The electron-phonon interaction with forward scattering peak is dominant in high Tc superconductors of FeSe films on SrTiO3 TiO2

The theory of the electron–phonon interaction (EPI) with strong forward scattering peak (FSP) in an extreme delta-peak limit (Kulić and Zeyher 1994 Phys. Rev. B 49 4395; Kulić 2000 Phys. Rep. 38 1–264; Kulić and Dolgov 2005 Phys. Status Solidi b 242 151; Danylenko et al 1999 Eur. Phys. J. B 9 201) is recently applied in (Lee et al 2014 Nature 515 245; Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009) for the explanation of high \({T}_{{\rm{c}}}(\sim 100\,{\rm{K}})\,\) in a monolayer FeSe grown on \({{\rm{SrTiO}}}_{3}\) (Lee et al 2014 Nature 515 245) and TiO2 (Rebec et al 2016 arXiv:1606.09358v1) substrates. The EPI is due to a long-range dipolar electric field created by high-energy oxygen vibrations (\({\rm{\Omega }}\sim 90\) meV) at the interface (Lee et al 2014 Nature 515 245; Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009). In leading order (with respect to \({T}_{{\rm{c}}0}/{\rm{\Omega }}\)) the mean-field critical temperature \({T}_{{\rm{c}}0}={\langle {V}_{{\rm{epi}}}(q)\rangle }_{q}/4)\) ∼ \({({{aq}}_{{\rm{c}}})}^{2}{V}_{{\rm{epi}}}(0)\) and the gap \({{\rm{\Delta }}}_{0}=2{T}_{{\rm{c}}0\text{}}\) are due to an interplay between the maximal EPI pairing potential \({V}_{{\rm{epi}}}(0)\) and the FSP-width q c. For \({T}_{{\rm{c}}0}\sim 100\) K one has \({{\rm{\Delta }}}_{0}\sim 16\) meV in a satisfactory agreement with ARPES experiments. In leading order T c0 is mass-independent and a very small oxygen isotope effect is expected in next to leading order. In clean systems T c0 for s-wave and d-wave pairing is degenerate but both are affected by non-magnetic impurities, which are pair-weakening in the s-channel and pair-breaking in the d-channel. The self-energy and replica bands at T = 0 and at the Fermi surface are calculated and compared with experimental results at \(T\gt 0\) ( Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009). The EPI coupling constant \({\lambda }_{{\rm{m}}}={\langle {V}_{{\rm{epi}}}(q)\rangle }_{q}/2{\rm{\Omega }}\) is mass-dependent (\({M}^{1/2}\)) and at \(\omega (\ll {\rm{\Omega }})\) makes the slope of the self-energy \(\ {\rm{\Sigma }}(k,\omega )(\approx -{\lambda }_{{\rm{m}}}\omega )\) and the replica intensities \({A}_{i}(\sim {\lambda }_{{\rm{m}}})\) mass-dependent. This result, overlooked in the literature, is contrary to the prediction of the standard Migdal–Eliashberg theory f