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 (Kulic and Zeyher 1994 Phys. Rev. B 49 4395; Kulic 2000 Phys. Rep. 38 1-264; Kulic 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-c(similar to 100 K) in a monolayer FeSe grown on SrTiO3 (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 (Omega similar to 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-c0/Omega) the mean-field critical temperature T-c0 = < V-epi (q) >(q)/4) similar to (aq(c))(2) V-epi (0)and the gap Delta(0) = 2T(c0) are due to an interplay between the maximal EPI pairing potential V-epi (0) and the FSP-width qc. For T-c0 similar to 100 Kone has Delta(0) similar to 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 nonmagnetic 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 > 0 (Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009). The EPI coupling constant lambda(m) = < V-epi (q) >(q)/2 Omega is mass-dependent (M-1/2) and at omega (<< Omega) makes the slope of the self-energy Sigma(k, w)(approximate to-lambda(m)omega) and the replica intensities Ai (similar to lambda(m)) mass-dependent. This result, overlooked in the literature, is contrary to the prediction of the standard Migdal-Eliashberg theory for EPI. The small oxygen isotope effect in T-c0 and pronounced isotope effect in Sigma(k, omega) and ARPES spectra Ai of the replica bands in FeSe films on SrTiO3 and TiO2 is a smoking-gun experiment for validity of the EPI-FSP theory to these systems. The EPI-FSP theory predicts a large number of low-laying pairing states, thus causing internal pair fluctuations. The latter reduce T-c0 additionally, by creating a pseudogap state for T-c< T< T-c0. Possibilities to increase T-c0, by designing novel structures are discussed in the framework of the EPIFSP theory.