  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=(\pi,\pi) 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=(\pi,\pi)) in the unfolded Brillouin zone.
