Electrostatics Modes in Mono-Layered Graphene

In this paper, we investigated the corrected plasmon dispersion relation for graphene in presence of a constant magnetic field which it includes a quantum term arising from the collective electron density wave interference effects. By using quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, the longitudinal plasmons are the electrostatic collective excitations of the solid electron gas. It shows the importance of quantum term from the collective electron density wave interference effects. By plotting the dispersion relation derived, it has been found that dispersion relation of surface modes depends significantly on Bohm’s potential and statistical terms and it should be taken into account in the case of magnetized or unmagnetized plasma; we have noticed successful description of the quantum hydrodynamic model. So, the quantum corrected hydrodynamic model can effectively describe the Plasmon dispersion spectrum in degenerate plasmas, since it takes into account the full picture of collective electron-wave interference via the quantum Bohm’s potential. By plotting the dispersion relation, the behavior of different wave types was predicted. It was found that one of them should not be propagated to the specific wave number. By drawing of contour curve of these modes, the areas that modes can be propagated were obtained.