Anisotropy of the electron momentum density of graphite studied by(γ,eγ)and(e,2e)spectroscopy

Abstract

The electron momentum density ͑EMD͒ of two different modifications of graphite has been measured and the results of the measurements have been compared with theoretical calculations from three different theories: a full potential linear muffin-tin orbital, a modified augmented plane wave, and a pseudopotential calculation. Experimental results have been obtained by two different methods. The complete three-dimensional EMD is determined by inelastic photon-electron scattering, i.e., by the so-called (␥,e␥) experiment, and by electronelectron scattering, the (e,2e) experiment, cuts in the spectral electron momentum density are studied. For the (␥,e␥) experiment 180 keV synchrotron radiation from the PETRA storage ring at the Deutsches Elektronen-Synchrotron has been used with coincident detection of the recoil electrons. The (e,2e) experiments were carried out at the new (e,2e) spectrometer at the Australian National University using 40 keV primary electron energy and simultaneous detection of the outgoing electrons in an equal energy sharing mode. As samples we have prepared approximately 20 nm thin self-supporting graphite foils either by thermal evaporation ͑TE͒ or by laser plasma ablation ͑LPA͒. They are thin enough to suppress in essence electron multiple scattering. Electron diffraction analysis revealed that the LPA foil contains graphitic basal planes with a random distribution of c axes, whereas the TE foil was strongly c-axis oriented in the sense that the basal planes were parallel to the foil surface. In the analysis of the results special attention was devoted to anisotropies in the EMD revealed by comparison of TE and LPA foils. The (e,2e) measurements showed furthermore a strong orientation dependence of the intensity of and states ͑here we have for comparison additionally measured highly oriented pyrolytic graphite͒. The EMD's obtained by both techniques show anisotropies in the momentum distribution of graphite and are discussed in view of the theoretical results.

Multiple satellites in materials with complex plasmon spectra: From graphite to graphene

“…Overall there is too much broadening to draw reliable conclusions only from the data. In previous experimental studies [10,25], features beyond the QP peaks have been attributed to extrinsic background effects and subtracted from the raw data in order to obtain an "intrinsic" spectrum. Our work suggests a revision of this hypothesis, as we show below.…”

“…In other materials, e.g., graphite, the very existence of intrinsic satellite features has been questioned. In this system observed valence-band satellite structures have been attributed to extrinsic losses and subtracted from the measured spectrum [9,10]. These debates, even for supposedly simple materials, are in part due to the lack of a widely applicable theoretical approach for the description of satellites.…”

Theoretical study of the Compton effect with correlated three-photon emission: From the differential cross section to high-energy triple-photon entanglement

“…If we assume a photon flux of 2 × 10 12 /s (see Ref. [81]), and a 0.1 mm thick Al foil as the target, then we obtain about 900 photon triplets per second.…”

“…[34], since photons of this energy are available at synchrotron radiation sources [81] with a high photon flux, and stationary targets allow for a high electron density. The total cross section is calculated to be σ tot TC = 6 × 10 −8 b, which is rather low, but can be compensated for by the aforementioned high photon flux and large number of target electrons.…”

EMS Measurement of the Valence Spectral Function of Silicon – A Test of Many‐body Theory

“…In addition there is usually a significant background underlying the photo-electron spectrum and this can hide any continuous satellite contributions. Certain Compton scattering experiments in which the struck electron is detected in coincidence with the scattered photon, so-called (γ, eγ) experiments, can in principle map out the spectral function [19,20]. However, the energy resolution is such that it is extremely difficult to resolve even the valence contributions from that of the core electrons [21].…”