Semimetallic spin-density wave state in iron pnictides

We examine the existence of semimetallic spin-density wave states in iron pnictides. In the experimentally observed metallic spin-density wave state, the symmetry-protected Dirac cones are located away from the Fermi surface giving rise to tiny pockets and there are also additional Fermi pockets such as one around $\Gamma$. We find that the location of a pair of Dirac points with respect to the Fermi surface exhibits significant sensitivity to the orbital splitting between the $d_{xz}$ and $d_{yz}$ orbitals. Besides, in the presence of orbital splitting, the Fermi pockets not associated with the Dirac cones, can be suppressed so that a semimetallic spin-density wave state can be realized. We explain these finding in terms of difference in the slopes and orbital contents of the bands which form the Dirac cone, and obtain the necessary conditions dependent on these two and other parameters for the coexisting Dirac semimetallic and spin-density wave states. Additionally, the topologically protected edge states are studied in the ribbon geometry when the same are oriented either along $x$ or $y$ axes.