Suppression of superconductivity by spin fluctuations

Abstract

We revisit the superconducting instability mediated by spin fluctuations in generic electron systems on a square lattice. We employ the standard Eliashberg theory, include the electron self-energy, keep a fine momentum resolution, and achieve numerical calculations down to very low temperatures so that the onset temperature of superconductivity (SC) can be determined. We find that spin fluctuations necessarily contain a contribution to suppress SC even though the superconducting instability can eventually occur at lower temperatures. This self-restraint effect stems from the repulsive pairing interaction induced by spin fluctuations, which leads to phase frustration of the pairing gap and consequently the suppression of SC. The self-restraint effect is a special feature of spin fluctuations and does not occur when SC is driven by the attractive pairing interaction from, for example, nematic fluctuations, orbital fluctuations, and electron-phonon coupling.