Thermodynamic fluctuations in the superconductor ${\mathrm{Y}}_1$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{9\mathrm{-}\mathrm{\delta }}$: Evidence for three-dimensional superconductivity

The rounding of resistivity near and above the superconductivity transition temperature $T_c$, observed in the ${\mathrm{Y}}_1$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{9\mathrm{-}\mathrm{\delta }}$ superconductor, is found to be a manifestation of thermodynamic fluctuations. A quantitative agreement between the experiment and the three-dimensional (3D) Aslamazov-Larkin theory was achieved near $T_c$ Low-field measurements of the excess diamagnetism are also in agreement with the 3D theory of Prange. These results strongly suggest that superconductivity in high-$T_c$ copper oxides (${\mathrm{Y}}_1$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{9\mathrm{-}\mathrm{\delta }}$) is basically 3D in nature.