Investigation of the superconductivity in novel iron-based superconductors is one of the main trends in modern condensed matter physics [1]. Some of iron chalcogenide superconductors [2] have qualitatively different electronic properties from other iron-based superconductors (e.g. iron pnictides) [3]. Among them, the K_xFe_2−ySe₂ compound and the FeSe monolayer on the SrTiO₃ substrate take quite a special place. Early days angular resolved photoemission spectroscopy (ARPES) experiments practically could not resolve hole-like  Fermi surface sheets near the Γ-point of the Brillouin zone in contrast to the iron pnictides and some iron chalcogenides (e.g. bulk FeSe).

       Recently in the work [4]  ARPES observation of a “hidden” hole-like band approaching the Fermi level near the Γ-point for the K_0.622Fe_1.7Se₂ system and thus proposing a hole-like Fermi surface near the Γ-point was reported.

       Inspired by the work [4] we show by LDA+DMFT [6] study that for K_0.62Fe_1.7Se₂ system near the Γ-point there are two hole-like bands crossing the Fermi level and forming the Fermi surface near the Γ-point. Its appearance can justify  spin-fluctuation mechanism of superconductivity in this class of systems [6] with a rather high critical temperature T_c∼30K. Good qualitative and even quantitative agreement of the calculated and ARPES Fermi surfaces is obtained.