Generalized Pomeranchuk instabilities in graphene

We study the presence of Pomeranchuk instabilities induced by interactions on a Fermi-liquid description of a graphene layer. Using a recently developed generalization of the Pomeranchuk method, we present a phase diagram in the space of fillings versus on-site and nearest-neighbors interactions. We find that for both interactions being repulsive, an instability region exists near the Van Hove filling, in agreement with earlier theoretical work. In contrast, near-half filling, the Fermi-liquid behavior appears to be stable, in agreement with theoretical results and experimental findings using angle-resolved photoemission spectroscopy. The method allows for a description of the phase diagram for arbitrary filling.