On the theory of plasmon dispersion in electron-doped cuprates

An explicit expression for the dynamic charge susceptibility for electron-doped cuprates has been derived. This expression accurately reproduces the wave vector dependence of the plasmon frequency observed in inelastic X-ray scattering experiments for Nd$_{2-x}$Ce$_{x}$CuO$_{4}$. The imaginary part of the charge susceptibility along the triangular path in the Brillouin zone is plotted. It is demonstrated that the spectral weight of the plasmon mode near $q=0$ is negligibly low. The calculated frequencies of the plasmon mode for all wave vectors in the Brillouin zone turn out to lie outside the range of damping related to electron-hole excitations. A formula for the charge susceptibility is derived within the $t{-}t'{-}t''{-}J$ model supplemented by the Coulomb interaction operator and three-site terms. The derivation is performed by the Green’s function technique employing the formalism of composite Hubbard operators and the Mori projection method, which have proved themselves in the analysis of collective spin excitations. The used Fourier transform of the Coulomb interaction corresponds to the monolayer model with a spatially periodic structure, which is embedded in a three-dimensional crystal lattice.