Doping dependence of the dynamic critical exponent in Pr$_{2-x}$Ce$_x$CuO$_4$*

Scaling analysis of voltage vs. current isotherms is a favorite tool to study the normal-superconducting phase transition in cuprate superconductors. This measurement has never been performed on the electron-doped cuprate superconductor Pr$_{2-x}$Ce$_x$CuO$_4$, despite unusual behaviors which may alter this phase transition and yield interesting results (behaviors such as the extended doping range of the anti-ferromagnetic phase and the quantum critical point). This is perhaps due to the lack of consensus regarding the analysis of voltage vs.\ current isotherms, due in part to finite-thickness effects even in thick ($d \approx 3000$\AA) films.\footnote{ Phys. Rev. B \textbf{69}, 214524 (2004)} If finite-thickness effects are taken into consideration, we can find the dynamic critical exponent $z$ in our Pr$_{2-x}$Ce$_x$CuO$_4$ films. We present our results of the dynamic critical scaling exponent $z$ as a function of doping.