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) greater-than-or-equal-to 2 with a fairly high tau(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.