Title: On the origin of the shallow and "replica" bands in FeSe monolayer superconductors,
Abstract: We compare electronic structures of single FeSe layer films on SrTiO$_3$
substrate (FeSe/STO) and K$_x$Fe$_{2-y}$Se$_{2}$ superconductors obtained from
extensive LDA and LDA+DMFT calculations with the results of ARPES experiments.
It is demonstrated that correlation effects on Fe-3d states are sufficient in
principle to explain the formation of the shallow electron -- like bands at the
M(X)-point. However, in FeSe/STO these effects alone are apparently
insufficient for the simultaneous elimination of the hole -- like Fermi surface
around the $\Gamma$-point which is not observed in ARPES experiments. Detailed
comparison of ARPES detected and calculated quasiparticle bands shows
reasonable agreement between theory and experiment. Analysis of the bands with
respect to their origin and orbital composition shows, that for FeSe/STO system
the experimentally observed "replica" quasiparticle band at the M-point
(usually attributed to forward scattering interactions with optical phonons in
SrTiO$_3$ substrate) can be reasonably understood just as the LDA calculated
Fe-3d$_{xy}$ band, renormalized by electronic correlations. The only
manifestation of the substrate reduces to lifting the degeneracy between
Fe-3d$_{xz}$ and Fe-3d$_{yz}$ bands in the vicinity of M-point. For the case of
K$_x$Fe$_{2-y}$Se$_{2}$ most bands observed in ARPES can also be understood as
correlation renormalized Fe-3d LDA calculated bands, with overall semi --
quantitative agreement with LDA+DMFT calculations.