TY - JOUR
AU - Rost, Stefan
AU - Blügel, Stefan
AU - Friedrich, Christoph
TI - Efficient calculation of k -integrated electron energy loss spectra: Application to monolayers of MoS 2 , hBN , and graphene
JO - Physical review / B
VL - 107
IS - 8
SN - 2469-9950
CY - Woodbury, NY
PB - Inst.
M1 - FZJ-2023-01434
SP - 085132
PY - 2023
AB - 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.
LB - PUB:(DE-HGF)16
UR - <Go to ISI:>//WOS:000944014500003
DO - DOI:10.1103/PhysRevB.107.085132
UR - https://juser.fz-juelich.de/record/1005325
ER -