Lindhard and RPA susceptibility computations in extended momentum space in electron-doped cuprates

Abstract

We present an approximation for efficient calculation of the Lindhard susceptibility ${\ensuremath{\chi}}^{L}(\mathbf{q},\ensuremath{\omega})$ in a periodic system through the use of simple products of real space functions and the fast Fourier transform (FFT). The method is illustrated by providing ${\ensuremath{\chi}}^{L}(\mathbf{q},\ensuremath{\omega})$ results for the electron doped cuprate Nd${}_{2\ensuremath{-}x}$Ce${}_{x}$CuO${}_{4}$ extended over several Brillouin zones. These results are relevant for interpreting inelastic x-ray scattering spectra from cuprates.