Effect of doping on the linear temperature dependence of the magnetic   penetration depth in cuprate superconductors
  We report on measurements of the low temperature dependence of the magnetic penetration depth lambda_ab in several single crystals of La_2-xSr_xCuO_4, Bi_2Sr_2CaCu_2O_8 and YBa_2Cu_3O_6+x at various doping levels ranging from the under- to the overdoped regimes by using a novel single-coil technique achieving 10 pm resolution. We have found a linear dependence of lambda_ab in all samples with a rapidly increasing slope dlambda_ab/dT as doping decreases. Our analysis of the data indicates that a superconducting gap with d-wave symmetry is sufficient to quantitatively account for the above slope values in the optimally or over- doped samples. In the underdoped samples, the d-wave model predicts much smaller values than those measured by assuming realistic values for the zero-temperature lambda_ab and gap delta. The experimental data are compatible with a model of thermodynamic phase fluctuations of the order parameter. Therefore, we put forward the hypothesis that the gapless properties observed in cuprates may have qualitatively different physical origins depending on the doping level. 
J. Le Cochec, G. Lamura, A. Gauzzi, F. Licci, A. Revcolevschi, A. Erb,   G. Deutscher and J. Bok