Crossover analysis of the heat capacity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ near ${\mathit{T}}_{\mathit{c}}$: Evidence for XY-like critical behavior

The heat-capacity anomaly of a largely untwinned single crystal of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ is reanalyzed by means of a crossover model. The conventional Gaussian-corrected BCS shape is shown to be inadequate to fit the data within ±4 K of ${\mathit{T}}_{\mathit{c}}$, a range much larger than estimated from the Ginzburg criterion. Improved fits in the vicinity of ${\mathit{T}}_{\mathit{c}}$ were obtained using the approach of Chen, Albright, and Sengers, who introduced a crossover function to interpolate smoothly between critical and mean-field behavior. The best fit was obtained for the three-dimensional XY model, the expected ‘‘intermediate’’ critical behavior of a superconductor. From the crossover analysis, we estimate the zero-temperture coherence length to be ${\xi }_0$≃12 Å.