Conformal invariance and shape-dependent conductance of graphene samples

Dmitry A. Abanin, Leonid S. Levitov

Research output: Contribution to journalArticlepeer-review


For a sample of an arbitrary shape, the dependence of its conductance on the longitudinal and Hall conductivity is identical to that of a rectangle. We use analytic results for a conducting rectangle, combined with the semicircle model for transport coefficients, to analyze the properties of the graphene monolayer and bilayer samples in the quantized Hall regime. A conductance plateau centered at the neutrality point, predicted for square geometry, is in agreement with recent experiments. For rectangular geometry, the conductance exhibits maxima at the densities of compressible quantum Hall states for wide samples and minima for narrow samples. The positions and relative sizes of these features are different in the monolayer and bilayer cases, indicating that the conductance can be used as a tool for sample diagnostic.

Original languageAmerican English
Article number035416
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
StatePublished - Jul 10 2008
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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