Nematic-like band splitting and crystal field splitting in newly discovered hybrid 12442 iron-based superconductors

Abstract

We present theoretical results of crystal field splitting and nematic-like band splitting based on density functional theory first principles electronic structure and Wannier fitted tight binding calculations on the newly discovered quasi two-dimensional ${\mathrm{ACa_2Fe_4As_4F_2}}$ (where A = K, Rb, Cs) i.e., 12442 iron-based superconductors. The orbital selective anisotropy of band structures as well as Fermi surfaces are discussed through electronic structure calculations. The degeneracy of $d_{xz}$ and $d_{yz}$ orbitals are lifted in 12442 compounds due to the reduction of local symmetry $D_{2d}$ to $C_{2v}$ of Fe-site. This degeneracy lifting of $d_{xz}$ and $d_{yz}$ cause band reconstruction which in turn induce emergence of nematic-like splitting of some bands in these compounds. This splitting is maximum at the electron bands near the Brillouin zone corner. The details of band reconstruction and band splittings are explored using relativistic pseudopotential including spin orbit coupling. To verify the degeneracy lifting of $d_{xz/yz}$ level in 12442 compounds, crystal field splitting is calculated with tight binding fitting using maximally localized Wannier functions. In contrary to its parent 1111 and 122 compounds, the degeneracy lifting of $d_{xz/yz}$ may be responsible for intrinsic band splitting in tetragonal phase of these compounds.