Bethe-Salpeter equation calculations of core excitation spectra

J. Vinson, J. J. Rehr, J. J. Kas, and E. L. Shirley

Phys. Rev. B 83, 115106 – Published 4 March 2011

Abstract

We present a hybrid approach for Bethe-Salpeter equation (BSE) calculations of core excitation spectra, including x-ray absorption (XAS), electron energy loss spectra (EELS), and nonresonant inelastic x-ray scattering (NRIXS). The method is based on ab initio wave functions from the plane-wave pseudopotential code abinit; atomic core-level states and projector augmented wave (PAW) transition matrix elements; the NIST core-level BSE solver; and a many-pole self-energy model to account for final-state broadening and self-energy shifts. Multiplet effects are also approximately accounted for. The approach is implemented using an interface dubbed OCEAN (Obtaining Core Excitations using abinit and NBSE). To demonstrate the utility of the code we present results for the K edges in LiF as probed by XAS and NRIXS, the K edges of KCl as probed by XAS, the Ti $L_{2, 3}$ edge in SrTiO $_{3}$ as probed by XAS, and the Mg $L_{2, 3}$ edge in MgO as probed by XAS. These results are compared with experiment and with other theoretical approaches.

Received 29 September 2010

DOI:https://doi.org/10.1103/PhysRevB.83.115106

Authors & Affiliations

J. Vinson, J. J. Rehr, and J. J. Kas

Department of Physics, University of Washington, Seattle, Washington 98195, USA

E. L. Shirley

National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA

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Issue

Vol. 83, Iss. 11 — 15 March 2011

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Images

Figure 1
(a) Imaginary part of the dielectric function (top) $ε_{2} (ω)$ calculated with AI2NBSE (red, solid line) and experiment[30] (blue, dotted line) (data taken from Puschnig and Ambrosch-Draxl[31]); and (b) loss function $- Im ε^{- 1} (ω)$ (bottom) with (inset) real and imaginary parts of the self-energy calculated from AI2NBSE. The self-energy is calculated from the loss function using the many-pole self-energy method (see text) and is shown relative to the valence band maximum. This self-energy is applied to the LiF K edges providing energy dependent broadening and energy shifts to correct the single-particle energies from DFT.Reuse & Permissions
Figure 2
(a) The x-ray absorption near-edge structure (XANES) spectra for the Li K edge of LiF (top) and (b) the F K edge (bottom). The BSE spectra (solid, red line) are compared to the same spectra convoluted with the MPSE correction (green, dashed line) and experiment[34, 35] (Li data from Olovsson et al.[36]) (blue, dotted line). In (a) the result of another BSE code,[36] (light blue, dashed-dotted line) and in (b) a calculation with the feff9 code (light blue, dashed-dotted line) are shown for comparison.Reuse & Permissions
Figure 3
The theoretical (above) and experimental[41] (below) NRIXS spectra for LiF for momentum transfer $q = 3.55$ Å $^{- 1}$ , 7.25Å $^{- 1}$ , and 8.26Å $^{- 1}$ normalized to the height of the main peak. Note that momentum transfer only affects the edge-spectra due to the behavior of the $s$ -type exciton in this system.Reuse & Permissions
Figure 4
(a) The K-edge XAS of potassium (top) and (b) the Cl K edge in KCl calculated with OCEAN (red, solid line) and compared to experimental results[42] (blue, dotted line).Reuse & Permissions
Figure 5
Calculated XANES spectra for the Mg $L_{2, 3}$ edge of MgO compared with experimental reflection ( $R^{1 / 2}$ ) data.[43] The calculated spectra has been broadened and by a Gaussian of 0.9 eV FWHM in addition to the MPSE.Reuse & Permissions
Figure 6
Calculated XANES spectra for the Ti $L_{2, 3}$ edge of SrTiO $_{3}$ (red, solid line) compared to experimental data (blue, dotted line) and a multiplet calculation[44] (green, dashed line). Due to the close spacing of the edges the full MPSE was not included. Instead, the imaginary part of the self-energy was applied by aligning the onset with respect to each edge and including a core-hole lifetime (0.10 eV and 0.24 eV), shifting between the two at $461.5$ eV. This lifetime broadening also neglects solid-state Coster-Kronig and phonon effects.Reuse & Permissions

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