Dynamical class of a two-dimensional plasmonic Dirac system

Since the advent of graphene as a tunable plasmonic material, the dynamics of surface plasmons became a hot research topic in nanophotonics. Graphene plasmons have a high capability of light confinement and have been considered feasible to mediate interactions between externally controlled signals and small quantum systems, e.g. quantum dots. However, in spite of significant progress in the field, graphene plasmons damping is still a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, the dimensionality $d$ and the shape $\sigma$ of the realized Hilbert space are the static properties that characterize time correlation functions of a dynamical variable in a system towards relaxation process. Therefore one can state if different systems are dynamically equivalent if they have the same $d$ and $\sigma$, i.e., identical relaxation functions, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.