Magnetoplasmons for the α-T3 model with filled Landau levels.

Using the $\alpha-T_3$ model, we carried out analytical and numerical calculations for the static and dynamic polarization functions in the presence of a perpendicular magnetic field. The model involves a parameter $\alpha$ which is the ratio of the hopping strength from an atom at the center of a honeycomb lattice to one of the atoms on the hexagon to the hopping strength around its rim. Our results were employed to determine the longitudinal dielectric function and the magnetoplasmon dispersion relation. The magnetic field splits the continuous valence, conduction and at energy subband into discrete Landau levels which present significant effects on the polarization function and magnetoplasmon dispersion. This includes the fact that the energies of the Landau levels are valley dependent which leads to different behaviors of the polarization function as the hopping parameter $\alpha$ (or $\phi = tan^{-1}\alpha$) is reduced continuously toward zero. This essential critical behavior of the polarization function leads to a softening of a magnetoplasmon mode. We present results for a doped layer in the integer quantum Hall regime for fixed hopping parameter $\alpha$ and various magnetic fields as well as chosen magnetic field and different $\alpha$ in the random phase approximation.