  Muffin-tin methods have been instrumental in the design of honeycomb lattices
that show, in contrast to graphene, separated s and in-plane p bands, a p
orbital Dirac cone, and a p orbital flat band. Recently, such lattices have
been experimentally realized using the 2D electron gas on Cu(111). A possible
next avenue is the introduction of spin-orbit coupling to these systems.
Intrinsic spin-orbit coupling is believed to open topological gaps, and create
a topological flat band. Although Rashba coupling is straightforwardly
incorporated in the muffin-tin approximation, intrinsic spin-orbit coupling has
only been included either for a very specific periodic system, or only close to
the Dirac point. Here, we introduce general intrinsic and Rashba spin-orbit
terms in the Hamiltonian for both periodic and finite-size systems. We observe
a strong band opening over the entire Brillouin zone between the p orbital flat
band and Dirac cone hosting a pronounced edge state, robust against the effects
of Rashba spin-orbit coupling.
