The zero-field superconducting phase transition obscured by finite-size effects in thick $\mathrm{\bf{YBa_{2}Cu_{3}O_{7-δ}}}$ films

Abstract

We report on the normal-superconducting phase transition in thick $\mathrm{YBa_{2}Cu_{3}O_{7-δ}}$ films in zero magnetic field. We find significant finite-size effects at low currents even in our thickest films ($d = 3200$ Å). Using data at higher currents, we can unambiguously find $T_c$ and $z$, and show $z = 2.1 \pm 0.15$, as expected for the three-dimensional XY model with diffusive dynamics. The crossover to two-dimensional behavior, seen by other researchers in thinner films ($d \leq 500$ Å), obscures the three-dimensional transition in both zero field and the vortex-glass transition in field, leading to incorrect values of $T_c$ (or $T_g$), $ν$, and $z$. The finite-size effects, usually ignored in thick films, are an explanation for the wide range of critical exponents found in the literature.