The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of renormalization group techniques. The low-temperature properties of the system are determined by fixed points where the strength of the interactions remains finite, as in one-dimensional Luttinger liquids. These fixed points can be either stable, when the disorder is associated to topological defects in the lattice or to a random mass term, or unstable when the disorder is induced by impurities outside the graphene planes.

• Received 24 September 2004

DOI:https://doi.org/10.1103/PhysRevB.71.041406