Pseudogap transition within the superconducting phase in the three-band Hubbard model*

We use cluster dynamical mean field theory on a three-band Hubbard model for high-T_c superconductors to study the superconducting phase at zero temperature, obtained when doping the charge transfer insulator, for several values of U. We observe a first-order transition within the superconducting phase, which separates the so-called underdoped and overdoped solutions. The transition to the underdoped solution is marked by a jump in the spectral gap, and on further underdoping the spectral gap increases while the superconducting order parameter decreases. This, we conclude, is caused by the onset of the pseudogap in the underdoped region, which contributes to the increasing spectral gap; this is consistent with the change in the source of condensation energy from potential energy, in the overdoped region, to kinetic energy in the underdoped region. We also observe that the d-wave node disappears within the superconducting phase at low values of hole doping, within the underdoped region. We see this as a manifestation of Mott physics operating at very low doping.