Resonant inelastic X-ray scattering in a Mott insulator

TL;DR

This paper calculates the RIXS response in a Mott insulator using the Falicov-Kimball model within DMFT, revealing resonance-enhanced features and dispersion of charge transfer excitations, aligning with experimental observations.

Contribution

It provides an exact calculation of the RIXS response in a Mott insulator model, highlighting resonance effects and excitation dispersions, which were previously observed experimentally but not theoretically detailed.

Findings

Resonance greatly enhances RIXS response.

Transition from single to double peak structure with photon frequency.

Charge transfer excitations disperse monotonically across the Brillouin zone.

Abstract

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 calculated RIXS response is accurate up to a local background correction. We find that on resonance the RIXS response is greatly enhanced over various other non-resonant background effects and 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 as well as across the Mott gap into the lower Hubbard band, as we vary the incident photon frequency to access states from the bottom of the lower Hubbard band to the top of the upper Hubbard band. The charge transfer excitations are found to disperse monotonically outwards (as a function of transfered energy) as we go from the center of the Brillouin zone towards the zone corner. These correlation induced features have been observed by Hasan {\it et. al.} (Science {\bf 288}, 1811 (2000)) and many other experimentalists in RIXS measurements over various transition metal oxide compounds and are found to be robust and survive even for large Auger lifetime broadening effects. 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.