Plasmonic Excitations in 4-MLG Structures: Background Dielectric Inhomogeneity Effects

We investigate the plasmonic excitations and the broadening functions of the plasmon dispersions in multilayer structures consisting of four parallel monolayer graphene (4-MLG) sheets on an inhomogeneous background dielectric within the random-phase approximation. By finding the zeroes of the frequency-dependent dielectric function, we determine one optical and three acoustic plasmon modes in the system. We observed that the dependence of plasmon properties in the inhomogeneous 4-MLG system on the parameters differs significantly from that in the homogeneous one. Once the inhomogeneity of the background dielectric is taken into account, the plasmon frequencies get smaller values, compared to those in the homogeneous situation as well as in the MLG at the same parameters. As the interlayer separation increases, the plasmon branches in the inhomogeneous system move downward while only the optical branch in the homogeneous one does this, the acoustic plasmon branches shift to the opposite direction. With the efficiently large separations, plasmon lines in the homogeneous case become identical while those in the inhomogeneous case separate from each other in the large momentum region. For homogeneous 4-MLG systems, the decrease in carrier density leads to the decrease in plasmon frequency, but for inhomogeneous 4-MLG structures, the decrease in the doping density of the first graphene layer increases remarkably the frequencies of all plasmon branches. Finally, the broadening function of the plasmon dispersions gets the larger values as plasmon lines go far away from the inter single-particle excitation boundary.