Spin orbital interplay and topology in the nematic phase of iron pnictides

The origin of the nematic state is an important puzzle to be solved in iron pnictides. Iron superconductors are multiorbital systems and these orbitals play an important role at low energy. The singular ${C}_{4}$ symmetry of ${d}_{zx}$ and ${d}_{yz}$ orbitals has a profound influence at the Fermi surface since the $\mathrm{\ensuremath{\Gamma}}$ pocket has vortex structure in the orbital space and the $X/Y$ electron pockets have $yz/zx$ components, respectively. We propose a low-energy theory for the spin-nematic model derived from a multiorbital Hamiltonian. In the standard spin-nematic scenario, the ellipticity of the electron pockets is a necessary condition for nematicity. In the present model, nematicity is essentially due to the singular ${C}_{4}$ symmetry of $yz$ and $zx$ orbitals. By analyzing the ($\ensuremath{\pi},0$) spin susceptibility in the nematic phase, we find a spontaneous generation of orbital splitting, extending previous calculations in the magnetic phase. We also find that the ($\ensuremath{\pi},0$) spin susceptibility has an intrinsic anisotropic momentum dependence due to the nontrivial topology of the $\mathrm{\ensuremath{\Gamma}}$ pocket.