Nonlinear density waves on graphene electron fluids

Abstract

The hydrodynamic behavior of charged carriers leads to nonlinear phenomena such as solitary waves and shocks, among others. As an application, such waves might be exploited on plasmonic devices either for modulation or signal propagation along graphene waveguides. We study the nature of nonlinear perturbations following an approach similar to Sagdeev potential analysis and also by performing the reductive perturbation method on the hydrodynamic description of graphene electrons, taking into consideration the effect of Bohm quantum potential and odd viscosity. Thus, deriving a dissipative Kadomtsev-Petviashvili-Burgers (KPB) equation for the bidimensional flow as well as its unidimensional limit in the form of Korteweg--de Vries--Burgers (KdVB). The stability analysis of these equations unveils the existence of unstable modes that can be excited and launched through graphene plasmonic devices.