Effect of repulsion on superconductivity at low density

Abstract

Here we examine the effect of repulsion on superconductivity in a three-dimensional system with a Bardeen-Pines-like interaction in the low-density limit, where the chemical potential μ is much smaller than the phonon frequency ω L . We parametrize the strength of the repulsion by a dimensionless parameter f, and find that the superconducting transition temperature T c approaches a nonzero value in the μ = 0 limit as long as f is below a certain threshold f * . In this limit, we find that T c goes to zero as a power of f * - f, in contrast to the high density limit, where T c goes to zero exponentially quickly as f approaches f * . For all nonzero f, the gap function Δ(ω m ) changes sign along the Matsubara axis, which allows the system to partially overcome the repulsion at high frequencies. We trace the position of the gap node with f and show that it approaches zero frequency as f approaches f * . To investigate the robustness of our conclusions, we then go beyond the Bardeen-Pines model and include full dynamical screening of the interaction, finding that T c still saturates to a nonzero value at μ = 0 when f < f * .