Suppression of superconductivity by spin fluctuations

It is well established that antiferromagnetic spin fluctuations can drive superconductivity (SC). This spin fluctuation mechanism was extensively discussed in a wide variety of materials such as heavy electron systems, iron-based superconductors, and cuprate superconductors.
Here we revisit the superconducting instability mediated by spin fluctuations in a generic electron system 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 SC (Tc) 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. We find that the self-restraint effect reduces Tc nearly 20 % in a minimal two-band model of iron-based superconductors [1] and nearly 50 % in a typical one-band model applicable to overdoped cuprates and heavy electron systems [2]. Our results suggest that although spin fluctuations can drive SC, its Tc in general tends to become low due to the self-restraint effect. In this sense, some favorable situation would be required to achieve high Tc in the spin fluctuation mechanism, which will be discussed in the present talk. 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.

[1] H. Yamase and A. Agatsuma, Phys. Rev. B 102, 060504(R) (2020).
[2] H. Yamase, unpublished.