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arXiv:1006.1832 · Physical Review B

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

O. P. Matveev, Andrij M. Shvaika, James K. Freericks

Published Oct 8, 2010• 3 citations
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Abstract

We calculate the total electronic Raman scattering spectrum for a system with a charge density wave on an infinite-dimensional hypercubic lattice. The problem is solved exactly for the spinless Falicov-Kimball model with dynamical mean-field theory. We include the nonresonant, mixed, and resonant contributions in three common experimental polarizations, and analyze the response functions for representative values of the energy of the incident photons. The complicated scattering response can be understood from the significant temperature dependence of the many-body density of states and includes a huge enhancement for photon frequencies near the charge-density-wave gap energy.

DOI
10.1103/physrevb.82.155115

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We calculate the total electronic Raman scattering spectrum for a system with a charge density wave on an infinite-dimensional hypercubic lattice. The problem is solved exactly for the spinless Falicov-Kimball model with dynamical mean-field theory. We include the nonresonant, mixed, and resonant contributions in three common experimental polarizations, and analyze the response functions for representative values of the energy of the incident photons. The complicated scattering response can be understood from the significant temperature dependence of the many-body density of states and includes a huge enhancement for photon frequencies near the charge-density-wave gap energy.
We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean-field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the infinite-dimensional spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. We do find that the Raman response is large near the double resonance, where the transfered frequency is close to the incident photon frequency. We also find a joint resonance of both the charge-transfer peak and the low-energy peak when the incident photon frequency is on the order of the interaction strength. In general, the resonance effects can create order of magnitude (or more) enhancements of features in the nonresonant response, especially when the incident photon frequency is somewhat larger than the frequency of the nonresonant feature. Finally, we find that the resonant effects also exhibit isosbestic behavior, even in the A1g{A}_{1\mathrm{g}}A1g​ and B2g{B}_{2\mathrm{g}}B2g​ sectors, and it is most prominent when the incident photon frequency is on the order of the interaction energy.
The total electronic Raman scattering spectrum, including the nonresonant, mixed and resonant components, is determined for the charge-density-wave (CDW) phase of the spinless Falicov-Kimball model at half filling within dynamical mean-field theory. Its frequency dependence is investigated for different values of the energy of the incident photons. The spectra reflect the different structures in the density of states and how they are modified by screening and resonance effects. The calculations are performed for the B1gB_{\rm 1g}B1g​, B2gB_{\rm 2g}B2g​ and A1gA_{\rm 1g}A1g​ symmetries (which are typically examined in experiment). Our results for the resonance effects of the Raman spectra, found by tuning the energy of the incident photons, give information about the many-body charge dynamics of the CDW-ordered phase.
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 infinite-dimensional hypercubic lattice at half-filling. At zero temperature, the charge gap in the density of states is exactly equal to UUU; 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 Tc{T}_{c}Tc​. 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 (A1g{A}_{1g}A1g​ and B1g{B}_{1g}B1g​); dynamical screening is also present in the A1g{A}_{1g}A1g​ Raman signal. Finally, we derive and verify the first-moment sum rules for the (nonresonant) 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.
For years, theories for Raman scattering have been confined to either the insulating or fully metallic state.While much can be learned by focusing attention on the metal or insulator, recent experimental work on the cuprate systems points to the desirability of formulating a theory for Raman response which takes one through a quantum critical point -the metalinsulator transition.Using the Falicov-Kimball model as a canonical model of a MIT, we employ dynamical mean-field theory to construct an exact theory for non-resonant Raman scattering.In particular we examine the formation of charge transfer peaks and pseudogaps as well as the low-energy dynamics.The results are qualitatively compared to the experimental B 1g Raman spectra in the cuprates, which probes the hot quasiparticles along the Brillouin zone axes.The results shed important information on normal state electronic transport and the pseudo-gap in the cuprates.
We derive the dynamical mean-field theory equations for transport in an ordered charge-density-wave phase on a bipartite lattice. The formalism is applied to the spinless Falicov-Kimball model on a hypercubic lattice at half filling. We determine the many-body density of states, the dc charge and heat conductivities, and the optical conductivity. Vertex corrections continue to vanish within the ordered phase, but the density of states and the transport coefficients show anomalous behavior due to the rapid development of thermally activated subgap states. We also examine the optical sum rule and sum rules for the first three moments of the Green's functions within the ordered phase and see that the total optical spectral weight in the ordered phase either decreases or increases depending on the strength of the interactions.
We develop the theory for nonresonant Raman scattering of strongly correlated electrons in time-resolved pump- probe experiments. The electrons are initially pumped with an intense pulse of light and then a probe pulse measures the Raman response function after an adjustable time delay. We describe how the width of the probe pulse and the strength of the electron correlations affect the Raman cross section. The theory is developed for the case of B1g symmetry, where incident and scattered light are polarized perpendicular to each other. We illustrate the exact solution with the Falicov-Kimball model, which is solved via nonequilibrium dynamical mean-field theory.