Plasmons and demons in graphene*

We study theoretically the optical response of graphene in a range of temperature and doping where both electrons and holes are present. We show that two types of collective modes should exist in this systems. Besides the higher-frequency mode, which is the familiar plasmon, graphene should support a lower-frequency mode, which is variously referred to as the sound, acoustic plasmon, energy wave, or, as we prefer, the demon. The demon can be studied using the relativistic hydrodynamics approach. We discuss linear and nonlinear phenomena enabled by the demons and how they can be observed in nano-optics experiments. We also address nonlinear electric and thermal transport in graphene in the hydrodynamic regime.