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

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

2008-01-27

arxiv.org/abs/0801.4155v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Revised in connection with publication in PRL, editing

Scientific paper

10.1103/PhysRevLett.100.186806

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.

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