New Exponent for the Nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">IV</mml:mi></mml:math>Characteristics of a Two Dimensional Superconductor

Minnhagen, Petter; Westman, Olof; Jönsson, Anna; Olsson, Peter

doi:10.1103/physrevlett.74.3672

Cited by 42 publications

(52 citation statements)

References 14 publications

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“…8), where the slopes of the lines in the log-log plot correspond to z ≈ 2 for both RSJD and RD. Consequently, our result z ≈ 2.0 is in accordance with other existing theoretical predictions 23,24 while it contradicts recently suggested, very large values in Refs. 29 and 30. In order to determine z at the KT transition for the PBC we use the following finite-size scaling form Eq.…”

Section: Critical Temperaturesupporting

confidence: 88%

“…24, where z has been obtained from a simple scaling argument and the observed 1/t behavior of the correlation function G(t).…”

Section: A 2d Xy Modelmentioning

confidence: 99%

“…32: ξ is obtained from the wavevector dependence of the static dielectric function 1/ǫ(0) introduced in Eq. (24). The characteristic frequency ω 0 ∼ 1/τ is determined from the frequency dependence of 1/ǫ(ω); ω 0 is the position of the dissipation peak in |Im1/ǫ(ω)|.…”

Section: High-temperature Phasementioning

confidence: 99%

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Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

2000

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The dynamic critical exponent z is determined numerically for the d-dimensional XY model (d = 2, 3, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of z are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the the same boundary condition do not always give the same value of z. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of z consistent with expectations for superfluids and superconductors: z = 2, 3/2, and 2 for d = 2, 3, and 4, respectively.

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Section: Critical Temperaturesupporting

confidence: 88%

“…24, where z has been obtained from a simple scaling argument and the observed 1/t behavior of the correlation function G(t).…”

Section: A 2d Xy Modelmentioning

confidence: 99%

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Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

2000

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“…Despite the relatively simple construct of the theory, its experimental and numerical verification has remained controversial [5][6][7][8][9][10]. It has been noted that boundary and finite-size effects can dominate the measured voltage drop across the sample at sufficiently low temperatures, making it difficult to achieve an unambiguous comparison between theory and experiments.An alternative theory of vortex flow dissipation which also yields nonlinear I-V curves in the superconducting state derives from the dynamic scaling hypothesis [11,12]. For superconducting films and Josephson junction arrays (JJA), the two approaches differ in their predictions of the exponent a(T ) characterizing the power-law behavior V ∼ I a below the Kosterlitz-Thouless-Berezinskii (KTB) transition temperature T KT .…”

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confidence: 99%

Anomalous Finite-Size Effect in Superconducting Josephson Junction Arrays

2001

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We report large-scale simulations of the resistively-shunted Josephson junction array in strip geometry. As the strip width increases, the voltage first decreases following the dynamic scaling ansatz proposed by Minnhagen et al. [Phys. Rev. Lett. 74, 3672 (1995)], and then rises towards the asymptotic value predicted by Ambegaokar et al. [Phys. Rev. Lett. 40, 783 (1978)]. The nonmonotonic size-dependence is attributed to shortened life time of free vortices in narrow strips, and points to the danger of single-scale analysis applied to a charge-neutral superfluid state. 74.50.Fg, 05.60.Gg, 67.40.Rp, 75.10.Hk Dissipation of the supercurrent through superfluid and superconducting films is caused by the flow of free vortices transverse to the current [1][2][3]. This phenomenon was analyzed in detail by Ambegaokar, Halperin, Nelson, and Siggia (AHNS) [4]. In the context of a uniform superconducting film in zero magnetic field, their theory predicts a power-law current-voltage (I-V ) relationship with a temperature-dependent exponent. Despite the relatively simple construct of the theory, its experimental and numerical verification has remained controversial [5][6][7][8][9][10]. It has been noted that boundary and finite-size effects can dominate the measured voltage drop across the sample at sufficiently low temperatures, making it difficult to achieve an unambiguous comparison between theory and experiments.An alternative theory of vortex flow dissipation which also yields nonlinear I-V curves in the superconducting state derives from the dynamic scaling hypothesis [11,12]. For superconducting films and Josephson junction arrays (JJA), the two approaches differ in their predictions of the exponent a(T ) characterizing the power-law behavior V ∼ I a below the Kosterlitz-Thouless-Berezinskii (KTB) transition temperature T KT . According to the AHNS theory,where χ = πJ R /k B T and J R is the renormalized spinwave stiffness. On the other hand, the dynamic scaling analysis of Minnhagen et al.[12] suggestsThe two expressions coincide at T KT where χ = 2, but the difference grows rapidly as one moves to low temperatures. While there seem to be ample numerical support for the Minnhagen et al. scaling [10,[12][13][14], agreement with the AHNS theory has also been reported [8]. To rationalize the two scenarios, Bormann [15] made an interesting suggestion that strong current creates a dense set of vortex-antivortex pairs, thereby invalidating the AHNS treatment. Nevertheless, the AHNS theory should still apply at sufficiently weak currents. This picture has not been borne out by a recent numerical study [10] which shows persistently larger value of a than Eq. (1) predicts.In this Letter, we present I-V results from large-scale simulations of the resistively shunted Josephson-junction (RSJ) array. A rectangular strip geometry is used to decouple boundary effects introduced by the current leads from finite-size effects arising from vortex/antivortex motion transverse to the current I. The main finding of our work is the exis...

