Plasmons in realistic graphene/hexagonal boron nitride moire patterns

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 paper we investigate theoretically the role of moire-pattern superlattices in nearly aligned graphene on hBN by using a continuum-model Hamiltonian derived from ab initio calculations. We calculate the system's energy-loss function for a range of chemical potential values that are accessible in gated devices. Our calculations reveal that the electron-hole asymmetry of the moire 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.