Conformal Invariance and Shape-Dependent Conductance of Graphene Samples

Details Conformal Invariance and Shape-Dependent Conductance of Graphene Samples Conformal Invariance and Shape-Dependent Conductance of Graphene Samples

2008-04-25

arxiv.org/abs/0804.4043v2

Phys. Rev. B 78, 035416 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 6 figures

Scientific paper

10.1103/PhysRevB.78.035416

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 study properties of the monolayer and bilayer graphene. 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.

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