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Quantum criticality and minimal conductivity in graphene with long-range disorder

P. M. Ostrovsky·I. V. Gornyi·A. D. Mirlin
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Abstract

We consider the conductivity $σ_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class $σ$-model including a topological term with $θ=π$. 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 $σ_{xx}$ acquires the value characteristic for the quantum Hall transition.

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P. M. Ostrovsky, I. V. Gornyi, A. D. Mirlin. 2007-02-05. Quantum criticality and minimal conductivity in graphene with long-range disorder. https://doi.org/10.1103/physrevlett.98.256801

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