Abstract
A recently proposed two-orbital model for the Fe-based superconductors is studied using the Lanczos
method on small clusters as well as pairing mean-field approximations. Our main goals are i to provide a
comprehensive analysis of this model using numerical techniques with focus on the magnetic state at halffilling
and the quantum numbers of the state with two more electrons than half-filling and ii to investigate the
nodal structure of the mean-field superconducting state and compare the results with angle-resolved photoemission
data. In particular, we provide evidence that the dominant magnetic state at half-filling contains spin
“stripes,” as observed experimentally using neutron scattering techniques. Competing spin states are also
investigated. The symmetry properties of the state with two more electrons added to half-filling are also
studied: depending on parameters, either a spin-singlet or spin triplet state is obtained. Since experiments
suggest spin-singlet pairs, our focus is on this state. Under rotations, the spin-singlet state transforms as the B2g
representation of the D4h group. We also show that the s pairing operator transforms according to the A1g
representation of D4h and becomes dominant only in an unphysical regime of the model where the undoped
state is an insulator. We obtain qualitatively very similar results both with hopping amplitudes derived from a
Slater-Koster approximation and with hoppings selected to fit band-structure calculations, the main difference
between the two being the size of the Fermi surface pockets. For robust values of the effective electronic
attraction producing the Cooper pairs, assumption compatible with recent angle-resolved photoemission spectroscopy
ARPES results that suggest a small Cooper-pair size, the nodes of the two-orbital model are found
to be located only at the electron pockets. Note that recent ARPES efforts have searched for nodes at the hole
pockets or only in a few directions at the electron pockets. Thus, our results for the nodal distribution will help
us to guide future ARPES experiments in their search for the existence of nodes in the Fe-based superconductors.
More in general, the investigations reported here aim to establish several of the properties of the
two-orbital model. Only a detailed comparison with experiments will clarify whether this simple model is or
not a good approximation to describe the Fe pnictides.
