Spectrum of $\pi$-electrons in Graphene As a Macromolecule

Abstract

We report the exact solution of spectral problem for a graphene sheet framed by two armchair- and two zigzag-shaped boundaries. The solution is found for the $\pi$ electron Hamiltonian and gives, in particular, a closed analytic expression of edge-state energies in graphene. It is shown that the lower symmetry of graphene, in comparison with $C_{6h}$ of 2D graphite, has a profound effect on the graphene band structure. This and other obtained results have far going implications for the understanding of graphene electronics. Some of them are briefly discussed.

Revised in connection with publication in PRL, editing

References in corpus (1)

• Zero modes and the edge states of the honeycomb lattice

Cited by in corpus (6)

• Charge Transport in Disordered Graphene-Based Low Dimensional Materials
• Andreev reflection in graphene nanoribbons
• Spectrum of $\pi$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance
• Large Berry phases in layered graphene
• Quantum Conductance of Achiral Graphene Ribbons and Carbon Nanotubes
• Electronic and transport properties of rectangular graphene macromolecules and zigzag carbon nanotubes of finite length