Consistency between transmission and reflection EELS measurements of a strange metal

Attempts to measure the dynamic charge response of strange metals with electron energy loss spectroscopy (EELS) have revealed an apparent disagreement between transmissive and reflective techniques. In the small-momentum limit, both techniques agree with optical data, but at finite momenta, discrepancies appear. Resolving this issue is critical for the understanding of strongly interacting quantum many-body systems, as accurately measuring the dynamic charge response is key to understanding collective behavior.

Based on a framework originally developed for understanding the Raman response of layered electron gases in semiconductor heterostructures, an approach was developed for computing the dynamic charge response of a finite-sized layered structure. The response of both transmission- and reflection EELS experiments can be calculated, allowing for direct comparison of the results from both techniques. A layered Lindhard electron gas model is used as a sanity check, but the framework was also employed to compute the dynamic charge response of a strange metal, using the single-layer response measured with optics as input. This is directly compared with recent measurements obtained with both techniques. Insights in the subtle differences between the techniques provide a perspective for historic discrepancies and help understanding future measurements of the dynamic charge response of layered structures using transmission- and reflection EELS.