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Pairing Symmetries of a Hole-Doped Extended Two-Orbital Model for the Pnictides

The hole-doped ground state of a recently introduced extended "t-U-J" two-orbital Hubbard model for the Fe-based superconductors is studied via exact diagonalization methods on small clusters. Similarly as in the previously studied case of electron doping, A. Nicholson et al., Phys. Rev. Lett. 106 21702 (2011), upon hole doping it is observed that there are several competing pairing symmetries including A_{1g}, B_{1g}, and B_{2g}. However, contrary to the electron-doped case, the ground state of the hole-doped state has pseudocrystal momentum k=(π,π) in the unfolded Brillouin zone. In the two Fe-atom per unit cell representation, this indicates that the ground state involves anti-bonding, rather than bonding, combinations of the orbitals of the two Fe atoms in the unit-cell. The lowest state with k=(0,0) has only a slightly higher energy. These results indicate that this simple two-orbital model may be useful to capture some subtle aspects of the hole-doped pnictides since calculations for the five-orbital model have unveiled a hole pocket centered at M (k=(π,π)) in the unfolded Brillouin zone.