s- and p-wave pairings in the dilute electron gas: Superconductivity mediated by the Coulomb hole in the vicinity of the Wigner-crystal phase

Yasutami Takada

doi:10.1103/PhysRevB.47.5202

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s- and p-wave pairings in the dilute electron gas: Superconductivity mediated by the Coulomb hole in the vicinity of the Wigner-crystal phase

Yasutami Takada

DOI 10.1103/PhysRevB.47.5202 · Physical Review B

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Abstract

The superconducting transition temperature Tc of both s- and p-wave pairings is calculated in the electron gas without phonons by the solution of the full Eliashberg equation in both frequency and momentum variables. The exchange and correlation effects are included in the form of the model proposed by Kukkonen and Overhauser with suitable local-field corrections. The ground state of the electron gas exhibits p-wave superconductivity for the electronic-density parameter rs around 4 or larger, but it is superseded by s-wave superconductivity for rs larger than about 8.5. The ratio of Tc to the Fermi energy increases monotonically with rs, but it is saturated to have the value of about 0.04 for rs>40. The physical origin of this superconductivity in the dilute electron gas is explained in terms of the pairing mediated by the Coulomb hole near the Wigner-crystal phase.