Topological features of engineered arrays of adsorbates in honeycomb lattices

Hydrogen adatoms are one of the most the promising proposals for the functionalization of graphene. The adatoms induce narrow resonances near the Dirac energy, which lead to the formation of magnetic moments. Furthermore, they also create local lattice distortions which enhance the spin-orbit coupling. The combination of magnetism and spin-orbit coupling allows for a rich variety of phases, some of which have non-trivial topological features. We analyze the interplay between magnetism and spin-orbit coupling in ordered arrays of adsorbates on honeycomb lattice monolayers, and classify the different phases that may arise. We extend our model to consider arrays of adsorbates in graphene-like crystals with stronger intrinsic spin-orbit couplings. We also consider a regime away from half-filling in which the Fermi level is at the bottom of the conduction band, we find a Berry curvature distribution corresponding to a Valley-Hall effect.