# Electronic Band Structure of Armchair and Zigzag Graphene Nanoribbons

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Graphene nanoribbons (GNRs) are nanometer-wide stripes of carbon atoms arranged in a honeycomb lattice. According to the geometry of their edge, in their simplest forms, they can be either armchair (AGNRs) or zigzag (ZGNRs), although more complicated GNRs with irregular edges are also possible. The width of a GNR is given by the number of dimer lines , whereas the number of carbon atoms inside a GNR unit cell is . For instance, an armchair GNR with 8 dimer lines can be denoted concisely as 8-AGNR.

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Contributed by: Jessica Alfonsi (July 2012)

(Padova, Italy)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: tight-binding electronic band structure of a metallic armchair graphene nanoribbon (8-AGNR)

Snapshot 2: tight-binding electronic band structure of a zigzag graphene nanoribbon (6-ZGNR) with points sampled in the Brillouin zone

Snapshot 3: tight-binding electronic band structure of a semiconducting armchair graphene nanoribbon (7-AGNR)

The matrix expressions are taken from [1]. For further developments beyond tight-binding electronic structure methods for GNRs, a comprehensive review can be found in [2].

References

[1] A. Cresti, N. Nemec, B. Biel, G. Niebler, F. Triozon, G. Cuniberti, and S. Roche, "Charge Transport in Disordered Graphene-Based Low Dimensional Materials," *Nano Research*, 1, 2008 pp. 361–394. doi:10.1007/s12274-008-8043-2.

[2] J. Alfonsi and M. Meneghetti, "Excitonic Properties of Armchair Graphene Nanoribbons from Exact Diagonalization of the Hubbard Model," *New Journal of Physics*, 14, 2012 053047. doi:10.1088/1367-2630/14/5/053047.

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