• Fe-based superconductors;
  • electronic structure;
  • tight-binding;
  • downfolding;
  • magnetism;
  • interlayer coupling.


This paper explains the multi-orbital band structures and itinerant magnetism of the iron-pnictide and chalcogenide superconductors. We first describe the generic band structure of a single, isolated FeAs layer. Use of its Abelian glide-mirror group allows us to reduce the primitive cell to one FeAs unit. For the lines and points of high symmetry in the corresponding large, square Brillouin zone, we specify how the one-electron Hamiltonian factorizes. From density-functional theory, and for the observed structure of LaOFeAs, we generate the set of eight Fe d and As p localized Wannier functions and their tight-binding (TB) Hamiltonian, h (k) . For comparison, we generate the set of five Fe d Wannier orbitals. The topology of the bands, i. e. allowed and avoided crossings, specifically the origin of the d6 pseudogap, is discussed, and the role of the As p orbitals and the elongation of the FeAs4 tetrahedron emphasized. We then couple the layers, mainly via interlayer hopping between As pz orbitals, and give the formalism for simple tetragonal and body-centered tetragonal (bct) stackings. This allows us to explain the material-specific 3D band structures, in particular the complicated ones of bct BaFe2As2 and CaFe2As2 whose interlayer hoppings are large. Due to the high symmetry, several level inversions take place as functions of kz or pressure, and linear band dispersions (Dirac cones) are found at many places. The underlying symmetry elements are, however, easily broken by phonons or impurities, for instance, so that the Dirac points are not protected. Nor are they pinned to the Fermi level because the Fermi surface has several sheets. 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 in detail as a function of the exchange potential, Δ, or moment, m, using Stoner theory. Gapping of the Fermi surface (FS) for small Δ requires matching of FS dimensions (nesting) and d-orbital characters. The interplay between pd hybridization and magnetism is discussed using simple 4 × 4 Hamiltonians. The origin of the propeller-shaped Fermi surface is explained in detail. Finally, we express the magnetic energy as the sum over band-structure energies and this enables us to understand to what extent the magnetic energies might be described by a Heisenberg Hamiltonian, and to address the much discussed interplay between the magnetic moment and the elongation of the FeAs4 tetrahedron.