Quantum Criticality and Minimal Conductivity in Graphene with Long-Range Disorder

We consider the conductivity σ 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 sigma 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 e²/h. When the effective time-reversal symmetry is broken, the symmetry class becomes unitary, and σ acquires the value characteristic for the quantum Hall transition.