Dynamical structure factor computations in extended momentum space in electron doped cuprates

We report first principles computations of the dynamical structure factor $S(q,\omega)$ in the electron doped cuprates Nd$_{2-x}$Ce$_{x}$CuO$_{2}$ as a function of energy $\omega$ and momentum $q$ extended over several Brillouin zones. We show the efficacy of obtaining $S(q,\omega)$ through the use of simple products of real space Green functions and fast Fourier transform (FFT). We also calculate the susceptibility $\chi(q,\omega)$ efficiently by recalling that $S(q,\omega)$ is proportional to the imaginary part of the susceptibility $\chi(q,\omega)$. The present work is useful in going beyond the standard LDA-based modeling of various highly resolved spectroscopies.[1-4] We will provide some illustrative examples. Work supported by the US DOE.\\ \mbox{[1]} R. S. Markiewicz \textit{et al.}, Phys. Rev. Lett. {\bf 96}, 107005 (2006).\\ \mbox{[2]} S. Sahrakorpi \textit{et al.}, Phys. Rev. Lett. {\bf 95}, 157601 (2005).\\ \mbox{[3]} G. Stutz \textit{et al.}, Phys. Rev. B {\bf 60}, 7099 (1999).\\ \mbox{[4]} J. Nieminen \textit{et al.}, Phys. Rev. Lett. {\bf 102}, 037001 (2009).