What is the influence of the band structure on the dielectric function?

In this talk, I will introduce various analytical approaches used in the literature to compute the dielectric function. These methods are based on the homogeneous electron gas/liquid. Our ultimate goal is to describe properly the plasmon peak in core level spectroscopies and model its variations as a function of the outgoing angle. For this, we need a good description of the dielectric function both in frequency AND momentum, and especially along the plasmon dispersion. I will show that most, if not all, the methods developed in the literature can be seen as particular cases of the memory function scheme, which will be explicated. In order to assess the validity of this approach for our goal, I will then compare our results based on the homogeneous electron gas with ab initio calculations (i.e. taking fully into account the band structure). This comparison will be made for a metal with a simple band structure, Al and for a semiconductor GaN.