Properties of the multiorbital Hubbard models for the iron-based superconductors

A brief review of the main properties of multiorbital Hubbard models for the Fe-based superconductors is presented. The emphasis is on the results obtained by our group at the University of Tennessee and Oak Ridge National Laboratory, Tennessee, USA, but results by several other groups are also discussed. The models studied here have two, three, and five orbitals, and they are analyzed using a variety of computational and mean-field approximations. A “physical region” where the properties of the models are in qualitative agreement with neutron scattering, photoemission, and transport results is revealed. A variety of interesting open questions are briefly discussed such as: what are the dominant pairing tendencies in Hubbard models? Can pairing occur in an interorbital channel? Are nesting effects of fundamental relevance in the pnictides or approaches based on local moments are more important? What kind of magnetic states are found in the presence of iron vacancies? Can charge stripes exist in iron-based superconductors? Why is transport in the pnictides anisotropic? The discussion of results includes the description of these and other open problems in this fascinating area of research.