Universal values for the static and dynamic critical exponents in thin-film and bulk crystalline YBCO

Many researchers have used scaling of current vs.\ voltage curves to study the normal-superconducting phase transition of the high-temperature superconductors, searching for the static and dynamic critical exponents; however, there is little consensus among experimentalists as to the values of the exponents. We have studied this phase transition in optimally-doped YBa$_2$Cu$_3$O$_{7-\delta}$ thin films and bulk crystals. We consistently find $z=1.5\pm0.2$ for the dynamic critical exponent in films (when finite-size effects are taken into consideration) and in crystals (where there are no finite size effects). We also find for the static critical exponent $\nu=0.68\pm0.1$ for crystals and $\nu=0.63 \pm 0.1$ for films. The failure to account for finite-thickness effects in thin films may account for the wide ranges of values for $\nu$ and $z$ previously reported in the literature.