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One-Parameter Scaling at the Dirac Point in Graphene
Open accessAbstract
We numerically calculate the conductivity sigma of an undoped graphene sheet (size L) in the limit of a vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function beta(sigma)=dlnsigma/dlnL. Contrary to a recent prediction, the scaling flow has no fixed point (beta>0) for conductivities up to and beyond the symplectic metal-insulator transition. Instead, the data support an alternative scaling flow for which the conductivity at the Dirac point increases logarithmically with sample size in the absence of intervalley scattering--without reaching a scale-invariant limit.
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Citations
Cites
Zitterbewegung, chirality, and minimal conductivity in graphene
Katsnelson, M. I. (2006) · The European Physical Journal B - Condensed Matter and Complex Systems · doi:10.1140/epjb/e2006-00203-1 · Cited by 660
Cited by
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
Classification of topological insulators and superconductors in three spatial dimensions
Schnyder, A. P., Ryu, S., Furusaki, A., & Ludwig, A. W. W. (2008) · Physical Review B · doi:10.1103/physrevb.78.195125 · Cited by 3,322
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Vafek, O., & Vishwanath, A. (2014) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031113-133841 · Cited by 614
Symmetry-protected topological photonic crystal in three dimensions
Lu, L., Fang, C., Fu, L., Johnson, S. G., Joannopoulos, J. D., & Soljačić, M. (2016) · Nature Physics · doi:10.1038/nphys3611 · Cited by 329
Metadata
- Authors
- Bardarson, J. H., Tworzydło, J., Brouwer, P. W., & Beenakker, C. W. J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-09-05
- Volume
- 99
- Issue
- 10
- Pages
- 106801-106801
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1821170246
- Cited by
- 335
- References
- 1
- FWCI
- 12.07
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bardarson, J. H., Tworzydło, J., Brouwer, P. W., & Beenakker, C. W. J. (2007). One-Parameter Scaling at the Dirac Point in Graphene. Physical Review Letters. https://doi.org/10.1103/physrevlett.99.106801
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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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