Spectrum of $π$-electrons in Graphene As a Macromolecule

Lyuba Malysheva; Alexander Onipko

doi:10.1103/physrevlett.100.186806

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arXiv · 0801.4155

Spectrum of $π$-electrons in Graphene As a Macromolecule

Lyuba Malysheva·Alexander Onipko

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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 $π$ 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.

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Lyuba Malysheva, Alexander Onipko. 2008-04-29. Spectrum of $π$-electrons in Graphene As a Macromolecule. https://doi.org/10.1103/physrevlett.100.186806

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