Plasmon Mechanism of Superconductivity in the Multivalley Electron Gas

The Eliashberg equation is solved in both frequency and momentum variables to obtain the superconducting transition temperature T c in the multivalley electron gas without phonons. Both the one-particle Green's function and irreducible two-electron interaction are evaluated in the random-phase approximation which provides exact results in the limit of large valley degeneracy g v and is known to give sufficiently accurate ones even for g v as small as 3 or 4. Among s -, p -, and d -waves, the s -wave pairing is most stable for g v ≥2 with a fairly high T c . For g v ≫1, our solution is reduced to "bipolaronic superconductivity". We discuss implications of the present results to the exotic superconductors with relatively low carrier concentration.