  The recent discovery of unconventional surface-state pairs, which give rise
to Fermi arcs and spin textures, in antiferromagnetically ordered rare-earth
monopnictides attracted the interest in these materials. We use angle-resolved
photoemission spectroscopy (ARPES) measurements in conjunction with density
functional theory (DFT) calculations to investigate the evolution of the
electronic structure of GdBi and DyBi. We find that new surface states,
including a Dirac cone, emerge in the AFM state. However, they are located
along a direction in momentum space that is different than what was found in
NdSb, NdBi, and CeBi. The observed changes in the electronic structure are
consistent with the presence of AFM-II-A type order.
