Enhanced superconductivity in Fe Se /Sr Ti O3 from the combination of forward scattering phonons and spin fluctuations

We study the effect of combining spin fluctuations and forward scattering electron-phonon (e-ph) coupling on the superconductivity in the Fe Se /Sr Ti O₃ system modeled by a phenomenological two-band Hubbard model with long-range e-ph interactions. We treat the electron and phonon degrees of freedom on an equal footing using a fully self-consistent fluctuation-exchange plus Migdal-Eliashberg calculation, which includes a self-consistent determination of the spin fluctuation spectrum. Based on FeSe monolayers, we focus on the case where one of the bands lies below the Fermi level (i.e., incipient), and demonstrate that the combined interactions can enhance or suppress T_c, depending on their relative strength. For a suitable choice of parameters, the spin fluctuation mechanism yields a T_c≈46.8 K incipient s_± superconductor, consistent with surface-doped FeSe thin films. A forward-focused e-ph interaction further enhances the T_c, as observed in monolayer FeSe on Sr Ti O₃ .