Low-energy electronic excitations and band-gap renormalization in CuO

Combining nonresonant inelastic x-ray scattering experiments with state-of-the-art ab initio many-body calculations, we investigate the electronic screening mechanisms in strongly correlated CuO in a large range of energy and momentum transfers. The excellent agreement between theory and experiment, including the low-energy charge excitations, allows us to use the calculated dynamical screening as a safe building block for many-body perturbation theory and to elucidate the crucial role played by $d\text{−}d$ excitations in renormalizing the band gap of CuO. In this way we can dissect the contributions of different excitations to the electronic self-energy which is illuminating concerning both the general theory and this prototypical material.

Figure 1

Dynamic structure factor $S(\mathbf{q},\omega )$ for momentum transfers $\mathbf{q}$ along the [110] (a) and [100] (b) directions of the conventional chemical unit cell. Experimental data from IXS (dots) are compared to calculated spectra in the RPA (lines). For better visibility, the spectra for different $\mathbf{q}$ are offset vertically.

Figure 2

(a) Direction-averaged loss function $-Im{\varepsilon }^{-1}(\mathbf{q}\to 0,\omega )$ in the RPA, with QP corrections (QP-RPA), and QP corrections plus excitonic effects (BSE). Experimental EELS data are given for comparison. The direction-averaged real and imaginary part of the macroscopic dielectric function $\varepsilon (\mathbf{q}\to 0,\omega )$ in the RPA is also displayed. Relevant peak structures are highlighted by arrows and the QP band gap is indicated by a vertical dashed line. (b) Band structure of CuO. (c) Direction-averaged optical absorption spectrum in the RPA. The contributions from relevant interband transitions around the fundamental gap are shown. The involved states are highlighted in the band structure (b) by the corresponding coloring scheme.

Figure 3

Impact of the magnetic ordering on the dielectric function and the loss function for $\mathbf{q}\to 0$.

Figure 4

Comparison of the imaginary part of the self-energy for Si and CuO for the highest valence band at $\mathrm{\Gamma }$. The respective QP peaks are aligned at zero. In the inset, the peaks in the self-energy that are due to the low-energy plasmonlike excitations in the loss function of CuO are highlighted.

Figure 5

Shifting the peaks in the loss function by shifting the first conduction-band complex.

Figure 6

One-shot $G_0{W}_0$ band gap of CuO including screening contributions up to a momentum transfer $q_{\text{cut}}$. The inset shows the relative share of band-gap renormalization $\mathrm{\Delta }{E}_{\text{g}}^{\text{rel}}$ obtained when screening contributions up to a cutoff $q_{\text{cut}}$ are taken into account.