Critical dynamics of superconductingBi2Sr2CaCu2O8+δfilms

We report on a systematic investigation of the critical fluctuations in the complex conductivity of epitaxially grown ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ films for $T\ensuremath{\lesssim}{T}_{c}$ using a two-coil inductive technique at zero applied field. We observe the static three-dimensional (3D) $\mathrm{XY}$ critical exponent in the superfluid density near ${T}_{c}.$ Linear scaling analysis close to the critical temperature yields a dynamic critical exponent of $z\ensuremath{\approx}2.0$ for small drive currents, but nonlinear effects are seen to be important. At ${T}_{c},$ a nonlinear scaling analysis also yields a 3D dynamic exponent of $z=2.0\ifmmode\pm\else\textpm\fi{}0.1.$