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, $\chi (\mathbf{q},\omega )$. The imaginary part, ${\chi }^{\prime \prime }(\mathbf{q},\omega )$, 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 $\chi (\mathbf{q},\omega )$ 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 ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ 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.

26 pages, 10 sections, 7 figures, and an appendix

References in corpus (11)

• Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7
• Interplay of electron-lattice interactions and superconductivity in Bi2Sr2CaCu2O8+d
• Spin-Orbital Separation in the quasi 1D Mott-insulator Sr2CuO3
• A Systematic Study of Electron-Phonon Coupling to Oxygen Modes Across the Cuprates
• Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+δ
• The Role of SrTiO3 Phonon Penetrating into thin FeSe Films in the Enhancement of Superconductivity
• Linear Response Theory and the Universal Nature of the Magnetic Excitation Spectrum of the Cuprates
• Quasiparticle Interference and Strong Electron-Mode Coupling in the Quasi-One-Dimensional Bands of Sr${}_2$RuO${}_4$
• Symmetries and selection rules in the measurement of the phonon spectrum of graphene and related materials
• Electron energy loss spectroscopy with parallel readout of energy and momentum
• Temperature-resolution anomalies in the reconstruction of time dynamics from energy-loss experiments

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• Probing Fermi liquid exceptional points through AC conductivity
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• Joule heating in bad and slow metals
• Direct evidence of a charge depletion region at the interface of Van der Waals monolayers and dielectric oxides: The case of superconducting FeSe/STO
• The Future of the Correlated Electron Problem
• Dielectric response of electrons with strong local correlations and long-ranged Coulomb interactions
• Bulk-Sensitive Spin-Resolved Resonant Electron Energy-Loss Spectroscopy (SR-rEELS): Observation of Element- and Spin-Selective Bulk Plasmons
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• Dimensionality-Dependent Exciton Dispersion in a Single-Band Mott Insulator
• An Exactly Solvable Model of Randomly Pinned Charge Density Waves in Two Dimensions
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• Temperature evolution of the Fermi surface of the FeSe monolayer on SrTiO${}_3$