  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.
