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arXiv:cond-mat/0211387 · Physical review. B, Condensed matter

Nonresonant inelastic light scattering in the Hubbard model

James K. Freericks, Thomas Devereaux, R. Bulla, Thomas Pruschke

Published Apr 4, 2003• 22 citations
arXivHTMLPDF

Abstract

Inelastic light scattering from electrons is a symmetry-selective probe of the charge dynamics within correlated materials. Many measurements have been made on correlated insulators, and recent exact solutions in large dimensions explain a number of anomalous features found in experiments. Here we focus on the correlated metal, as described by the Hubbard model away from half filling. We can determine the ${B}_{1\mathrm{g}}$ Raman response and the inelastic x-ray scattering along the Brillouin-zone diagonal exactly in the large dimensional limit. We find a number of interesting features in the light-scattering response, which should be able to be seen in correlated metals such as the heavy fermions.

DOI
10.1103/physrevb.67.155102

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Inelastic light scattering from electrons is a symmetry-selective probe of the charge dynamics within correlated materials. Many measurements have been made on correlated insulators, and recent exact solutions in large dimensions explain a number of anomalous features found in experiments. Here we focus on the correlated metal, as described by the Hubbard model away from half filling. We can determine the B1g{B}_{1\mathrm{g}}B1g​ Raman response and the inelastic x-ray scattering along the Brillouin-zone diagonal exactly in the large dimensional limit. We find a number of interesting features in the light-scattering response, which should be able to be seen in correlated metals such as the heavy fermions.
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.
We construct an exact dynamical mean-field theory for nonresonant inelastic light scattering in the infinite-dimensional Falicov-Kimball model, which can be tuned through a quantum critical metal-insulator transition. Due to the projection of the polarization orientations onto different regions of the Brillouin zone and due to the transfer of energy and momentum from the weakly to the strongly correlated charge excitations, the nature of the dynamics can be naturally interpreted as strongly temperature-dependent low-energy particle-hole excitations and weakly temperature-dependent high-energy charge-transfer excitations which depend delicately on the electronic correlations. These results can be used to provide important information concerning the evolution of charge dynamics in different regions of the Brillouin zone.
We use dynamical mean field theory to find an exact solution for inelastic light scattering in strongly correlated materials such as those near a quantum-critical metal-insulator transition. We evaluate the results for q=0 (Raman) scattering and find that resonant effects can be quite large, and yield a double resonance, a significant enhancement of nonresonant scattering peaks, a joint resonance of both peaks when the incident photon frequency is on the order of U, and the appearance of an isosbestic point in all symmetry channels for an intermediate range of incident photon frequencies.
A wide variety of strongly correlated materials including SmB6,{\mathrm{SmB}}_{6},SmB6​, FeSi, and the underdoped cuprates display anomalous behavior in their Raman response, which includes a low-temperature transfer of spectral weight from low to high energy (as T is reduced) and the appearance of an isosbestic point (a characteristic frequency where the Raman response is independent of temperature). We illustrate how these features appear in the Raman response of the infinite-dimensional Hubbard model, which is the simplest system to undergo the Mott transition from a Fermi liquid phase. We find that the qualitative behavior in the insulating phase is model independent, and that a number of new features arise as one approaches the metal-insulator transition from the Fermi-liquid phase. Such behavior has not yet been seen in experiment. We propose a number of different systems that are likely to show these new anomalies.
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.
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.