Exchange effect and magneto-plasmon mode dispersion in an anisotropic two-dimensional electronic system

The exchange effect and the magneto-plasmon mode dispersion are studied theoretically for an anisotropic twodimensional electronic system in the presence of a uniform perpendicular magnetic field.Employing an effective lowenergy model with anisotropic effective masses,which is relevant for a monolayer of phosphorus,the exchange effect due to the electron-electron interaction is treated within the self-consistent Hartree-Fock approximation.The magnetoplasmon mode dispersion is obtained by solving a Bethe-Salpeter equation for the electron density-density correlation function within the ladder diagram approximation.It is found that the exchange effect is reduced in the anisotropic system in comparison with the isotropic one.The magneto-plasmon mode dispersion shows a clear dependence on the direction of the wave vector.