Journal Article

FZJ-2023-01434

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Efficient calculation of k -integrated electron energy loss spectra: Application to monolayers of MoS 2 ,   hBN , and graphene

Rost, S. ; Blügel, S.FZJ* ; Friedrich, C. (Corresponding author)FZJ*

2023
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/34222  doi:10.1103/PhysRevB.107.085132

Abstract: The theoretical scattering cross section of electron energy loss spectroscopy (EELS) is essentially given by $-\text{Im}\,\varepsilon^{-1}(\mathbf{k},\omega)$ with the energy loss $\hbar\omega$ and the momentum transfer $\hbar\mathbf{k}$. The macroscopic dielectric function $\varepsilon(\mathbf{k},\omega)$ can be calculated from first principles using time-dependent density-functional theory.However, experimental EELS measurements have a finite $\mathbf{k}$ resolution or, when operated in spatial resolution mode, yield a $\mathbf{k}$-integrated loss spectrum, which deviates significantly from EEL spectra calculated for specific $\mathbf{k}$ momenta. On the other hand, integrating the theoretical spectra over $\mathbf{k}$ is complicated by the fact that the integrand varies over several (typically six) orders of magnitude around $k=0$.In this article, we present a stable technique for integrating EEL spectra over an adjustable range of momentum transfers. The important region around $k=0$, where the integrand is nearly divergent, is treated partially analytically, allowing an analytic integration of the near-divergence. The scheme is applied to three prototypical two-dimensional systems: monolayers of MoS$_2$ (semiconductor), hexagonal BN (insulator), and graphene (semimetal).Here, we are confronted with the added difficulty that the long-range Coulomb interaction leads to a very slow supercell (vacuum size) convergence. We address this difficulty by employing an extrapolation scheme, enabling an efficient reduction of the supercell size and thus a considerable speed-up in computation time. The calculated $\mathbf{k}$-integrated spectra are in very favourable agreement with experimental EEL spectra.

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Contributing Institute(s):

1. Quanten-Theorie der Materialien (PGI-1)

Research Program(s):

1. 5211 - Topological Matter (POF4-521) (POF4-521)

Appears in the scientific report 2023

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Database coverage:
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