By using a nonlocal, quantum mechanical response function we study graphene plasmons in a one-dimensional superlattice (SL) potential $V_0\cos G_{0}x$. The SL introduces a quantum energy scale $E_G\sim \hslash v_F{G}_0$ associated with electronic subband 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 nonlocal effects that delocalize the plasmons in the SL, making the system behave as a metamaterial even near singular points where the charge density vanishes.

• Received 11 December 2019
• Accepted 4 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.257401