Dynamic Scaling at the Zero-field 2D Superconducting Transition

Zero-field current-voltage (I-V) characteristics of a thin ("two-dimensional") $Bi_2Sr_2CaCu_2O_{8+\delta}$ crystal are reported and analyzed in two ways. The "conventional" approach yields ambiguous results while a dynamical scaling analysis offers new insights into the Kosterlitz-Thouless-Berezinskii transition. The scaling theory predicts that the universal jump of the $I$-$V$ exponent $\alpha$ should be between $z+1$ and 1. A value of $z \simeq 5.6$ is obtained for the dynamical critical exponent, and is corroborated by data from other 2D superconductors. A simple dynamical model is presented to account for the results.