Anomalous Finite-Size Effect in Superconducting Josephson Junction Arrays

Abstract

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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