Magnetic Penetration Depth in Overdoped Tl-2201 Superconductors

Studies of the magnetic penetration depth $\lambda_{ab}$ {\it via\/} the $\mu^+$SR lineshape in the vortex state has revealed a great deal about {\sl under\/}doped cuprate superconductors, including the original confirmation of $d$-wave superconductivity. However, {\sl over\/}doped cuprates have been neglected, partly due to the difficulty of doping sufficiently to decrease $T_c$, and partly because the overdoped materials are thought to be ``ordinary Fermi liquid'' superconductors, about which many presume we already know everything. In the belief that we may {\sl not\/} know everything about these materials, the UBC group has set out to grow high quality crystals of Tl$_2$Ba$_2$CuO$_{6+\delta}$ (Tl-2201), which can be made {\sl very\/} overdoped, to the point of $T_c \to 0$. We have now used $\mu^+$SR lineshape studies to measure $\lambda_{ab}$ as a function of $T$ and $H$ for crystal mosaics with $T_c$'s of 72, 60 and 46 K. As expected, $\lambda_{ab}^{-2}(T=0)$ continues to increase with doping beyond optimal doping, but then decreases again with higher doping. We also find a strong dependence on the applied field $H$. The low-$T$ behavior of $\lambda_{ab}^{-2}(T)$ is again strongly linear, as expected for a $d$-wave superconductor.