The dynamic critical exponent in optimally doped Pr$_{1.85}$Ce$_{0.15}$CuO$_4$ as a function of film inhomoegneity

Scaling analysis of voltage vs.\ current isotherms is a good tool to study the normal-superconducting phase transition in cuprate conductors. This measurement has never been performed on the optimally doped cuprate conductor Pr$_{1.85}$Ce$_{0.15}$CuO$_4$. If we take the finite thickness of the films into account,\footnote{Sullivan \textit{et al.}, Phys. Rev B \textbf{69}, 214524 (2004)} we can find the critical isotherm and determine the dynamic critical exponent \textit{z} in our Pr$_{1.85}$Ce$_{0.15}$CuO$_4$ films. We find that the critical exponent varies as a function of transition width, from which we can infer the effect of sample inhomogeneity on the dynamic critical exponent. We present our results of the critical exponent as a function of sample inhomogeneity and compare it to the hole-doped cuprate YBa$_2$Cu$_3$O$_{7-\delta}$.