  The electronic structure of iron pnictides is topologically nontrivial,
leading to the appearance of Dirac cones in the band structure for the
antiferromagnetic phase. Motivated by the analogy with Dirac cones in graphene,
we explore the possible existence of topologically protected surface states.
Surprisingly, bands of surface states exist even in the paramagnetic state. A
realistic five-orbital model predicts two such bands. In the antiferromagnetic
phase, these surface bands survive but split. We obtain the bulk and surface
dispersion from exact diagonalization of two- and five-orbital models in a
strip geometry and discuss the results based on topology.
