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Register a new userMeasurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)
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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.
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We employ Momentum-Resolved Electron Energy Loss Spectroscopy (M-EELS) on Bi2.1Sr1.9CaCu2O8+x to resolve the issue of the kink feature in the electron dispersion widely observed in the cuprates. To this end, we utilize the GW approximation to relate the density response function measured in in M-EELS to the self-energy, isolating contributions from phonons, electrons, and the momentum dependence of the effective interaction to the decay rates. The phononic contributions, present in the M-EELS spectra due to electron-phonon coupling, lead to kink features in the corresponding single-particle spectra at energies between 40 meV and 80 meV, independent of the doping level. We find that a repulsive interaction constant in momentum space is able to yield the kink attributed to phonons in ARPES. Hence, our analysis of the M-EELS spectra points to local repulsive interactions as a factor that enhances the spectroscopic signatures of electron-phonon coupling in cuprates. We conclude that the strength of the kink feature in cuprates is determined by the combined action of electron-phonon coupling and electron-electron interactions.
Lattice contribution to the electronic self-energy in complex correlated oxides is a fascinating subject that has lately stimulated lively discussions. Expectations of electron-phonon self-energy effects for simpler materials, such as Pd and Al, have
resulted in several misconceptions in strongly correlated oxides. Here we analyze a number of arguments claiming that phonons cannot be the origin of certain self-energy effects seen in high-$T_c$ cuprate superconductors via angle resolved photoemission experiments (ARPES), including the temperature dependence, doping dependence of the renormalization effects, the inter-band scattering in the bilayer systems, and impurity substitution. We show that in light of experimental evidences and detailed simulations, these arguments are not well founded.
Experimental valence electron energy loss spectra (VEELS), up to the Li K edge, obtained on different phases of LixFePO4 are compared to first principles calculations using the density functional code WIEN2k. In the 4-7 eV range, a large peak is identified in the FePO4 spectrum, but is absent in LiFePO4, which could allow the easy formation of energy filtered images. The intensity of this peak, non sensitive to the precise orientation of the crystal, is large enough to rapidly determine existing phases in the sample and permit future dynamical studies. Solid solution and two-phases regions are also differentiated using Fe M2,3 / Li K edges.
Exploiting the information provided by electron energy-loss spectroscopy (EELS) requires reliable access to the low-loss region where the zero-loss peak (ZLP) often overwhelms the contributions associated to inelastic scatterings off the specimen. Here we deploy machine learning techniques developed in particle physics to realise a model-independent, multidimensional determination of the ZLP with a faithful uncertainty estimate. This novel method is then applied to subtract the ZLP for EEL spectra acquired in flower-like WS$_2$ nanostructures characterised by a 2H/3R mixed polytypism. From the resulting subtracted spectra we determine the nature and value of the bandgap of polytypic WS$_2$, finding $E_{rm BG} = 1.6_{-0.2}^{+0.3},{rm eV}$ with a clear preference for an indirect bandgap. Further, we demonstrate how this method enables us to robustly identify excitonic transitions down to very small energy losses. Our approach has been implemented and made available in an open source Python package dubbed EELSfitter.
The Fe pnictide parent compound EuFe2As2 exhibits a strongly momentum dependent carrier dynamics around the hole pocket at the center of the Brillouin zone. The very different dynamics of electrons and holes cannot be explained solely by intraband scattering and interband contributions have to be considered. In addition, three coherently excited modes at frequencies of 5.6, 3.1 and 2.4 THz are observed. An estimate of the electron-phonon coupling parameter reveals lambda < 0.5, suggesting a limited importance of e-ph coupling to superconductivity in Fe pnictides.
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