Anisotropic resistivity and paraconductivity of ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ single crystals

The anisotropic resistivity and paraconductivity of ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ single crystals were measured. The in-plane and c-axis resistivities are, respectively, ∼7×${10}^{\mathrm{-}4}$ and ${10}^{\mathrm{-}1}$ Ω cm at room temperature. The c-axis resistivity decreases with decreasing temperature in the temperature range from room temperature down to the superconducting transition temperature, and the second derivative of ${\mathrm{\rho }}_{\mathit{c}}$ is negative, which is not characteristic of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_{2.2}$ ${\mathrm{Ca}}_{0.8}$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$ single crystals, in which the second derivative is either positive or zero. The in-plane paraconductivity is obtained from the in-plane resistivity, and a method without the critical temperature as an adjustable parameter is employed to obtain the dimensionality. The data show that the superconductivity is two dimensional, but a crossover from two to three dimensions has also been observed near the transition temperature in some samples.