Screened plasmons of graphene near a perfect electric conductor

Screened plasmon properties of graphene near a perfect electric conductor are investigated using classical electrodynamics and a linearized hydrodynamic model that includes Fermi correction. A general expression for the dispersion relation of the mentioned screened plasmonic waves is given and illustrated graphically. The result indicates that for realistic wavenumbers, the dispersion relation of plasmonic waves of isolated graphene is almost unaffected by the Fermi correction, while this correction is an important factor for the screened plasmons of graphene near a perfect electric conductor, where it increases the frequency of surface waves. The results show that near the graphene neutrality point, the surface wave has a linear dispersion with a universal speed close to $v_{\mathrm{F}}/\sqrt{2}$. Such linear dispersion for surface waves (also known as energy waves) appears to be a common occurrence when a splitting of plasma frequencies occurs, e.g. in the electron-hole plasma of 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 are derived. Also, the analytical expressions are derived and analyzed for the damping function and surface plasmon and electromagnetic field strength functions of surface waves of the system with small intrinsic damping.