Conductivity of disordered graphene at half filling

Abstract

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity $4e^2/\pi h$ in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma model including a topological term with $\theta =\pi$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.

11 pages, 2 EPS figures; Proceedings of Graphene Conference, MPIPKS Dresden 2006

References in corpus (10)

• Electric Field Effect in Atomically Thin Carbon Films
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Weak localisation magnetoresistance and valley symmetry in graphene
• Strong suppression of weak (anti)localization in graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Quantum transport of massless Dirac fermions in graphene
• Electron transport in disordered graphene
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• Effect of Disorder on Transport in Graphene
• Low energy theory of disordered graphene

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• Electron-hole asymmetry in two-terminal graphene devices
• Magnetoconductivity of Dirac fermions in graphene under charged impurity scatterings
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• ${\mathcal{L}}^2$ localization landscape for highly-excited states
• Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion
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• Graphene resistivity in diffusive limit due to scalar and vector potential electron-phonon scattering