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Molecular Graphene under the Eye of Scattering Theory

The recent experimental observations of designer Dirac Fermions and topological phases in molecular graphene are addressed theoretically. Using scattering theory we calculate the electronic structure of finite lattices of scattering centers dual to the honeycomb lattice. In good agreement with experimental observations, we obtain a V-shaped electron density of states around the Fermi energy. By varying the lattice parameter we simulate electron and hole doping of the structure and by adding and removing scattering centers we simulate respectively vacancy and impurity defects. Specifically for the vacancy defect we verify the emergence of a sharp resonance near the Fermi energy for increasing strength of the scattering potential.