Quasiparticles for a quantum dot array in graphene and the associated magnetoplasmons

We calculate the low-frequency magnetoplasmon excitation spectrum for a square array of quantum dots on a two-dimensional (2D) graphene layer. The confining potential is linear in the distance from the center of the quantum dot. The electron eigenstates in a magnetic field and confining potential are mapped onto a 2D plane of electron-hole pairs in an effective magnetic field without any confinement. The tight-binding model for the array of quantum dots leads to a wave function with interdot mixing of the quantum numbers associated with an isolated quantum dot. For chosen confinement, magnetic field, wave vector, and frequency, we plot the dispersion equation as a function of the period d of the lattice. We obtain those values of d which yield collective plasma excitations. For the allowed transitions between the valence and conduction bands in our calculations, we obtain plasmons when d less than or similar to 100 A.