On the multi-orbital band structure and itinerant magnetism of iron-based superconductors

This paper explains the multi-orbital band structures and itinerant magnetism of the iron-pnictide and chalcogenides. We first describe the generic band structure of an isolated FeAs layer. Use of its Abelian glide-mirror group allows us to reduce the primitive cell to one FeAs unit. From density-functional theory, we generate the set of eight Fe $d$ and As $p$ localized Wannier functions for LaOFeAs and their tight-binding (TB) Hamiltonian, $h(k)$. We discuss the topology of the bands, i.e. allowed and avoided crossings, the origin of the d6 pseudogap, as well as the role of the As $p$ orbitals and the elongation of the FeAs$_{4}$ tetrahedron. We then couple the layers, mainly via interlayer hopping between As $p_{z}$ orbitals, and give the formalism for simple and body-centered tetragonal stackings. This allows us to explain the material-specific 3D band structures. Due to the high symmetry, several level inversions take place as functions of $k_{z}$ or pressure, resulting in linear band dispersions (Dirac cones). The underlying symmetry elements are, however, easily broken, so that the Dirac points are not protected, nor pinned to the Fermi level. From the paramagnetic TB Hamiltonian, we form the band structures for spin spirals with wavevector $q$ by coupling $h(k)$ and $h (k+q)$. The band structure for stripe order is studied as a function of the exchange potential, $\Delta$, using Stoner theory. Gapping of the Fermi surface (FS) for small $\Delta$ requires matching of FS dimensions (nesting) and $d$-orbital characters. The origin of the propeller-shaped FS is explained. Finally, we express the magnetic energy as the sum over band-structure energies, which enables us to understand to what extent the magnetic energies might be described by a Heisenberg Hamiltonian, and the interplay between the magnetic moment and the elongation of the FeAs4 tetrahedron.