Plasma Instabilities in Graphene

We discuss the possibility of the occurrence of plasma instabilities under non-equilibrium conditions in graphene. Specifically, we investigate the stability of the electronic collective modes in graphene with two counter-streaming distributions of carriers by studying the frequency-dependent dielectric function $\epsilon({\bf q},\omega)$ of the system. We find that the linear electronic dispersion of graphene results in instabilities that are qualitatively different from the standard two-stream instabilities for classical plasmas and parabolic-band systems.