Long-range correlations in disordered graphene

The appearance of long-range correlations near the Dirac point of a Dirac-type spinor model with random vector potential is studied. These correlations originate from a spontaneously broken symmetry and their corresponding Goldstone modes. Using a strong-disorder expansion, correlation functions and matrix elements are analyzed and compared with results from a weak-disorder expansion. The local density of states correlation and the overlap between states above and below the Dirac point are characterized by a long-range behavior. The correlation range decreases with the distance from the Dirac point. Transport is diffusive and the diffusion coefficient is proportional to the one-particle scattering time for any strength of disorder. A consequence of the special properties of particle-hole scattering is a constant microwave conductivity for weak, as well as for strong disorder, describing a deviation from conventional Drude-type transport. Some properties of the model can be linked to a kind of Kondo scale, which is generated by disorder. Finally, the properties of the wave functions at the Dirac point are characterized by their participation ratios, indicating a critical state at the Dirac point.