Scaling behavior of fluctuation conductivity of high-temperature superconductors in a magnetic field

Abstract

Fluctuation conductivities of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ and ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{x}}$ films have been analyzed beyond the Gaussian approximation by using the two- (2D) and three-dimensional (3D) scaling functions in the critical region. Near the mean-field transition temperature ${\mathit{T}}_{\mathit{c}}$(H), the fluctuation conductivity of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ shows a 3D scaling behavior similar to that seen in the single crystal, suggesting that fluctuations are coherent over the adjacent Cu-O layers in this region. The fluctuation conductivity of ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{x}}$ shows good agreement with 2D scaling behavior for temperatures higher than a few degrees above ${\mathit{T}}_{\mathit{c}}$(H), but a deviation occurs very near and below ${\mathit{T}}_{\mathit{c}}$(H). The poor scaling in that region may be caused by double transitions, which are systematically seen in the highly anisotropic high-${\mathit{T}}_{\mathit{c}}$ superconductors like ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{x}}$, preventing the determination of the validity of a 2D scaling formula near and below ${\mathit{T}}_{\mathit{c}}$(H).