Discontinuity of the dielectric function at Bragg reflexes

As an example for layered materials, the loss function of graphite was studied for momentum transfers $q$ beyond the first Brillouin zone. Surprisingly, near Bragg reflexes, the spectra are highly dependent on very small changes in $q$, which reminds the non-analyticity of the loss function in the optical limit ($q\!\to\!0$). The effect is investigated by means of first principle calculations within the random phase approximation (RPA) and is confirmed by inelastic x-ray spectroscopy (IXS) measurements. We find crystal local field effects to be crucial and propose a simple $2\!\times\! 2$ model dielectric function for explanation.