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

Abstract

The dynamical mean-field theory formalism to describe nonresonant inelastic light and x-ray scattering in a charge-density-wave phase is developed and applied to the spinless Falicov-Kimball model on an infinitedimensional hypercubic lattice at half-filling. At zero temperature, the charge gap in the density of states 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 addition, the spectra have significant changes in shape as the temperature is raised from zero to T c . In the case of x-ray scattering ͑when both energy and momentum are transferred͒, the response function illustrates features of dynamical screening ͑vertex corrections͒ in the different ͑nonresonant͒ symmetry channels ͑A 1g and B 1g ͒; dynamical screening is also present in the A 1g Raman signal. Finally, we derive and verify the first-moment sum rules for the ͑nonresonant͒ Raman and inelastic x-ray response functions in the charge-density-wave phase and we discuss experimental implications for how the sum rules might be employed in data analysis.

Resonant Raman scattering effects in a nesting-driven charge-density-wave insulator: Exact analysis of the spinless Falicov-Kimball model with dynamical mean-field theory

“…In particular, the irreducible charge vertex is known exactly, and that is needed to examine the charge screening effects. Our work also extends recent results on transport, optical conductivity, and nonresonant x-ray scattering in CDW systems [14][15][16] to the realm of resonant inelastic light scattering. A brief report on resonant Raman scattering has also appeared as a conference proceeding 17 .…”

“…The CDW order parameter displays anomalous behavior at weak coupling 20,21 , and higher-period ordered phases are possible, and have been examined on the Bethe lattice 22 . In previous works [14][15][16] , the transport properties and nonresonant inelastic light and x-ray scattering were examined in the commensurate CDW phase. A detailed description of the DMFT solution for the CDW phase of the Falicov-Kimball model has also appeared in our previous papers 15,16 , so we restrict ourselves to a brief summary in order to establish our notation.…”

“…One would hence expect the Raman response to have much more temperature dependence than what was seen in the normal state and to have more striking resonant effects because of the sharp peaks which develop due to a pileup of the DOS at the gap edge. Indeed, the nonresonant Raman response, in the CDW phase, shows dramatic ef-fects due to the singularity in the DOS in some of the symmetry channels 16 .…”

Electron-hole asymmetry in electron systems with orbital degeneracy and correlated hopping

“…Within DMFT for Falicov-Kimball model, an exact two-pole structure was obtained for Green function, while for a general case of Hubbard model, a finite-temperature perturbation theory with electron hopping term as a perturbation parameter was built [26].On this basis, a rigorous approach for description of correlated hopping within the Falicov-Kimball model was built, thermodynamics of the model and temperatureinduced MIT were studied [27,28]. Within the elaborated scheme, considerable progress was achieved in theoretical description of inelastic Raman and X-ray scattering in the vicinity of MIT [29,30] and in charge-density wave phase [31,32]. The model with correlated hopping was shown to manifest a peculiar optical conductivity [33] and thermoelectric properties [34]- [36] due to the correlated hopping of electrons.…”

Celebrating the 60th anniversary of Andrij Shvaika

“…This collaboration resulted in an analytical derivation and calculation of the electronic Raman (and inelastic x-ray) scattering cross section [27][28][29][30][31][32][33], and x-ray photoemission spectroscopy [34] for the metallic and insulator phases of the Falicov-Kimball model. In addition to the homogeneous phase, Andrij generalized the formalism onto the case of the charge-density-wave (CDW) ordered phase, where along with Raman scattering, he also examined optical and dc-transport properties of the system [35][36][37]. This collaboration formed the basis for a successful sequence of cooperative grants from the U.S.…”