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

Abstract

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.

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

References in corpus (9)

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• Quantum Conductance of Achiral Graphene Ribbons and Carbon Nanotubes
• Wave functions and edge states in rectangular honeycomb lattices revisited: nanoflakes, armchair and zigzag nanoribbons and nanotubes
• Interplay of relativistic and nonrelativistic transport in atomically precise segmented graphene nanoribbons
• Topological Interface States and Nonlinear Thermoelectric Performance in Armchair Graphene Nanoribbon Heterostructures
• Influence of chirality on the electron transmission through step-like potential in zigzag, armchair, and (2m,m) carbon nanotubes
• Topological edge states of the hexagonal linear chain