Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials

It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through selected boundary conditions and an ad hoc prescription. We analytically recover some results from the literature, in particular, the presence of Dirac cones for α-, β- and (6,6,12)-graphynes; for γ-graphyne, our model presents a band gap (according to the literature), but only for a range of parameters, with a transition at a certain point with quadratic touch and then the presence of Dirac cones.