Phonon-Induced Wake Potential in a Graphene-Insulator -Graphene Structure

The aim of this study is to explore the potential which arises in a graphene-insulator-graphene structure when an external charged particle is moving parallel to it with a speed smaller than the Fermi speed in graphene. This is achieved by employing the dynamic polarization function of graphene within the random phase approximation, where its π electrons are modeled as Dirac fermions, and utilizing a local dielectric function for bulk insulators. Three different insulators are considered: SiO₂, HfO₂, and Al₂O₃. It is observed that the wake potential is induced by the surface optical phonons originating from the insulator layer, and that total potential could be effectively decomposed into two components, each corresponding to different phonon branches, as long as those branches do not interact amongst themselves.