  The exchange effect and the magneto-plasmon mode dispersion are studied
theoretically for an anisotropic two-dimensional electronic system in the
presence of an uniform perpendicular magnetic field. Employing an effective
low-energy 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 magneto-plasmon 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.
