%0 Journal Article
%A Rost, Stefan
%A Blügel, Stefan
%A Friedrich, Christoph
%T Efficient calculation of k -integrated electron energy loss spectra: Application to monolayers of MoS 2 , hBN , and graphene
%J Physical review / B
%V 107
%N 8
%@ 2469-9950
%C Woodbury, NY
%I Inst.
%M FZJ-2023-01434
%P 085132
%D 2023
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000944014500003
%R 10.1103/PhysRevB.107.085132
%U https://juser.fz-juelich.de/record/1005325