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001005325 0247_ $$2doi$$a10.1103/PhysRevB.107.085132
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001005325 1001_ $$0P:(DE-Juel1)171929$$aRost, Stefan$$b0
001005325 245__ $$aEfficient calculation of k -integrated electron energy loss spectra: Application to monolayers of MoS 2 ,   hBN , and graphene
001005325 260__ $$aWoodbury, NY$$bInst.$$c2023
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001005325 520__ $$aThe 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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001005325 7001_ $$0P:(DE-Juel1)130548$$aBlügel, Stefan$$b1
001005325 7001_ $$0P:(DE-Juel1)130644$$aFriedrich, Christoph$$b2$$eCorresponding author
001005325 773__ $$0PERI:(DE-600)2844160-6$$a10.1103/PhysRevB.107.085132$$gVol. 107, no. 8, p. 085132$$n8$$p085132$$tPhysical review / B$$v107$$x2469-9950$$y2023
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