Evidence for intertwining orders in the electronic nematic state of FeSe

We report the temperature evolution of the detailed electronic band structure in FeSe single-crystals, including the degeneracy removal of the $d_{xz}$ and $d_{yz}$ orbitals at the $\Gamma$/Z and M points, and the orbital-selective hybridization between the $d_{xy}$ and $d_{xz/yz}$ orbitals. The temperature dependences of the splittings at the $\Gamma$/Z and M points are different, indicating that they might be controlled by different order parameters. We also identify the symmetry of the band hybridization. Our finding cannot be explained simply by the onsite ferro-orbital ordering together with spin-orbit coupling. If the orbital ordering exists, it includes an order defined on Fe-Fe bonds with a $d-wave$ form in the reciprocal space that breaks the rotational symmetry. The nematicity is not limited to the interactions between the $d_{xz}$ and $d_{yz}$ orbitals, but involves other $d$ orbitals as well. These findings provide strong evidence that these are intertwining orders in the nematic state of this material.