Minimal longitudinal dc conductivity of perfect bilayer graphene

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Abstract

We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain σ xx min = (Jπ/2) e2 /h while from the other formula used in the above-mentioned work we find σ̄ xx min = (4J/π) e2 /h, where J=1 for single-layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for the single-layer case one of our results agrees with many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single-layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron.

Original languageEnglish
Article number033405
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume75
Issue number3
DOIs
Publication statusPublished - 2007

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Graphene
graphene
conductivity
Magnetoelectronics
Fermions
predictions
Gases
fermions
disorders
Electrons
gases
electrons
Experiments

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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title = "Minimal longitudinal dc conductivity of perfect bilayer graphene",
abstract = "We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain σ xx min = (Jπ/2) e2 /h while from the other formula used in the above-mentioned work we find σ̄ xx min = (4J/π) e2 /h, where J=1 for single-layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for the single-layer case one of our results agrees with many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single-layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron.",
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