Theoretical description of optical and x-ray absorption spectra of MgO including many-body effects

Here we report the optical and x-ray absorption spectra of the wide-band-gap oxide MgO using density functional theory and many-body perturbation theory (MBPT). Our comprehensive study of the electronic structure shows that while the band gap is underestimated with the exchange-correlation functional PBEsol (4.58 eV) and the hybrid functional HSE06 (6.58 eV) compared to the experimental value (7.7 eV), it is significantly improved (7.52 eV) and even overcompensated (8.53 eV) when quasiparticle corrections are considered. Inclusion of excitonic effects by solving the Bethe-Salpeter equation (BSE) yields the optical spectrum in excellent agreement with experiment. Excellent agreement is observed also for the O and Mg K-edge absorption spectra, demonstrating the importance of the electron-hole interaction within MBPT. Projection of the electron-hole coupling coefficients from the BSE eigenvectors on the band structure allows us to determine the origin of prominent peaks and identify the orbital character of the relevant contributions. The real-space projection of the lowest energy exciton wave function of the optical spectrum indicates a Wannier-Mott type, whereas the first exciton in the O K edge is more localized.

Figure 1

(a) Kohn-Sham and $G_0{W}_0$ band structure and (b–d) total and projected density of states (PDOS) of MgO calculated with PBEsol within vasp.

Figure 2

Oxygen (a–c) and Mg (d–f) orbital-resolved contributions projected on the ground-state band structure within vasp.

Figure 3

Optical spectrum of bulk MgO obtained with vasp: (a, c) real part and (b, d) imaginary part of the dielectric function for PBEsol and HSE06 as the starting functional, respectively. A Lorentzian broadening of 0.3 eV is employed for all the calculated spectra. The IP, $\mathrm{IP}+G_0{W}_0$, and $G_0{W}_0+\mathrm{BSE}$ results are shown by brown solid, green dash-dotted, and red solid lines, respectively. Additionally, the experimental data from Exp. 1 [4] (black solid line) and Exp. 2 [41] (black dashed line) are displayed.

Figure 4

Optical spectrum with PBEsol including many-body corrections calculated with the $\mathtt{exciting}$ code: (a) real and (b) imaginary part of the dielectric function. A Lorentzian broadening of 0.3 eV is employed for the calculated spectrum for the $G_0{W}_0+\mathrm{BSE}$ corrections (red line) and the red vertical bars represent the oscillator strength (arb. units). The direct band gap at 7.26 eV is marked by a vertical green line. Experimental spectra from Roessler and Walker [4] (black solid line) and Bortz et al. [41] (black dashed line) are shown for comparison. (c–f) Electron-hole coupling coefficients represented as circles in reciprocal space for the peaks at different energies marked in (b), where the size of the circle is proportional to the magnitude of the $e\text{−}h$ contribution.

Figure 5

XAS spectrum of the O K edge using $G_0{W}_0+\mathrm{BSE}$ calculated with the $\mathtt{exciting}$ code: (a) calculated absorption spectra with $G_0{W}_0+\mathrm{BSE}$ (red line) and within the independent quasiparticle approximation (IQPA, brown shaded area) are compared with experimental spectra from Luches et al. [24] (black line). A shift of 34.4 eV was applied to the calculated spectra to align to the first peak of the experiment and a Lorentzian broadening of 0.55 eV is adopted to mimic the excitation lifetime. The green line at 535.2 eV marks the direct band gap. The red vertical bars represent the oscillator strength (arb. units). (b–g) Excitonic contributions to the final states in the CB of the peaks marked in (a).

Figure 6

XAS spectrum of the Mg K edge including $G_0{W}_0+\mathrm{BSE}$ corrections calculated with the $\mathtt{exciting}$ code: (a) calculated absorption spectra with $G_0{W}_0+\mathrm{BSE}$ (red line) and within IQPA (brown shaded area) are compared with experimental spectra from Luches et al. [24] on a MgO film on Ag(001), with grazing/normal incidence of the photon beam (black dash-dotted/solid line), and on polycrystalline MgO (black dashed line). A shift of 58.8 eV was applied to the calculated spectra to achieve coincidence with the first peak of the experiment and a Lorentzian broadening of 0.55 eV is adopted for the theoretical curve to mimic the excitation lifetime. The vertical green line at 1306.6 eV marks the direct band gap. The red vertical bars represent the oscillator strength (arb. units). (b–k) Excitonic contributions to the final states in the CB of the peaks marked in (a).

Figure 7

Analysis of the first exciton in the optical spectrum (a) and O K-edge XAS (b) in reciprocal space. The lower panels show the density associated with the electronic part of the excitonic wave functions for a selected cross section in real space: (c) along ($56\overline{1}$) for the optical excitation shown in (a); (d) along ($\overline{5}1\overline{6}$) for the O K-edge XAS in (b). The color code visualizes the spatial extension of the wave functions: Blue colors refer to vanishing or low densities; orange to red colors refer to elevated densities. The hole is fixed near the oxygen (fractional coordinate: 0.52, 0.52, 0.52) and is marked by a white cross.

Figure 8

Comparison of the $G_0{W}_0+\mathrm{BSE}$ spectrum calculated with PBEsol as the starting functional with $\mathtt{exciting}$ (red solid line) and vasp (blue solid line). The spectra are compared with the experiments of Roessler and Walker [4] (black solid line) and Bortz et al. [41] (black dashed line). A Lorentzian broadening of 0.3 eV is employed for the theory spectra.

Figure 9

Comparison of the spectrum obtained with mBSE on top of DFT ($k$ mesh of $21\times 21\times 21$) and with $G_0{W}_0+\mathrm{BSE}$ corrections ($k$ mesh of $15\times 15\times 15$). The spectra were calculated with HSE06 as the starting functional and compared with the experiments of Roessler and Walker [4] (black solid line) and Bortz et al. [41] (black dashed line). A Lorentzian broadening of 0.3 eV is employed for the theory spectra.