Muon spin rotation study of the correlation between ${\mathit{T}}_{\mathit{c}}$ and ${\mathit{n}}_{\mathit{s}}$/${\mathit{m}}^{\mathrm{*}}$ in overdoped ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CuO}}_{6+\mathrm{\delta }}$

The muon spin depolarization rate σ was measured in overdoped ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_3$ ${\mathrm{CuO}}_{6+\mathrm{\delta }}$. σ(T→0) was found to decrease proportional to the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ as doping δ is increased. In the framework of the clean-limit London model, σ(0)∼${\lambda }^{\mathrm{-}2}$∼${\mathit{n}}_{\mathit{s}}$/${\mathit{m}}^{\mathrm{*}}$, this implies that the depression of ${\mathit{T}}_{\mathit{c}}$ by overdoping is associated with a decrease of the superconducting condensate density ${\mathit{n}}_{\mathit{s}}$ in spite of the increasing normal-state carrier density. This can be largely accounted for in terms of strong pair breaking, which depresses both the condensate density and ${\mathit{T}}_{\mathit{c}}$ with increased doping.