Magnetoplasmons in the pseudospin S=1 α-T₃ lattice

We calculate the dynamical polarizability and the dispersion relation for magnetoplasmons for the α-T₃ model at zero temperature at integer filling. In the absence of magnetic field, the low energy spectrum described by a Dirac-Weyl Hamiltonian consists of a pair of Dirac cones and a dispersionless (flat) band in the K and K' valleys. We use the Peierls substitution to generate the Landau level spectrum for this structure with pseudospin S = 1 which is characterized by a parameter α for measuring the coupling strength between an additional atom at the center of the honeycomb graphene lattice and the A and B atoms of graphene. We present results for a doped layer for various α and magnetic fields in the random-phase approximation. These modes may be observed with the aid of inelastic light-scattering experiments.