LAUSR

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 in a monolayer FeSe grown on (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 ( 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 ) the mean-field critical temperature ~ and the gap are due to an interplay between the maximal EPI pairing potential and the FSP-width q c. For K one has 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 ( Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009). The EPI coupling constant is mass-dependent () and at makes the slope of the self-energy and the replica intensities 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 and pronounced isotope effect in and ARPES spectra A i 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 . Possibilities to increase T c0, by designing novel structures are discussed in the framework of the EPI–FSP theory.