the insulating phase. At a fixed interaction strength (within a certain range, Fig. \[fig:fig4\](a)), the system goes from a metal to an OSMP and then to a MI with increasing temperature. The MI phase is suppressed by electron doping. By contrast, the OSMP can survive, as shown in Fig. \[fig:fig4\](b) for n=6.15, which roughly corresponds to the filling of the superconducting state from ARPES measurements. From the evolution of the orbitally resolved quasiparticle spectral weight, $Z_{\alpha}$, as a function of the temperature (Fig. \[fig:fig4\](c)), we show that the OSMP corresponds to the [$d_{xy}$]{} orbital being Mott localized ($Z=0$) and the rest of the $3d$ orbitals remaining delocalized ($Z>0$). This result originates primarily from a combined effect of the orbital dependence of the projected density of states and the interplay between the Hund’s coupling and crystal level splitting (see SI and Ref. ).

To compare with the ARPES measurements, we have calculated the quasiparticle spectral function A(k,E) in the 2-Fe BZ. At low temperature and in the non-interacting limit U=0 (Fig. \[fig:fig4\](d)), the electronic structure of the model agrees well with that from LDA, with the [$d_{xy}$]{} band deeper than the [$d_{xz}$/$d_{yz}$]{} band at X. This order switches with sufficiently strong 