Band structure modification due to the spin-orbit coupling in the three-orbital model for iron pnictides

We study the effect of the spin-orbit coupling on the band structure and the Fermi surface of the three-orbital model within the two-iron Brillouin zone. Due to the presence of two irons in the crystallographically correct unit cell, the spin-orbit coupling can be divided into the intra- and intercell parts with respect to the one-iron unit cell. We show that the intercell part produces the reconstruction of the Fermi surface in the form of the pronounced splitting between the previously degenerate electron $(\pi,\pi)$-pockets along the $(0,\pi)-(\pi,\pi)$ direction. Intracell part shifts the bands around $(0,0)$ point and removes degeneracy there. There are also some other band shifts but they should not affect the low-energy physics because they occur at energy scales of about $1$ eV below the Fermi level.