Scaling analysis of the static and dynamic critical exponents in under, over, and optimally-doped Pr\(_{2-x}\)Ce\(_x\)CuO\(_{4-y}\) films

We report on current-voltage measurements of the zero-field normal-superconducting phase transition in thin films of Pr\(_{2-x}\)Ce\(_x\)CuO\(_{4-y}\) as a function of doping. We find that the small size of the critical regime in these materials (\(\approx 25\) mK) gives rise to mean-field behavior at the phase transition with a static exponent of \(\nu \approx 0.5\) for all dopings (in contrast to hole-doped \(\mathrm{YBa_{2}Cu_{3}O_{7-\delta}}\)). We also find mean-field behavior in the dynamic exponent \(z\). This indicates that Pr\(_{2-x}\)Ce\(_x\)CuO\(_{4-y}\) behaves similarly to conventional superconductors in contrast to other cuprate superconductors. However, as the transition width in our samples decreases, the dynamic critical exponent approaches \(z=1.5\), similar to the critical exponent found in hole-doped \(\mathrm{YBa_{2}Cu_{3}O_{7-\delta}}\).