Phonon-plasmon cooperative effects in the dilute large-bipolaron gas: A possible mechanism for high-Tcsuperconductivity

A Hamiltonian for two interacting electrons coupled with longitudinal phonons and plasmons is set up. The phonons are treated in the Fröhlich scheme and the plasmons in the single-pole approximation. We are interested in systems with low electron density (n≤${10}^{20}$–${10}^{21}$) such as high-${\mathit{T}}_{\mathit{c}}$ superconductors. It is shown that, in this density range, the electron dynamics do not simply screen the electrostatic interaction but, also, cooperates to the bipolaron formation. Furthermore we find that the binding energies and the effective mass depend on the electronic density. The features of the effective electron-electron potential are discussed, mainly for what concerns the self-energy terms and the long-range tail; the former depends on the pair state and the second shows that the plasmon field tends to screen all the electrostatic interactions, even the electron-phonon one. It is also shown that the Hamiltonian formulation is equivalent to a dielectric formulation where the total dielectric function of the system is the sum of the dielectric function appropriate for an ionic of the system is the sum of the dielectric function appropriate for an ionic material and that appropriate for the electron gas. Within this model we calculate the Bose-condensation critical temperature of a system of correlated pairs and free carriers in a two-fluid model at thermodynamical equilibrium.