Finite-size effects and dynamical scaling in two-dimensional Josephson junction arrays

Abstract

In recent years many groups have used Fisher, Fisher, and Huse (FFH) dynamical scaling to investigate and demonstrate details of the superconducting phase transition. Some attention has been focused on two dimensions where the phase transition is of the Kosterlitz-ThoulessBerezinskii (KTB) type. Pierson et al. used FFH dynamical scaling almost exclusively to suggest that the dynamics of the two-dimensional superconducting phase transition may be other than KTB-like. In this work we investigate the ability of scaling behavior by itself to yield useful information on the nature of the transition. We simulate current-voltage (IV) curves for two-dimensional Josephson junction arrays with and without finite-size-induced resistive tails.We find that, for the finite-size effect data, the values of the scaling parameters, specifically the transition temperature and the dynamical scaling exponent z, depend critically on the magnitude of the contribution that the resistive tails make to the IV curves. In effect, the values of the scaling parameters depend on the noise floor of the measuring system. 3

Estimation of the critical dynamics and thickness of superconducting films and interfaces

“…[3][4][5][6][7] Alternatively, the application of the conductivity relation ͑2͒ requires the explicit form of the correlation length. Since superconducting thin films and interfaces are expected to undergo a Berezinskii-Kosterlitz-Thouless ͑BKT͒ transition from the superconducting to the normal state the correlation length adopts for T Ն T c the characteristic form 8,9 ͑T͒ = 0 expͩ 2…”

Vortex-unbinding and finite-size effects inTl2Ba2CaCu2Jin1, Wen2 2003Phys. Rev. B2020View full textAdd to dashboardCite

“…Following this approach, we show the scaling results of our I-V data of Tl 2 Ba 2 CaCu 2 O 8 film with z = 2 and z = 5.6 in Figure 3(a) and (b), respectively. The data are plotted in lines rather than points in order to expose any shortcomings in the scaling collapse as suggested by Holzer et al 22 . The upper (lower) branch of the plots corresponds to the temperatures below (above) T KT .…”

“…Holzer et al 22 showed that for a finite-size system, the critical exponent z derived from dynamic scaling becomes larger if the noise floor is lowered. This implies that the data with a fixed noise floor can be scaled with a z value larger than the one characterizing a true phase transition, so there is some uncertainty if it is judged only from the dynamic scaling results Fig.…”

“…Holzer et al 22 simulated I-V curves for 2D Josephson junction arrays, and argued that for the finite-size effect data, the scaling parameters z and T KT depends critically on the noise floor of the measuring system, and that the value z ≈ 6 for a variety of 2D systems is related to the nature of data collection or the resolution of instrument, rather than characterizing some universality of physics.…”

Zero-magnetic-field dynamic scaling inBi2Sr2CaCu2O8Sefrioui1, Arias2, León3 et al. 2004Phys. Rev. B10020View full textAdd to dashboardCite

“…5 A first issue which deserves discussion is size effects. 17 Free vortices can be induced below T BKT resulting from size effects when the critical distance r c is larger than min͓W , Ќ ͔, where W is sample width. Since no free vortices are expected for r c Ӷ min͓W , Ќ ͔ size effects may yield an apparent transition, termed "ghost" transition by Medvedyeva et al 16 obeying a specific scaling behavior.…”