Charge collective modes and dynamic pairing in the three-band Hubbard model. II. Strong-coupling limit

We analyze the dynamics of the charge degrees of freedom in the extended Hubbard model for the ${\mathrm{CuO}}_2$ planes in copper oxides in the strong-coupling limit. We analyze the behavior of the collective modes near the charge-transfer instability (CTI). The CTI is driven by an overdamped zero-sound mode when the Landau stability criterion ${\mathit{F}}_0^{\mathit{s}}$>-1 is violated due to the charge-transfer mode-mediated attraction. The divergence of the compressibility at the CTI requires a Maxwell construction, which determines a region of phase separation. Near the phase-separation boundary, at intermediate doping, the singlet Cooper coupling is attractive both in the s- and d-wave channels. In the strong-coupling limit the excitonic energy ${\mathrm{\omega }}_{\mathrm{exc}}$ is large and the energy scale for pairing is the Fermi energy itself.