Nonresonant Raman and inelastic X-ray scattering in the charge-density-wave phase of the spinless Falicov-Kimball model

TL;DR

This paper investigates nonresonant Raman and X-ray scattering in the charge-density-wave phase of the spinless Falicov-Kimball model, revealing how the response functions relate to the electronic structure and sum rules.

Contribution

It provides a detailed analysis of the nonresonant scattering response in the charge-density-wave phase, including the effects of temperature, Coulomb interaction, and symmetry channels, with derivation of sum rules.

Findings

Charge gap equals Coulomb repulsion U at zero temperature.

Temperature increases fill the gap with subgap states.

Response functions show peaks related to gap and subgap transitions.

Abstract

Nonresonant inelastic light and X-ray scattering is investigated for the spinless Falicov-Kimball model on an infinite-dimensional hypercubic lattice with a charge-density-wave phase at half filling. The many-body density of states (DOS) is found for different values of the Coulomb repulsion $U$, ranging from a dirty metal to a Mott insulator. At zero temperature, the charge gap is exactly equal to $U$; increasing the temperature rapidly fills the gap with subgap states. The nonresonant response function for Raman and inelastic X-ray scattering shows peaks connected with transitions over the gap and transitions that involve subgap states. In the case of X-ray scattering (when both energy and momentum are transferred), the response function illustrates features of dynamical screening (vertex corrections) in the different (nonresonant) symmetry channels ($A_{\rm 1g}$ and $B_{\rm 1g}$). We also derive and verify the first moment sum rules for the (nonresonant) Raman and inelastic X-ray response functions.