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 two-dimensional electronic system in the presence of a 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.