  Using a multi-orbital tight-binding model, we have studied the edge states of
zigzag silicene, germanene, and stanene nanoribbons (ZSiNRs, ZGeNRs and ZSnNRs,
respectively) in the presence of the Coulomb interaction and a vertical
electric field. The resulting edge states have non-linear energy dispersions
due to multi-orbital effects, and the nanoribbons show induced magnetization at
the edges. Owing to this non-linear dispersion, ZSiNRs, ZGeNRs and ZSnNRs may
not provide superior performance in field effect transistors, as has been
proposed from single-orbital tight-binding model calculations. We propose an
effective low-energy model that describes the edge states of ZSiNRs, ZGeNRs,
and ZSnNRs. We demonstrate that the edge states of ZGeNR and ZSnNR show
anti-crossing of bands with opposite spins, even if only out-of-plane edge
magnetization is present. The ability to tune the spin polarizations of the
edge states by applying an electric field points to future opportunities to
fabricate silicene, germanene and stanene nanoribbons as spintronics devices.
