Spectrum of π electrons in graphene as an alternant macromolecule and its specific features in quantum conductance

An exact description of pi electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped edges. This suggests an instructive alternative to the most commonly used approach, where the reference is made to the honeycomb lattice periodic in its A and B sublattices. Several advantages of the macromolecule model are demonstrated. The newly derived analytical relations detail our understanding of pi electron nature in achiral graphene ribbons and carbon tubes and classify these structures as quantum wires.