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“…is the dynamic exponent first considered by Minnhagen and co-workers [17]. The temperature dependence of z scale is shown in Fig.…”

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confidence: 99%

Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids

2013

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An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature TKT . An approximate solution for quenches at and above above TKT provides insights into the origin of logarithmic transients in the vortex decay, and is in general agreement with recent simulations of the quenched XY model. These results confirm that there is no "creation" of vortices whose density increases with the quench rate as predicted by the Kibble-Zurek theory, but only monotonic decay of the thermal vortices already present at the initial temperature. PACS numbers: 64.60.Ht, 67.25.dj, 67.25.dk, 67.25.dpAlthough the phase-ordering kinetics of temperaturequenched thermodynamic systems have been studied for many decades [1], there are only a few exact results for the dynamics of the recovery to equilibrium [2,3]. For many systems, progress in the field has been made by asserting that dynamic scaling should apply to a quenched system, that for a system with non-conserved order parameter the dynamics will be characterized by a growing length scale ξ(t) = ξ 0 t 1/z , where z ≈ 2 is the dynamical exponent of model A in the classification of Halperin and Hohenberg [4] and t is the time from the quench to low temperature. Scaling holds if solutions involving a length scale r only depend on the ratio r/ξ. The growing length scale characterizes the domain growth of the topological defects of the order parameter as the system becomes completely ordered at long times. A phenomenological argument [1,5] is commonly used to predict the time dependence of the decaying defect density:where n is the number of components of the order parameter. Superfluids are in the n = 2 universality class, where the defects are quantized vortices, so if z = 2 then dynamic scaling predicts a 1/t decay of the vortex density. Computer simulations of spin systems with varying n gave general agreement with Eq. (1), though only at long time and length scales [6]. However, a problematic case for dynamic scaling has been two-dimensional superfluids, where the defects are the vortex pairs of the Kosterlitz-Thouless theory [7] characterizing the equilibrium phase transition occurring at the critical temperature T KT . The above arguments would give a vortex density decaying as t −1 for quenches from well above T KT to very low temperatures. Simulations of the XY model [8][9][10], however, showed the initial vortex decay to be considerably slower than this, and then only at very long times finally approached the predicted exponent of −1. The behavior could be modeled as a ln t/t variation, but this requires altering the dynamic length scale to vary as (t/ ln t) 1/z for initial temperatures above T KT . This change has been cited [11] as a breakdown of dynamic scaling, though others [12] find such a sudden change in the dynamic scale still fully consistent with scaling. To further complicate the issue, numerical solutions of the Fokker-Planck equation f...

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New Exponent for the NonlinearIVCharacteristics of a Two Dimensional Superconductor

Cited by 42 publications

References 14 publications

Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

Anomalous Finite-Size Effect in Superconducting Josephson Junction Arrays

Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids

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