Spin-Orbit Interactions and the Nematicity Observed in the Fe-Based Superconductors

High-resolution angle-resolved photoelectron spectroscopy is used to examine the electronic band structure of FeTe$_{0.5}$Se$_{0.5}$ near the Brillouin zone center. A consistent separation of the $\alpha_{1}$ and $\alpha_{2}$ bands is observed with little $k_{z}$ dependence of the $\alpha_{1}$ band. First-principles calculations for bulk and thin films demonstrate that the antiferromagnetic coupling between the Fe atoms and hybridization-induced spin-orbit effects lifts the degeneracy of the Fe $d_{xz}$ and $d_{yz}$ orbitals at the zone center leading to orbital ordering. These experimental and computational results provide a natural microscopic basis for the nematicity observed in the Fe-based superconductors.