Condensation energy of the homogeneous electron gas from the density functional theory for superconductors

TL;DR

This paper calculates the condensation energy of the homogeneous electron gas using density functional theory for superconductors, considering exchange and correlation energies, and explores superconductivity at various densities and angular momenta.

Contribution

It introduces a detailed DFT-based approach to evaluate the condensation energy in the homogeneous electron gas, including high angular momentum pairing and Coulomb interactions.

Findings

Homogeneous gas remains nonsuperconducting up to r_s ≈ 9.

Very weak negative condensation energy found for f-waves at r_s=10.

Superconductivity is suppressed at high densities and angular momenta.

Abstract

The condensation energy of the homogeneous electron gas is calculated within the density functional theory for superconductors. Purely electronic considerations include the exchange energy exactly and the correlation energy on a level of the random phase approximation. The singlet superconductivity is assumed, and the Coulomb interaction is studied with a model pairing potential at the angular momentum up to $l$=9 and at densities 1$\leq$$r_s$$\leq$10. The homogeneous gas remains nonsuperconducting up to $r_s$$\simeq$9. Very weak negative value of the condensation energy has been found for f-waves and higher-$l$ pairing at $r_s$=10.