Notes on the minimal longitudinal dc conductivity of perfect bilayer graphene

Abstract

We calculated the minimal longitudinal conductivity in prefect single and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig et al. in Phys. Rev. B {\bf 50}, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain ${\sigma }_{xx}^{\text{m}in}=(J\pi /2)e^2/h$ while from the other formula used in the above mentioned work we find ${\bar{\sigma }}_{xx}^{\text{m}in}=(4J/\pi )e^2/h$, 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 single layer case one of our result agrees 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.

4 pages, no figure, corrected typos and added references in v2

References in corpus (14)

• Electric Field Effect in Atomically Thin Carbon Films
• Chiral tunneling and the Klein paradox in graphene
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Unconventional Integer Quantum Hall effect in graphene
• Quantum-limited shot noise in graphene
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Specular Andreev reflection in graphene
• Electronic states and Landau levels in graphene stacks
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• Josephson effect in ballistic graphene
• Transport in Bilayer Graphene: Calculations within a self-consistent Born approximation
• Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems
• Tunneling conductance of graphene NIS junctions
• Minimal conductivity in bilayer graphene

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• Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
• Role of the trigonal warping on the minimal conductivity of bilayer graphene
• Phenomenological study of the electronic transport coefficients of graphene
• Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly
• Optical properties of graphene antidot lattices
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• Electric transport and magnetic properties in multilayer graphene
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• Average Density of States in Disordered Graphene systems
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• Anisotropic minimal conductivity of graphene bilayers
• Long-range correlations in disordered graphene
• Suppression of magnetotransport in strongly disordered graphene
• Type-II Dirac cone and Dirac cone protected by nonsymmorphic symmetry in carbon-lithium compound (C4Li)
• Anderson Transition in Disordered Bilayer Graphene
• Linear magnetoresistance of two-dimensional massless Dirac fermions in the quantum limit
• Quantum transport of Dirac fermions in selected graphene nanosystems away from the charge-neutrality point
• Non-linear photoconductivity of strongly driven graphene