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Screened plasmon properties of graphene near a perfect electric conductor areinvestigated using classical electrodynamics and a linearized hydrodynamicmodel that includes Fermi correction. A general expression for the dispersionrelation of the mentioned screened plasmonic waves is given and illustratedgraphically. The result indicates that for realistic wavenumbers, thedispersion relation of plasmonic waves of isolated graphene is almostunaffected by the Fermi correction, while this correction is an importantfactor for the screened plasmons of graphene near a perfect electric conductor,where it increases the frequency of surface waves. The results show that nearthe graphene neutrality point, the surface wave has a linear dispersion with auniversal speed close to $v_{\mathrm{F}}/\sqrt{2}$. Such linear dispersion forsurface waves (also known as energy waves) appears to be a common occurrencewhen a splitting of plasma frequencies occurs, e.g. in the electron-hole plasmaof graphene [W. Zhao \textit{et al}., Nature \textbf{614}, 688 (2023)].Furthermore, analytical expressions for the energy parameters (the power flow,energy density, and energy velocity) of screened plasmons of the system arederived. Also, the analytical expressions are derived and analyzed for thedamping function and surface plasmon and electromagnetic field strengthfunctions of surface waves of the system with small intrinsic damping.

Screened plasmons of graphene near a perfect electric conductor