Graphene via large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>: A renormalization group study

Abstract

We analyze the competing effects of moderate to strong Coulomb electron-electron interactions and weak quenched disorder in graphene. By using a one-loop renormalization group calculation controlled within the large-$N$ approximation, we demonstrate that at successively lower energy (temperature or chemical potential) scales, a type of non-Abelian vector potential disorder always asserts itself as the dominant elastic scattering mechanism for generic short-ranged microscopic defect distributions. Vector potential disorder is tied to both elastic lattice deformations (``ripples'') and topological lattice defects. We identify several well-defined scaling regimes, for which we provide scaling predictions for the electrical conductivity and thermopower, valid when the inelastic lifetime due to interactions exceeds the elastic lifetime due to disorder. Coulomb interaction effects should strongly figure into the physics of suspended graphene films, where ${r}_{s}&gt;1$; we expect the vector potential disorder to play an important role in the description of transport in such films.