Christoph Friedrich

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 $\hslash \omega$ and the momentum transfer $\hslash \mathbf{k}$. 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 ${\mathrm{MoS}}_2$ (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 speedup in computation time. The calculated $\mathbf{k}$-integrated spectra are in very favorable agreement with experimental EEL spectra.

The $GW$ method is a standard method to calculate the electronic band structure from first principles. It has been applied to a large variety of semiconductors and insulators but less often to metallic systems, in particular, with respect to a self-consistent employment of the method. In this work, we take a look at all-electron quasiparticle self-consistent $GW$ (QS$GW$) calculations for simple metals (alkali and alkaline earth metals) based on the full-potential linearized augmented-plane-wave approach and compare the results to single-shot (i.e., non-selfconsistent) $G_0{W}_0$ calculations, density-functional theory (DFT) calculations in the local-density approximation, and experimental measurements. We show that, while DFT overestimates the bandwidth of most of the materials, the $GW$ quasiparticle renormalization corrects the bandwidths in the right direction, but a full self-consistent calculation is needed to consistently achieve good agreement with photoemission data. The results mainly confirm the common belief that simple metals can be regarded as nearly free electron gases with weak electronic correlation. The finding is particularly important in light of a recent debate in which this seemingly established view has been contested.

We use the constrained random-phase approximation (cRPA) method to calculate the Hubbard $U$ parameter in four one-dimensional magnetic transition metal atom oxides of composition ${\mathrm{XO}}_2$ (X = Mn, Fe, Co, Ni) on Ir(100). In addition to the expected screening of the oxide, i.e., a significant reduction of the $U$ value by the presence of the metal substrate, we find a strong dependence on the electronic configuration (multiplet) of the $\mathrm{X}(d$) orbital. Each particular electronic configuration attained by atom X is dictated by the O ligands, as well as by the charge transfer and hybridization with the Ir(100) substrate. We find that ${\mathrm{MnO}}_2$ and ${\mathrm{NiO}}_2$ chains exhibit two different screening regimes, while the case of ${\mathrm{CoO}}_2$ is somewhere in between. The electronic structure of the ${\mathrm{MnO}}_2$ chain remains almost unchanged upon adsorption. Therefore, in this regime, the additional screening is predominantly generated by the electrons of the neighboring metal surface atoms. The screening strength for ${\mathrm{NiO}}_2$/Ir(100) is found to depend on the $\mathrm{Ni}(d$) configuration in the adsorbed state. The case of ${\mathrm{FeO}}_2$ shows an exceptional behavior, as it is the only insulating system in the absence of the metallic substrate and, thus, it has the largest $U$ value. However, this value is significantly reduced by the two mentioned screening effects after adsorption.

While first-principles calculations with different levels of sophistication predict a topologically trivial ${\mathbb{Z}}_2$ state for bulk bismuth, some photoemission experiments show surface states consistent with the interpretation of bismuth being in a topologically nontrivial ${\mathbb{Z}}_2$ state. We resolve this contradiction between theory and experiment by showing, based on quasiparticle self-consistent $GW$ calculations, that the experimental surface states interpreted as supporting a nontrivial phase are actually consistent with a trivial ${\mathbb{Z}}_2$ invariant. We identify this contradiction as the result of a crosstalk effect arising from the extreme penetration depth of the surface states into the bulk of Bi. A film of Bi can be considered bulklike only for thicknesses of about 1000 bilayers ($\approx 400$ nm) and more.

We calculate the strength of the effective on-site Coulomb interaction (Hubbard $U$) in two-dimensional transition-metal (TM) dihalides $M{X}_2$ and trihalides $M{X}_3$ ($M=\mathrm{Ti}$, V, Cr, Mn, Fe, Co, Ni; $X=\mathrm{Cl}$, Br, I) from first principles using the constrained random-phase approximation. The correlated subspaces are formed from $t_{2g}$ or $e_g$ bands at the Fermi energy. Elimination of the efficient screening taking place in these narrow bands gives rise to sizable interaction parameters $U$ between the localized $t_{2g}$ ($e_g$) electrons. Due to this large Coulomb interaction, we find $U/W>1$ (with the bandwidth $W$) in most TM halides, making them strongly correlated materials. Among the metallic TM halides in the paramagnetic state, the correlation strength $U/W$ reaches a maximum in $\mathrm{Ni}{X}_2$ and $\mathrm{Cr}{X}_3$ with values much larger than the corresponding values in elementary TMs and other TM compounds. Based on the Stoner model and the calculated $U$ and $J$ values, we discuss the tendency of the electron spins to order ferromagnetically.