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

TL;DR

This paper introduces M-EELS, a novel method for directly measuring the momentum- and energy-resolved charge response function of materials at meV scales, enabling detailed study of collective charge modes in quantum materials.

Contribution

The paper demonstrates a new technique, M-EELS, that achieves quantitative momentum resolution in measuring the charge response function using high-resolution electron energy-loss spectroscopy.

Findings

Successfully measured $ ext{Im} \, ext{chi}({f q}, ext{omega})$ with meV resolution.

Achieved better than 1% momentum accuracy within a Brillouin zone.

Applied method to study charge excitations in high-temperature superconductor Bi2212.

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. $\chi$ 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 elecronic materials. Here, we demonstrate a way to measure $\chi$ 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$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (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.