  The electronic band structure of iron pnictides exhibits four Dirac cones,
which are due to crystal symmetry and orbital bonding orientation. This
hallmark signature presents the pnictide family as an ideal candidate in the
search for quasi-two-dimensional topological crystalline insulators. In this
report, we explore interaction-induced topological phases which cannot be
described by conventional local order parameters. Based on a model Hamiltonian
our symmetry analysis shows that sponta- neous novel topological phases may be
realized in compounds with tetragonal crystal field symmetry, where the
electrons occupy the two degenerate t2g energy levels at low temperature. We
identify two stable topological phases in the ground state, which emerge from
spontaneous orbital current order. These currents are driven by electronic
correlations caused by inter-orbital Coulomb interactions. The first
topological phase is an anomalous orbital Hall phase, characterized by a
nonzero Chern number, while the second topological phase has a vanishing Chern
number, though with an extra Z2-like invariant that preserves parity. More
specifically, the interaction-induced novel phase of the quasi-two-dimensional
topological crystalline insulator is protected by mirror reflection symmetries
and therefore may be realized in pnictides.
