Plasmon Mechanism of Superconductivity in the Multivalley Electron Gas

Abstract

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.