Construction Method for an AB Bipartite Network with the pi Electronic Properties of Graphene: Generalization of the Edge States

We propose a method for constructing an AB bipartite lattice network class, termed a hypergraphene network. Edge states are defined as evanescent wave solutions with it dumping factor for the hypergraphene network. Bulk electronic states of some hypergraphene networks based on the single tight binding model are similar to the pi-electronic states of graphene, i.e., they display a linear dispersion relation, a massless Dirac spectrum, and zerogap semiconductor behavior. Our approach suggests a new method to design possible network structures having the character of graphene in not only two-dimensions, but also in systems with three- or more dimensions.