Superconductivity from nonphonon interactions

The claims that the electron-electron interaction via exchange of bosons with energies comparable to the Fermi energy yields a high superconducting transition temperature are studied here by solving the Eliashberg equation containing such interactions. A model for the boson exchange within the random-phase approximation yields an unrealistically high $T_c$. The inclusion of self-energy, vertex, and spin-fluctuation corrections in the electron-electron interaction lowers $T_c$ drastically. In our final estimates for a typical metal of Fermi temperature ${10}^5$ K, $T_c$ peaks at 60 K when the boson energy is increased to one-tenth of the Fermi energy. The Coulomb interaction including plasmon effects in the electron gas is estimated to yield net repulsive values of ${\mu }^{*}$ between 0.1 and 0.2 for $r_s$ between 2 and 6.