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The exchange effect and the magneto-plasmon mode dispersion are studiedtheoretically for an anisotropic two-dimensional electronic system in thepresence of an uniform perpendicular magnetic field. Employing an effectivelow-energy model with anisotropic effective masses, which is relevant for amonolayer of phosphorus, the exchange effect due to the electron-electroninteraction is treated within the self-consistent Hartree-Fock approximation.The magneto-plasmon mode dispersion is obtained by solving a Bethe-Salpeterequation for the electron density-density correlation function within theladder diagram approximation. It is found that the exchange effect is reducedin the anisotropic system in comparison with the isotropic one. Themagneto-plasmon mode dispersion shows a clear dependence on the direction ofthe wave vector.

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