Influence of spatial dispersion on plasmons along graphene sheets

Taking into account the spatial dispersion and tensor conductivity of graphene, the dispersion equations of plasmons along single sheets of graphene and two sheets, including those located on a substrate, are obtained. A method for determining the dispersion equation for an arbitrary number of sheets and layers is proposed. For slow plasmons with a large distance between the sheets, the equations split into two for single sheets. When the conduction tensor is reduced to a diagonal form, the equations are simplified, and when the plasmon moves along one of the axes, the equations for E-plasmons and H-plasmons that coincide with those known for scalar conductivity decay. Plasmons up to optical and near UV frequencies are considered and numerically investigated, the influence of spatial dispersion is revealed. Plasmons with a deceleration of more than 106 were found.