Theoretical Description of Resonant Inelastic X-ray Scattering – TRIXS

The aim of this project is to develop the theory and software for the ab initio predictive description, without adjustable parameters, of Resonant Inelastic X-ray Spectroscopy (RIXS). RIXS is an important experimental tool to probe elementary excitations in solids. It gives vital information about the (strong) electron correlation, thanks to the large variety of targeted excitations, including i) charge-transfer excitations (crucial to unravel the nature of an insulator, like charge transfer type or Mott-Hubbard); ii) crystal-field features such as dd excitations in strongly correlated materials. Other accessible and well studied excitations are excitons,
plasmons, phonons, and magnons.

Theory plays a crucial role in the interpretation and understanding of the experimental spectra, in particular to disentangle the many types of excitations in RIXS spectra. The physical picture of RIXS can be summarized as follows: i) an incoming photon promotes a core electron to an empty conduction state; ii) a different electron from the valence region fills the core hole. The net result is a final state with an electron-hole excitation, whose energy and momentum are defined by the conservation laws. Therefore, in RIXS one combines an excitation from a core level and a de-excitation to the same core level, the net result begin an excitation for the valence. So RIXS is not (only) a measure of core levels, but of valence states.

In order to simulate RIXS spectra one has to describe the electron-hole interactions of the intermediate and final states. Therefore we will use the Bethe-Salpeter equation (BSE), an ab initio theory that explicitly takes into account electron-hole interactions in absorption spectra. The project has two main parts:

1) Extend both the theory and the implementation of the BSE to the calculation of RIXS spectra. This requires the description of high-energy photons and non-zero momentum transfer. It is important to note that we already have some preliminary results; we successfully generalized the BSE formalism to finite momentum transfer. In particular, the ab initio tool we will develop will describe the physics of the complex transition metal L and M edges, for which currently no ab initio approach exists. Moreover, the theory will be able to describe the so-called strongly correlated materials, for which a wealth of RIXS data have been collected.

2) Describe the electron correlation relevant to RIXS. In particular, RIXS is a powerful tool to study strong correlation. However, current approaches cannot accurately treat strong correlation without using adjustable parameters. To treat strongly correlated systems we will generalize an ab initio method developed by ourselves which has been successful in describing strong correlation. The starting point of our approach is the spectral representation of the Green function, whose imaginary part is linked to the photoemission spectrum, which we have expressed in a series of n-body density matrices. We have shown that simple approximations to this series gives accurate spectra for model systems, for both weak and strong correlation. We have also been able to correctly predict, without breaking the symmetry, that NiO in its paramagnetic phase is an insulator. Although we obtain qualitative good results, we have to improve the accuracy. This will be an important goal of the TRIXS project.

Throughout the duration of the TRIXS project we will benchmark our results for semiconductors and correlated solids against high-resolution RIXS experimental spectra obtained by ourselves at the SEXTANTS beamline at SOLEIL.

Finally, the ab initio numerical tool developed in the TRIXS project will be made available to the scientific community through a open source code.