Conductivity of disordered graphene at half filling
Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany
2 Institut für Theorie der kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany
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 4e2/πh 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 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 the conductivity acquires the value characteristic for the quantum Hall transition.
© EDP Sciences, Springer-Verlag, 2007