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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 in a monolayer FeSe grown on (Lee et al 2014 Nature 515 245) and TiO 2 (Rebec et al 2016 arXiv: 1606.09358 v1) 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 ∼ …