arXiv:0709.4228 · Physical Review B

Spectral properties in the charge-density-wave phase of the half-filled Falicov-Kimball model

Syed R. Hassan, H. R. Krishnamurthy

Published Nov 16, 2007• 24 citations

Abstract

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 $U$. 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.

DOI: 10.1103/physrevb.76.205109

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arXiv:0709.4228 · Physical Review B

Spectral properties in the charge-density-wave phase of the half-filled Falicov-Kimball model

Syed R. Hassan, H. R. Krishnamurthy

Published Nov 16, 2007• 24 citations

arXiv HTML PDF

Abstract

U

. 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.

DOI: 10.1103/physrevb.76.205109

Related papers

Total electronic raman scattering in the charge-density-wave phase of the spinless Falicov–Kimball model

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

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 $B_{\rm 1g}$ , $B_{\rm 2g}$ and $A_{\rm 1g}$ 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 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 $B_{\rm 1g}$, $B_{\rm 2g}$ and $A_{\rm 1g}$ 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.

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The ground-state density of states of the half-filled Falicov-Kimball model contains a charge-density-wave gap. At finite temperature, this gap is not immediately closed, but is rather filled in by subgap states. For a specific combination of parameters, this leads to a stable phase where the system is in an ordered charge-density-wave phase, but there is high density of states at the Fermi level. We show that this property can be, in finite dimensions, traced to a crossing of sharp states resulting from the single particle excitations of the localized subsystem. The analysis of the inverse participation ratio points to a strong localization in the discussed regime. However, the pronounced subgap density of states can still lead to a notable increase of charge transport through a finite size system. We show this by focusing on the transmission in heterostructures where a Falicov-Kimball system is sandwiched between two metallic leads.The ground-state density of states of the half-filled Falicov-Kimball model contains a charge-density-wave gap. At finite temperature, this gap is not immediately closed, but is rather filled in by subgap states. For a specific combination of parameters, this leads to a stable phase where the system is in an ordered charge-density-wave phase, but there is high density of states at the Fermi level. We show that this property can be, in finite dimensions, traced to a crossing of sharp states resulting from the single particle excitations of the localized subsystem. The analysis of the inverse participation ratio points to a strong localization in the discussed regime. However, the pronounced subgap density of states can still lead to a notable increase of charge transport through a finite size system. We show this by focusing on the transmission in heterostructures where a Falicov-Kimball system is sandwiched between two metallic leads.

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Rubens D.B. Carvalho, M. A. Gusmão

In this work, we study the Anderson-Falicov-Kimball model within the dynamical mean field theory for the Bethe lattice, restricting our analysis to the nonmagnetic case. The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, since only the latter can detect localization in the absence of an energy gap. Varying the strengths of Coulomb interaction and disorder at zero temperature, we construct phase diagrams for this model, where we distinguish spectral regions with localized states, with extended states, or with a correlation-induced gap. With this, we identify metal-insulator transitions driven by correlation and disorder, as well as the competition between these effects. This is done for various band fillings, since our main interest here is to study how the variation of the electron density affects the phase diagrams previously obtained for half-filling. The picture revealed by the density of states is further checked by evaluating the static and dynamic conductivities, including temperature effects.In this work, we study the Anderson-Falicov-Kimball model within the dynamical mean field theory for the Bethe lattice, restricting our analysis to the nonmagnetic case. The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, since only the latter can detect localization in the absence of an energy gap. Varying the strengths of Coulomb interaction and disorder at zero temperature, we construct phase diagrams for this model, where we distinguish spectral regions with localized states, with extended states, or with a correlation-induced gap. With this, we identify metal-insulator transitions driven by correlation and disorder, as well as the competition between these effects. This is done for various band fillings, since our main interest here is to study how the variation of the electron density affects the phase diagrams previously obtained for half-filling. The picture revealed by the density of states is further checked by evaluating the static and dynamic conductivities, including temperature effects.

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Phase transition and phase diagram at a general filling in the spinless one-dimensional Holstein model

Sanjoy Datta, Sudhakar Yarlagadda

We derive the Luttinger liquid to charge density wave (CDW) transition condition, exact to second order in a blocked perturbative approach, for the spinless one-dimensional Holstein model in the adiabatic regime. The small parameter is the ratio of the electron-phonon coupling $g$ and the adiabaticity parameter $t∕{\ensuremath{\omega}}_{0}$. Here we correct the mean-field criterion for Peierls instability, by replacing the static noninteracting susceptibility at twice the Fermi momentum ${\ensuremath{\chi}}_{0}(2{k}_{F},0)$ with the dynamic one, and get $1+2{g}^{2}{\ensuremath{\omega}}_{0}{\ensuremath{\chi}}_{0}(2{k}_{F},{\ensuremath{\omega}}_{0})=0$. At non-half-filling, we present the phase diagram showing the surprising result that the CDW occurs in a more restricted region of the two-parameter (${g}^{2}{\ensuremath{\omega}}_{0}∕t$ and $t∕{\ensuremath{\omega}}_{0}$) space than at half-filling.We derive the Luttinger liquid to charge density wave (CDW) transition condition, exact to second order in a blocked perturbative approach, for the spinless one-dimensional Holstein model in the adiabatic regime. The small parameter is the ratio of the electron-phonon coupling $g$ and the adiabaticity parameter $t∕{\ensuremath{\omega}}_{0}$. Here we correct the mean-field criterion for Peierls instability, by replacing the static noninteracting susceptibility at twice the Fermi momentum ${\ensuremath{\chi}}_{0}(2{k}_{F},0)$ with the dynamic one, and get $1+2{g}^{2}{\ensuremath{\omega}}_{0}{\ensuremath{\chi}}_{0}(2{k}_{F},{\ensuremath{\omega}}_{0})=0$. At non-half-filling, we present the phase diagram showing the surprising result that the CDW occurs in a more restricted region of the two-parameter (${g}^{2}{\ensuremath{\omega}}_{0}∕t$ and $t∕{\ensuremath{\omega}}_{0}$) space than at half-filling.

arXiv:cond-mat/0606291Physical Review BJan 23, 20077 citations

U

B_{\rm 1g}

B_{\rm 2g}

and

A_{\rm 1g}

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.

g

and the adiabaticity parameter $t∕{\ensuremath{\omega}}_{0}$. Here we correct the mean-field criterion for Peierls instability, by replacing the static noninteracting susceptibility at twice the Fermi momentum ${\ensuremath{\chi}}_{0}(2{k}_{F},0)$ with the dynamic one, and get $1+2{g}^{2}{\ensuremath{\omega}}_{0}{\ensuremath{\chi}}_{0}(2{k}_{F},{\ensuremath{\omega}}_{0})=0$. At non-half-filling, we present the phase diagram showing the surprising result that the CDW occurs in a more restricted region of the two-parameter (${g}^{2}{\ensuremath{\omega}}_{0}∕t$ and $t∕{\ensuremath{\omega}}_{0}$) space than at half-filling.