The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Electronic states of graphene nanoribbons studied with the Dirac equation
Open accessAbstract
We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particlelike and a holelike band with evanescent wave functions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units has the form $3M+1$, with $M$ an integer, and insulating otherwise. A comparison of the wave functions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.
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Cites
Electric Field Effect in Atomically Thin Carbon Films
Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Zhang, Y., Dubonos, S. V., Grigorieva, I. V., & Firsov, A. A. (2004) · Science · doi:10.1126/science.1102896 · Cited by 66,834
Two-dimensional gas of massless Dirac fermions in graphene
Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Katsnelson, M. I., Grigorieva, I. V., Dubonos, S. V., & Firsov, A. A. (2005) · Nature · doi:10.1038/nature04233 · Cited by 21,611
Experimental observation of the quantum Hall effect and Berry's phase in graphene
Zhang, Y., Tan, Y.-W., Stormer, H. L., & Kim, P. (2005) · Nature · doi:10.1038/nature04235 · Cited by 13,435
Electronic properties of disordered two-dimensional carbon
Peres, N. M. R., Guinea, F., & Castro Neto, A. H. (2006) · Physical Review B · doi:10.1103/physrevb.73.125411 · Cited by 1,445
Cited by
Geim, A. K., & Novoselov, K. S. (2007) · Nature Materials · doi:10.1038/nmat1849 · Cited by 39,979
The electronic properties of graphene
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S., & Geim, A. K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.109 · Cited by 24,803
“The wavefun tions in the dis rete latti e must be real,and at large distan es the a tual solution found neara va an y tends to a superposition of two solutionsformed from wavefun tions from the two valleys withequal weight, in a way similar to the mixing at arm hairedges (Brey and Fertig, 2006b).”
BackgroundMethodSubstrate-induced bandgap opening in epitaxial graphene
Zhou, S. Y., Gweon, G.-H., Fedorov, A. V., First, P. N., de Heer, W. A., Lee, D.-H., Guinea, F., Castro Neto, A. H., & Lanzara, A. (2007) · Nature Materials · doi:10.1038/nmat2003 · Cited by 2,381
Colloquium : Andreev reflection and Klein tunneling in graphene
Beenakker, C. W. J. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1337 · Cited by 1,302
Two-dimensional surface state in the quantum limit of a topological insulator
Analytis, J. G., McDonald, R. D., Riggs, S. C., Chu, J.-H., Boebinger, G. S., & Fisher, I. R. (2010) · Nature Physics · doi:10.1038/nphys1861 · Cited by 595
Metadata
- Authors
- Brey, L., & Fertig, H. A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-06-15
- Volume
- 73
- Issue
- 23
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1491016379
- Cited by
- 1,405
- References
- 4
- FWCI
- 45.14
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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