The zero-field superconducting phase transition obscured by finite-size effects in thick $\mathbf{YB}{\mathbf{a}}_2\mathbf{C}{\mathbf{u}}_3{\mathbf{O}}_{7-\delta }$ films

Abstract

We report on the normal-superconducting phase transition in thick $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ 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 ($d\le 500$ 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 $T_g$), $\nu$, 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.

5 pages, 4 figures