Anomalous Angular Dependence of the Dynamic Structure Factor near Bragg Reflections: Graphite

Abstract

The electron energy-loss function of graphite is studied for momentum transfers q beyond the first Brillouin zone. We find that near Bragg reflections the spectra can change drastically for very small variations in q. The effect is investigated by means of first principle calculations in the random phase approximation and confirmed by inelastic x-ray scattering measurements of the dynamic structure factor S(q, omega). We demonstrate that this effect is governed by crystal local field effects and the stacking of graphite. It is traced back to a strong coupling between excitations at small and large momentum transfers.

Linear density response function in the projector augmented wave method: Applications to solids, surfaces, and interfaces

“…For many extended systems such a description is insufficient to account for optical excitations because the electron-hole attraction is not properly accounted for. However, dielectric properties, in particular collective plasmon excitations, are generally accurately reproduced by this approach 7,8 , and quantitative agreement with electron energy loss experiments have been reported for bulk metals 9,10 , surfaces 11,12 , graphene-based systems 13,14 , semiconductors 15,16 and even supercondutors 17 . Furthermore, the accurate evaluation of the density response function at the RPA or ALDA level is a prerequisite for implementation of most post-DFT schemes, such as RPA correlation energy 18 , exact-exchange optimized-effective-potential methods 19 , the GW approximation for quasi-particle excitations 20,21 , and the Bethe-Salpeter equation 21,22 for optical excitations.…”

Interplay between structure and electronic properties of layered transition-metal dichalcogenides: Comparing the loss function of1Tand2Hpolymorphs

“…In Refs. [20,21], it was shown that similarly to other layered materials [37][38][39][40], in 2H compounds LFE lead to a periodic behavior of the interband d z 2 + p z plasmon, which reappears at large q outside the first Brillouin zone. In fact, LFE induce a coupling between the plasmon at q r in the first Brillouin zone and the independent electron-hole excitations with momentum transfer q = q r + G 0 belonging to the higher Brillouin zone identified by G 0 .…”

“…In turn, this coupling causes the reappearance of the spectrum of the first Brillouin zone in higher zones. Moreover, it is possible to demonstrate [20,37,38] −1 and G 0 = (0,0,m) with m = 0,1,2, when LFE are taken into account (and is absent when LFE are neglected). Therefore, one can conclude that just by monitoring the periodicity of the low-energy plasmon, it is possible to identify the crystal structure of a given sample of layered TMD.…”

First-principles study of surface plasmons on Ag(111) and H/Ag(111)

“…These measurements revealed a significant change in surface-plasmon energy and dispersion upon adsorption of thiol-bonded molecules, which was rationalized using qualitative arguments. 6 Time-dependent density functional theory (TDDFT) has been successfully applied to describe plasmons in a wide range of materials, including simple metals and their surfaces, 7 graphene-based materials, 8,9 bulk transition metals, 10 and even superconductors. 11 However, its application to noble-metal surfaces has remained a challenge.…”