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

We analyze the role of the collective modes on the charge-transfer instability (CTI), phase separation, and the superconductivity in the extended Hubbard model. We show that, in the weak-coupling limit, the CTI appears when the zero-sound mode becomes unstable and the Landau stability criterion ${\mathit{F}}_0^{\mathit{s}}$>-1 is violated, due to a coupling to the charge-transfer exciton. We also study the frequency dependence of the effective interaction, mediated by the exchange of collective modes, between the quasiparticles.