Comparison of Ab initio Low-Energy Models for LaFePO, LaFeAsO, BaFe2As2, LiFeAs, FeSe, and FeTe: Electron Correlation and Covalency

Effective low-energy Hamiltonians for several different families of iron-based superconductors are compared after deriving them from the downfolding scheme based on first-principles calculations. Systematic dependences of the derived model parameters on the families are elucidated, many of which are understood from the systematic variation of the covalency between Fe-3d and pnictogen-/chalcogen-p orbitals. First, LaFePO, LaFeAsO (1111), (BaFeAs2)-As-2 (122), LiFeAs (111), FeSe, and FeTe (11) have overall similar band structures near the Fermi level, where the total widths of 10-fold Fe-3d bands are mostly around 4.5 eV. However, the derived effective models of the 10-fold Fe-3d bands (d model) for FeSe and FeTe have substantially larger effective onsite Coulomb interactions U similar to 4.2 and 3.4 eV, respectively, after the screening by electrons on other bands and after averaging over orbitals, as compared to similar to 2.5 eV for LaFeAsO. The difference is similar in the effective models containing p orbitals of As, Se or Te (dp or dpp model), where U ranges from similar to 4 eV for the 1111 family to similar to 7 eV for the 11 family. The exchange interaction J has a similar tendency. The family dependence of models indicates a wide variation ranging from weak correlation regime (LaFePO) to substantially strong correlation regime (FeSe). The origin of the larger effective interaction in the 11 family is ascribed to smaller spread of the Wannier orbitals generating larger bare interaction, and to fewer screening channels by the other bands. This variation is primarily derived from the distance h between the pnictogen/chalcogen position and the Fe layer: The longer h for the 11 family generates more ionic character of the bonding between iron and anion atoms, while the shorter h for the 1111 family leads to more covalent-bonding character, the larger spread of the Wannier orbitals, and more efficient screening by the anion p orbitals. The screened interaction of the d model is strongly orbital dependent, which is also understood from the Wannier spread. The dp and dpp models show much weaker orbital dependence. The larger h also explains why the 10-fold 3d bands for the 11 family are more entangled with the smearing of the pseudogap'' structure above the Fermi level seen in the 1111 family. While the family-dependent semimetallic splitting of the bands primarily consists of d(yz)/d(zx) and d(x2-y2) orbitals, the size of the pseudogap structure is controlled by the hybridization between these orbitals and d(xy)/d(3z2-r2): A large hybridization in the 1111 family generates a large band-insulating''-like pseudogap ( hybridization gap), whereas a large h in the 11 family weakens them, resulting in a half-filled'' like bands of orbitals. This may enhance strong correlation effects in analogy with Mott physics and causes the orbital selective crossover in the three orbitals. On the other hand, the geometrical frustration t'/t, inferred from the ratio of the next-nearest transfer t' to the nearest one t of the d model is relatively larger for the 1111 family than the 11 one. The models comprehensively derived here may serve as a firm starting basis of understanding both common and diverse properties of the iron-based superconductors including magnetism and superconductivity.