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, χ(q, ω). The imaginary part, χ (q, ω), defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. χ 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 χ(q, ω) at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure χ 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 χ (q, ω) 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.

Dual gauge field theory of quantum liquid crystals in two dimensions

“…Last but not least, one can attempt to use a low-energy, reflection mode EELS spectrometer. Only very recently proof of principle was delivered that such a machine can pick up bosonic excitations of the strongly-correlated electron system [23], and perhaps this approach might in some near future deliver conclusive information. The verdict is that because of the shortcomings of the existing experimental machinery, it cannot be decided whether fluctuating stripes exist or whether the interpretations are flawed.…”

“…Spin fluctuations were observed at energies associated with highly collective physics (∼0-80 meV) that reveal a high degree of spatial organization, although there is no sign of static translational symmetry breaking (for recent experimental results, see Refs. [22,23]). …”

“…The spin fluctuations represent an inherently indirect measure and one would like to measure instead the charge fluctuations. Roughly twenty years after the idea of "fluctuating stripes" emerged, this appears to be now on the verge of happening due to the arrival of the high resolution RIXS beam lines and of a novel EELS spectrometer [23]. Also in this context the computational progress is adding urgency to this affair by the very recent Quantum Monte Carlo results for a three-band model signaling strong stripe fluctuations at elevated temperatures [36].…”

“…Dealing with real systems (say the cuprates) this requires machinery with an energy resolution of the order of meV and momenta of the order of inverse nanometers. Such machines can be built and it appears that these are on the verge of being operational [23]. We will further discuss this is in Sec.…”

“…In order to stand a chance to detect this feature a very high (meV) resolution appears to be required. High-energy (transmissive) EELS and RIXS have still a long way to go, and it remains to be seen whether low energy electron loss is capable of picking up such genuine electronic features [23].…”