Resonant inelastic x-ray scattering in a Mott insulator

We calculate the resonant inelastic x-ray scattering (RIXS) response in a Mott insulator, which is described by the Falicov-Kimball model. The model can be solved exactly within the single site dynamical mean-field theory (DMFT) approximation and the RIXS response can also be calculated accurately up to a local background correction. We find that on resonance the RIXS response is greatly enhanced. The response systematically evolves from a single-peak structure, arising due to relaxation processes within the lower Hubbard band, to a two-peak structure, arising due to relaxation processes within the upper Hubbard band and across the Mott gap into the lower Hubbard band. This occurs as we vary the incident photon frequency to allow excitations from the lower Hubbard band to the upper Hubbard band. The charge transfer excitations are found to disperse monotonically as we go from the center of the Brillouin zone towards the zone corner. These correlation-induced features have been observed by Hasan et al. [Science 288, 1811 (2000)] and many other experimentalists in RIXS measurements over various transition-metal oxide compounds. They are found to be robust and survive even for large Auger lifetime broadening effects that can mask the many-body effects by smearing out spectral features. As a comparison, we also calculate the dynamic structure factor for this model, which is proportional to the nonresonant part of the response, and does not show these specific signatures.