  By using a non-local, quantum mechanical response function we study graphene
plasmons in a one-dimensional superlattice (SL) potential $V_0 \cos G_0x$. The
SL introduces a quantum energy scale $E_G \sim \hbar v_F G_0$ associated to
electronic sub-band transitions. At energies lower than $E_G$, the plasmon
dispersion is highly anisotropic; plasmons propagate perpendicularly to the SL
axis, but become damped by electronic transitions along the SL direction. These
results question the validity of semiclassical approximations for describing
low energy plasmons in periodic structures. At higher energies, the dispersion
becomes isotropic and Drude-like with effective Drude weights related to the
average of the absolute value of the local chemical potential. Full quantum
mechanical treatment of the kinetic energy thus introduces non-local effects
that delocalize the plasmons in the SL, making the system behave as a
meta-material even near singular points where the charge density vanishes.
