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

Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D.

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

Authors

Ostrovsky, P. M.

Gornyi, I. V.

Mirlin, A. D.

Description

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.
4 pages, 1 figure