Analysis of current-voltage characteristics of two-dimensional superconductors: finite-size scaling behavior in the vicinity of the Kosterlitz Thouless transition

It has been suggested [Pierson et al., Phys. Rev. B 60, 1309 (1999); Ammirata et al., Physica C 313, 225 (1999)] that for 2D superconductors there exists a phase transition with the dynamic critical exponent z\approx 5.6. We perform simulations for the 2D RSJ model and compare the results with the experimental data in Repaci et al. obtained for an ultrathin YBCO sample [Phys. Rev. B 54, R9674 (1996)]. We then use a different method of analyzing dynamic scaling than in Pierson et al., and conclude that both the simulations and the experiments are consistent with a conventional Kosterlitz Thouless (KT) transition in the thermodynamic limit for which z=2. For finite systems, however, we find both in simulations and experiments that the change in the current-voltage (IV) characteristics caused by the finite size shows a scaling property with an exponent alpha \approx 1/6, seemingly suggesting a vanishing resistance at a temperature for which z=1/alpha. It is pointed out that the dynamic critical exponent found in Pierson et al. corresponds to the exponent 1/alpha. It is emphasized that this scaling property does not represent any true phase transition since in reality the resistance vanishes only at zero temperature. Nevertheless, the observed scaling behavior associated with alpha \approx 1/6 appears to be a common and intriguing feature for the finite size caused change in the IV characteristics around the KT transition.