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 Pomeranchuk method we present a phase diagram in the space of fillings versus on-site and nearest neighbors interactions. Interestingly, 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 ARPES. The method allows for a description of the complete phase diagram for arbitrary filling.