very similar to those in KFS in the main text.

Orbital-selective Mott phase of the five-orbital Hubbard model for [K$_{x}$Fe$_{2-y}$Se$_2$]{}
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The five-orbital Hubbard model is given by $H=H_{\mathrm{kin}} + H_{\mathrm{int}}$, where $H_{\mathrm{kin}}$ and $H_{\mathrm{int}}$ respectively denote the kinetic and the on-site interaction parts of the Hamiltonian. $H_{\mathrm{int}}$ contains the intra- and inter-orbital Coulomb repulsion, as well as the Hund’s rule coupling and the pair hoppings.[@s8yu] The corresponding coupling strengths are respectively $U$, $U^\prime$, and $J$, which satisfy $U^\prime=U-2J$. [@s5castellani] For simplicity, we consider only the density-density interactions and neglect the spin-flip and pair-hopping terms. The results including these terms are qualitatively the same. The kinetic part $H_{\mathrm{kin}}$ is a tight-binding Hamiltonian, and is conveniently specified in the momentum space. In FeSCs, each unit cell contains two Fe ions. Hence, ideally the tight-binding Hamiltonian must be defined in the BZ corresponding to this two-Fe unit cell. However, the lattice symmetry of the FeSC system allows us to work in an unfolded BZ corresponding to one-Fe unit cell. Following Ref. [@s6wen] and notice that the ions are invariant under the transformation $P_zT_x$ and $P_zT_y$, where $T_{x(y)}$ is the translation along $x(y)$ direction by one Fe-lattice spacing, and $P_z$ refers to the 