Conformal invariance and shape-dependent conductance of graphene samples
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TLDR
In this article, a conducting rectangle is combined with the semicircle model for transport coefficients to analyze the properties of the graphene monolayer and bilayer samples in the quantized Hall regime.Abstract:
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.read more
Citations
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References
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Andrea C. Ferrari,Jannik C. Meyer,Vittorio Scardaci,Cinzia Casiraghi,Michele Lazzeri,Francesco Mauri,S. Piscanec,Da Jiang,K. S. Novoselov,S. Roth,A. K. Geim +10 more
TL;DR: This work shows that graphene's electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers, and allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.
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Experimental observation of the quantum Hall effect and Berry's phase in graphene
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Journal Article
Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
TL;DR: An experimental investigation of magneto-transport in a high-mobility single layer of graphene observes an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene.