Coulomb bound states and resonances due to groups of Ca dimers adsorbed on suspended graphene

The electronic bound states and resonances in the vicinity of the Dirac point energy due to the adsorption of calcium dimers on a suspended graphene monolayer are explored theoretically using density functional theory (DFT) and an improved extended H\"uckel model that includes electrostatic potentials. The Mulliken atomic charges and the electrostatic potentials are obtained from DFT calculations and reveal charge transfer from the Ca dimers to the graphene which is responsible for the emergence of resonant states in the electronic spectrum. The number of resonant states increases as the number of adsorbed dimers is increased. We find a bound "atomic-collapse" state in the graphene local density of states, as has been observed experimentally [Wang \textit{et al.}, Science {\bf 340}, 734 (2013)]. We find the formation of the atomic-collapse state and its population with electrons to require fewer adsorbed Ca dimers than in the experiment, possibly due to the different spacing between dimers and the dielectric screening by a boron nitride substrate in the experiment. We also predict the onset of filling of a second atomic-collapse state with electrons when six Ca dimers are adsorbed on the suspended graphene monolayer. Experiments testing these predictions would be of interest.