Spectrum of $π$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance

Details Spectrum of $π$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance Spectrum of $π$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance

2008-08-28

arxiv.org/abs/0808.3933v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

13 pages 8 figures, revised in line with referee's comments

Scientific paper

10.1103/PhysRevB.78.245412

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.

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