Using torque magnetometry in the Shubnikov state, we have studied the London penetration depth ${\lambda }_{\mathit{ab}}$(T) of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ and (${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{Bi}}_{1\mathrm{-}\mathit{x}}$${)}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ single crystals with different oxygen excess δ. With increasing charge carrier density ${\mathit{n}}_{\mathit{s}}$/${\mathit{m}}^{\mathrm{*}}$∝1/${\lambda }_{\mathit{ab}}^2$(0) the transition temperature at first increases, then approaches a maximum, and finally decreases. The sample independent, universal behavior found in the 1:2:3 family is not confirmed. Dependent on preparation prehistory of the samples, either linear or quadratic low temperature behavior of ${\lambda }_{\mathit{ab}}$(T) was observed. A linear term is seen for samples with high maximum ${\mathit{T}}_{\mathit{c}}$≊94 K, while samples with quadratic behavior show a significantly reduced ${\mathit{T}}_{\mathit{c}}$. The results are discussed in terms of d-wave superconductivity with resonant impurity scattering. © 1996 The American Physical Society.

• Received 8 December 1995

DOI:https://doi.org/10.1103/PhysRevB.53.11825