Universal Tc depression by irradiation defects in underdoped and overdoped cuprates

We report on a study of the influence of defects introduced in the CuO$_{2}$ planes of cuprates in a wide range of hole dopings n. T$_{c}$ and electrical resistivity $\rho (T)$ measurements have been performed on electron irradiated YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ and Tl$_{2}$Ba$_{2}$CuO$_{6+x}$ single crystals. A universal scaling between the decrease in T$_{c}$ and $\UNICODE[m]{0x394}\rho_{2D}\UNICODE[m]{0xd7}n$, where $\UNICODE[m]{0x394}\rho _{2D}$ is the increase of the 2D-resistance induced by the defects, is found for all the samples investigated here. This demonstrates that n is the relevant parameter to describe the transport properties all over the phase diagram, in contradiction with a recent suggestion of a change in the number of carriers from n to 1-n at the optimal doping. Moreover, the analysis of our data suggests that strong scattering persists on the overdoped side.