Pis’ma v ZhETF, vol. 105, iss. 6, pp. 354 – 355 2017 March 25 c On the origin of the shallow and “replica” bands in FeSe monolayer superconductors1) I.A.Nekrasov+1), N. S.Pavlov+2), M.V. Sadovskii+∗2) +Institute of Electrophysics, Russian Academy of Sciences, Ural Branch, 620016 Ekaterinburg, Russia ∗M.N.Mikheev Institute of Metal Physics, Russian Academy of Sciences, Ural Branch, 620290 Ekaterinburg, Russia Submitted 6 February 2017 DOI: 10.7868/S0370274X17060054 ARPES measurements [1] in FeSe/STO monolayer system demonstrated rather unusual band structure, characterized by the absence of hole-like bands at the center of Brillouin zone (Γ-point), with rather shallow electronic band at the M-point with very low Fermi energies of the order of 50meV, accompanied by the formation of “replica” of this band about 100meV below in energy. <...> Similar unusually shallow bands were also observed at X-point in ARPES experiments on intercalated KxFe2−ySe2 system [2]. <...> The existence of such peculiar bands rises many serious theoretical questions [3], such as probable considerable role of non-adiabatic interactions [4, 5] and the possibility of observation of BCS-BEC crossover effects in these systems. <...> In particular, the formation of the “replica” band in FeSe/STO is widely interpreted as being due to interaction with high-energy (∼100meV) optical phonons of Sr(Ba)TiO3 substrate [1] with some important conclusions on the possible role of these interactions for the significant enhancement of Tc in this system [4–7]. <...> In Fig. 1 we compare the theoretical LDA+DMFT results on panels (a,d,e,h) with experimental ARPES data [1] on panels (b,c,f,g). <...> LDA+DMFT spectral function maps of isolated FeSe monolayer are shown in Fig. 1a and Fig. 1d at Γ and M points respectively. <...> For FeSe/STO LDA+DMFT spectral function maps are shown on e, h panels at Γ and M points. <...> Most of features observed in the ARPES data (Fig. 1f, g) can be identified with our calculated LDA+DMFT spectral function maps (Fig. 1e, h). <...> The experimental quasiparticle bands around M-point marked by A, B, and C (Fig. 1g, h) correspond mainly <...>