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

Abstract

One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, \chi({\bf q},\omega). The imaginary part, \chi''({\bf q},\omega), defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. \chiχ 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 \chi({\bf q},\omega) at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure \chiχ 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 \chi''({\bf q},\omega) 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, Bi_22Sr_22CaCu_22O_{8+x}8+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.