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

TL;DR

This paper presents an exact tight-binding model of $c0$ electrons in graphene as an alternant macromolecule, providing new analytical insights into their behavior in ribbons and tubes, and highlighting features relevant to quantum conductance.

Contribution

It introduces a novel macromolecule-based model for graphene's $c0$ electrons, offering analytical relations and advantages over traditional lattice approaches.

Findings

Analytical relations for $c0$ electrons in graphene structures

Classification of graphene ribbons and tubes as quantum wires

Advantages of the macromolecule model over honeycomb lattice models

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.