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arXiv:cond-mat/0305140 · Physical review. B, Condensed matter

Inelastic x-ray scattering as a probe of electronic correlations

Thomas Devereaux, Gary McCormack, James K. Freericks

Published Aug 8, 2003• 10 citations
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Abstract

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.

DOI
10.1103/physrevb.68.075105

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The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions, which provides an interesting benchmark for the physics of locally correlated systems. In this review, the authors develop the formalism for solving the Falicov-Kimball model from a path-integral perspective and provide a number of expressions for single- and two-particle properties. Many important theoretical results are examined that show the absence of Fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge-density-wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including ${\mathrm{YbInCu}}_{4},$ ${\mathrm{EuNi}}_{2}({\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}{)}_{2},$ ${\mathrm{NiI}}_{2},$ and ${\mathrm{Ta}}_{x}\mathrm{N}].$

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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.
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.
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.
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.
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 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.
The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions, which provides an interesting benchmark for the physics of locally correlated systems. In this review, the authors develop the formalism for solving the Falicov-Kimball model from a path-integral perspective and provide a number of expressions for single- and two-particle properties. Many important theoretical results are examined that show the absence of Fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge-density-wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including YbInCu4,{\mathrm{YbInCu}}_{4},YbInCu4​, ${\mathrm{EuNi}}_{2}({\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}{)}_{2},$ NiI2,{\mathrm{NiI}}_{2},NiI2​, and TaxN].{\mathrm{Ta}}_{x}\mathrm{N}].Tax​N].