Dynamic scaling for two-dimensional superconductors, Josephson-junction arrays, and superfluids

Abstract

The value of the dynamic critical exponent z is studied for two-dimensional superconducting, superfluid, and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find z ≃ 5.6 ± 0.3, a relatively large value indicative of non-diffusive dynamics. Universality of the scaling function is tested and confirmed for the thinnest samples. We discuss the validity of the dynamic scaling analysis as well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition in these systems, the results of which seem to be consistent with simple diffusion (z = 2). Further studies are discussed and encouraged.

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

“…This method closely mirrors the procedure followed by Pierson, et al 11 For each of the parameters obtained from a scaling collapse, the uncertainty in the reported transition temperature is ±0.01 K and the uncertainty in the value for z is ±0.03.…”

“…In the KTB transition z is expected to be 2. Ammirata et al 11 have suggested that z is considerably larger than 2 in such systems, perhaps as large as 5 or 6. They base this conclusion on a scaling analysis of several experimental systems, some of which 10,13 have heretofore been assumed to display a KTB transition.…”

“…(2) as We can remove a factor of (I>/T) z from D ± and rename it C ± , yielding This is the form often preferred 11,25 for analysis since the coherence length, which tends toward infinity as the transition temperature is approached from above (or below in some systems), only appears in the argument of the scaling function.…”

“…Recently, Pierson et al 11,12 published a dynamic scaling analysis of IV data taken on ultra-thin (one unit cell thick) high-temperature superconducting films 7 as well as on prototypical 2D low-temperature superconducting systems in which it is believed that a KTB transition exists and has been observed. 5,10,13 Based primarily on the results of their scaling they propose that a re-evaluation of the dynamics of the KTB transition may be in order.…”

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

“…A zero field BKT transition has been reported for the highly anisotropic BSCCO and TBCCO superconductors 11-14 assuming but not testing the value z =2. In fact quite high values of z ϳ 6 have been reported 5 19,20 is used to arrive at the correct exponent and critical temperature from scaling arguments. Fresh Bi 2 Sr 2 CaCu 2 O 8 films show a BKT-like transition with z = 0.8, smaller than expected for the BKT transition but similar to that observed in frustrated Josephson junction arrays (JJA).…”