Changes of the Fermi surface topology in the three-orbital model for iron pnictides with the spin-orbit coupling

Effect of the spin-orbit coupling on the band structure and the Fermi surface of the three-orbital model is studied. The inter-orbital part of the model is reformulated to fully conform with the iron lattice symmetry. Because there are two iron ions in the unit cell, we introduce the intra- and inter-ion spin-orbit coupling constants to separate the effect of the related couplings on the band structure and the Fermi surface. Both the intra- and inter-ion parts lift the degeneracy of some bands at the $\Gamma=(0,0)$ point and the splitting of bands along the $(0,\pi)-(\pi,\pi)$ direction of the Brillouin zone. We show that the inter-ion part of the spin-orbit coupling leads to the topological change of the Fermi surface — the splitting of two Fermi surface sheets around the $M=(\pi,\pi)$ point.