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Sign-reversing orbital polarization in the nematic phase of FeSe due to the $C_2$ symmetry-breaking in the self-energy

To understand the nematicity in Fe-based superconductors, nontrivial $k$-dependence of the orbital polarization ($ΔE_{xz}(k)$, $ΔE_{yz}(k)$) in the nematic phase, such as the sign reversal of the orbital splitting between $Γ$- and X,Y-points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole- and electron-pockets are elongated along the $k_y$- and $k_x$-axes respectively, consistently with experiments. In addition, an electron-pocket splits into two Dirac cone Fermi pockets with increasing the orbital polarization. The orbital-order in Fe-based superconductors originates from the strong positive feedback between the nematic orbital order and spin susceptibility.