-field theory should provide an excellent description of this system. Our data agree well with this mean-field calculation, which predicts that T c (the temperature below which the array exhibits macroscopic phase coherence) shows very strong commensurability effects and scales with array size. [S0031-9007(97) We report an experimental investigation of ordered Josephson junction arrays with long-range interaction (ALRI), of the sort originally proposed in the disordered limit by Vinokur et al. [1]. Although such arrays had been fabricated by Sohn et al. [2], the samples used in the present Letter for the first time have low enough critical currents and hence low enough screening to be in the regime well described by existing theoretical models [3,4].These arrays consist of two perpendicular sets of N parallel superconducting wires, coupled by Josephson junctions at every point of crossing (see Fig. 1). In this geometry, any horizontal (vertical) wire is nearest neighbor to all vertical (horizontal) wires, and nextnearest neighbor to all other horizontal (vertical) wires. Hence we term the interaction long range. The number of nearest neighbors in these arrays is equal to the array size N. This is in sharp contrast to standard (shortrange interaction) 2D arrays where the number of nearest neighbors (typically 4 or 6) is independent of array size.Arrays with long-range interaction were first proposed by Vinokur et al.[1] as a physical realization of the Sherrington-Kirkpatrick (SK) model [5], which is an analytically studied model of a spin-glass. The SK model assumes the interaction between spins does not depend on the separation between the spins, and therefore does not describe most experimentally studied spin-glass systems. Vinokur et al. showed that for the case where the wires are positionally disordered and a sufficiently strong perpendicular magnetic field is applied, ALRI are very similar to the SK model and admit an analytic solution. More recently, Chandra et al. [4] have shown that even for an ordered array, glassy behavior is expected in a very weak field (less than one flux quantum per row).The equivalent of "spins" in these ALRI are the phases of the superconducting wires, which are well defined in any given gauge. Since field screening is negligible, the actual field equals the applied field, and we can make the gauge choice A fxF 0 ͞a 2ŷ , where a is the lattice constant and f is the flux per cell divided by a flux quantum. In the appropriate limit where the junction critical currents are negligible compared to the wire critical currents, we can write J 0, where J is the current density in the wires. J is given by the GinzburgLandau expressionwhere C is the order parameter of the wires. With our gauge choice, setting J to zero implies tha...

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“…2 The supercurrent transport and magnetic screening response of such proximity coupled Josephson-junction ͑JJ͒ ensembles, ordered or otherwise, have been studied extensively. [3][4][5][6][7][8] In absence of magnetic fields, coupled JJs in two-dimension ͑2D͒ approach zero resistance state via Kosterlitz-Thouless ͑KT͒ transition 9 at T KT . Increasing the temperature above T KT , dissociates the vortex-antivortex bound pairs and the resultant increase in entropy leads to some finite resistance.…”

Section: Introductionmentioning

confidence: 99%

Flux-closure pattern in a two-dimensional NbN–Fe superconductor-ferromagnet nanocomposite: Anisotropy of the angular magnetoresistance

Bose

Budhani

2010

Journal of Applied Physics

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The angular dependence of magnetoresistance ͑MR͒ of distributed NbN-Fe-NbN Josephson-junctions in the out-of-plane and in-plane magnetic field geometries shows a striking anisotropy on the polarity of the current ͑I + / I − ͒ and its direction with respect to the applied field. The origin of this anisotropy is suggested to be the difference in the degree of spin polarization of electrons injected from Fe nanoplaquettes into the superconducting NbN for I + and I − . Such a conclusion is based on the topography of flux-closure domains in Fe plaquettes. The anisotropy of MR is suppressed at high fields as the flux-closure domains transform into a single-domain structure.

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Phase transitions in Josephson-junction arrays with long-range interaction

Cited by 22 publications

References 16 publications

Josephson-junction arrays with long-range interactions

Josephson-junction arrays with long-range interactions

Transition Temperature of Josephson Junction Arrays with Long-Range Interaction

Flux-closure pattern in a two-dimensional NbN–Fe superconductor-ferromagnet nanocomposite: Anisotropy of the angular magnetoresistance

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