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arXiv:0708.2748 · Physical Review B

Optical and dc-transport properties of a strongly correlated charge-density-wave system: Exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory

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

Published Jan 2, 2008• 29 citations
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Abstract

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.

DOI
10.1103/physrevb.77.035102

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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.
Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the temperature increases. These subgap states should have a significant impact on transport properties, particularly the nonlinear response of the system to a large dc electric field.
We study the spectral properties of the charge-density-wave (CDW) phase of the half-filled spinless Falicov-Kimball model within the framework of the dynamical mean field theory. We present detailed results for the spectral function in the CDW phase as a function of temperature and UUU. We show how the proximity of the non-Fermi liquid phase affects the CDW phase, and show that there is a region in the phase diagram where we get a CDW phase without a gap in the spectral function. This is a radical deviation from the mean-field prediction where the gap is proportional to the order parameter.
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.
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.
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.
An exact solution is presented for the frequency-dependent charge susceptibility of the spinless Falicov-Kimball model by using dynamical mean-field theory. We develop a nontrivial application of the Baym-Kadanoff ``conserving approximation'' formalism to exactly determine the frequency-dependent vertex function (which turns out to assume a particularly simple form). We show how the static and dynamic susceptibilities are decoupled in this model and how the dynamic susceptibility generically does not show any signal of the low-temperature charge-density-wave phase transition. We also examine the temperature evolution of the dynamic charge susceptibility for the special case of half-filling.