  Van der Waals heterostructures employing graphene and hexagonal boron nitride
(hBN) crystals have emerged as a promising platform for plasmonics thanks to
the tunability of their collective modes with carrier density and record values
for plasmonics figures of merit. In this Article we investigate theoretically
the role of moir\'e-pattern superlattices in nearly aligned graphene on hBN by
using continuum-model Hamiltonians derived from ab initio calculations. We
calculate the system's energy loss function for a variety of chemical potential
values that are accessible in gated devices. Our calculations reveal that the
electron-hole asymmetry of the moir\'e bands leads to a remarkable asymmetry of
the plasmon dispersion between positive and negative chemical potentials,
showcasing the intricate band structure and rich absorption spectrum across the
secondary Dirac point gap for the hole bands.
