Hole concentration and phonon renormalization in Ca-doped YBa_2Cu_3O_y   (6.76 < y < 7.00)
  In order to access the overdoped regime of the YBa_2Cu_3O_y phase diagram, 2% Ca is substituted for Y in YBa_2Cu_3O_y (y = 7.00,6.93,6.88,6.76). Raman scattering studies have been carried out on these four single crystals. Measurements of the superconductivity-induced renormalization in frequency (Delta \omega) and linewidth (\Delta 2\gamma) of the 340 cm^{-1} B_{1g} phonon demonstrate that the magnitude of the renormalization is directly related to the hole concentration (p), and not simply the oxygen content. The changes in \Delta \omega with p imply that the superconducting gap (\Delta_{max}) decreases monotonically with increasing hole concentration in the overdoped regime, and \Delta \omega falls to zero in the underdoped regime. The linewidth renormalization \Delta 2\gamma is negative in the underdoped regime, crossing over at optimal doping to a positive value in the overdoped state. 
K. C. Hewitt, X. K. Chen, C. Roch, J. Chrzanowski, J. C. Irwin, E. H.   Altendorf, R. Liang, D. Bonn and W. N. Hardy