Conductivity of disordered graphene at half filling

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.Comment: 11 pages, 2 EPS figures; Proceedings of Graphene Conference, MPIPKS Dresden 200

Correlations of the local density of states in quasi-one-dimensional wires

We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric sigma-model, we obtain the full dependence of the two-point correlation function on the distance between the points. In the limit of zero energy difference, our calculation reproduces the statistics of a single localized wave function. At logarithmically large distances of the order of the Mott scale, we obtain a reentrant behavior similar to that in strictly one-dimensional chains.Comment: Published version. Minor technical and notational improvements. 16 pages, 1 figur

Metallic proximity effect in ballistic graphene with resonant scatterers

We study the effect of resonant scatterers on the local density of states in a rectangular graphene setup with metallic leads. We find that the density of states in a vicinity of the Dirac point acquires a strong position dependence due to both metallic proximity effect and impurity scattering. This effect may prevent uniform gating of weakly-doped samples. We also demonstrate that even a single-atom impurity may essentially alter electronic states at low-doping on distances of the order of the sample size from the impurity.Comment: 9 pages, 2 figure