Fluctuations in the microwave conductivity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals in zero dc magnetic field

We present a quantitative analysis of finite frequency fluctuation conductivity above and below ${\mathit{T}}_{\mathit{c}}$ in cuprate superconductors in zero dc magnetic field. In a ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystal showing a linear in temperature increase of the penetration depth at low temperatures, we find that two-dimensional (2D) finite frequency Gaussian conductivity fluctuations above ${\mathit{T}}_{\mathit{c}}$ cross over into a slower divergence of the conductivity as ${\mathit{T}}_{\mathit{c}}$ is approached from above. We find that the critical regime above ${\mathit{T}}_{\mathit{c}}$ is less than about 0.6 K wide. At and below ${\mathit{T}}_{\mathit{c}}$, 3D fluctuations dominate the conductivity, with evidence of 3D XY critical scaling of the imaginary part of the conductivity down to 5 K below ${\mathit{T}}_{\mathit{c}}$. © 1996 The American Physical Society.