Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)

One of the most fundamental properties of an interacting electron system is its frequency- A nd wave-vector-dependent density response function, (q,!). The imaginary part, 00(q,!), defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure (q,!) at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure with quantitative momentum resolution by applying alignment techniques from X-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as "M-EELS", allows direct measurement of 00(q,!) with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi2Sr2CaCu2O8+x (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.