Superconducting transition temperatures of strongly coupled electron-boson systems: A self-consistent method for fluctuation from the Bardeen-Cooper-Schrieffer limit to the bipolaronic limit

Superconducting transition temperatures Tc of a many-electron system coupling strongly with bosonic excitations are studied in the context of polaron theory. The boson clouds that move with electrons are taken into account within the variational method. The effect of fluctuation of the pairing order is also taken into account by the coherent-potential approximation. The resultant theory covers the whole region of the three basic parameters characterizing this system: the intersite transfer energy of the electron, T, the site-diagonal electron-boson coupling energy, S, and the energy of the boson, {ω}. Tc is found to become maximum in the transition region S{}T, which lies between the weak (Bardeen-Cooper-Schrieffer) region S{}T and the strong (bipolaronic) region S{}T. The width of this region is narrow in the adiabatic case {ω}{}T, but wide in the inverse-adiabatic case {ω}{}T. This region is characterized by the large ratio of the energy gap to kB{T}c$. These results are applied to the Cu-O--type new ceramics, and the breathing mode of oxygen is shown to be able to give a high ${T}c$ of about 100 K. The effects of other quasibosons with high frequencies, such as plasmons and excitons, are also studied.