Loss of antinodal coherence with a single d-wave superconducting gap leads to two energy scales for underdoped cuprate superconductors

We address the question of the two energy scales in the superconducting state of hole-doped copper-oxide superconductors below the optimal doping level. We show by performing temperature-dependent Raman scattering measurements on Bi2Sr2CaCu2O8+delta that the two energy scales often assigned to two distinct gaps, are both associated with coherent Bogoliubov quasiparticles and can be simply explained by a one single d-wave gap and the loss of antinodal coherence. We then establish that the critical temperature Tc is controlled by the fraction of coherent Fermi surface f(c) around the nodes such as: k(B)T(c)(alpha)f(c)center dot Delta(max), where Delta(max) is the maximum amplitude of the superconducting gap.