On the minimal conductivity of graphene

Abstract

The minimal conductivity of graphene is a quantity measured in the DC limit. It is shown, using the Kubo formula, that the actual value of the minimal conductivity is sensitive to the order in which certain limits are taken. If the DC limit is taken before the integration over energies is performed, the minimal conductivity of graphene is $4/\pi$ (in units of $e^2/h$) and it is $\pi /2$ in the reverse order. The value $\pi$ is obtained if weak disorder is included via a small frequency-dependent selfenergy. In the high-frequency limit the minimal conductivity approaches $\pi /2$ and drops to zero if the frequency exceeds the cut-off energy of the particles.

5 pages, 1 figure, extended version

References in corpus (8)

• The structure of suspended graphene sheets
• Unconventional Integer Quantum Hall effect in graphene
• Quantum-limited shot noise in graphene
• Quantum Hall Ferromagnetism in Graphene
• Electron transport in disordered graphene
• Robust Transport Properties in Graphene
• Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions
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• Colloquium: Graphene spectroscopy
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• Graphene: Piecing it together
• Phenomenological study of the electronic transport coefficients of graphene
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• Dynamics of the particle - hole pair creation in graphene
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• Average Density of States in Disordered Graphene systems
• Tunneling of Dirac electrons through spatial regions of finite mass
• Dirac electrons in graphene-based quantum wires and quantum dots
• Orbital Magnetism and Transport Phenomena in Two Dimensional Dirac Fermions in Weak Magnetic Field
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• Intrinsic optical conductivity of modified-Dirac fermion systems
• Transport across twist angle domains in moiré graphene
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Diffusion in the random gap model of mono- and bilayer graphene
• Valley symmetry breaking and gap tuning in graphene by spin doping
• Weak momentum scattering and the conductivity of graphene
• Quantum electrodynamic approach to the conductivity of gapped graphene
• Dynamical optical conductivity for gapped $\alpha -{\mathcal{T}}_3$ materials with a curved "flat" band
• Effect of Coulomb scattering on graphene conductivity
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• Diffusive transport in graphene: the role of interband correlation
• Emergence of bound states in ballistic magnetotransport of graphene antidots
• Non-abelian Einstein-Born-Infeld AdS black brane and color DC conductivity
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• Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions
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• Dynamical diffusion and renormalization group equation for the Fermi velocity in doped graphene
• Parity Anomalous Semimetal with Minimal Conductivity Induced by an In-Plane Magnetic Field
• Electron-hole collision-limited resistance of gapped graphene
• AdS black brane coupled to non-abelian logarithmic gauge theory and color DC conductivity
• Non-Abelian Exponential Yang-Mills AdS Black Brane and Transport Coefficients
• Nonlinear Yang-Mills AdS black brane and DC conductivity
• Linear magnetoresistance of two-dimensional massless Dirac fermions in the quantum limit
• Non-linear photoconductivity of strongly driven graphene
• Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimi-Polder Forces in and out of Thermal Equilibrium
• Non-Abelian Charge Transport in Three-Flavor Gauge Semimetal Model with Braiding Majoranas