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Physical review. B, Condensed matter

Optical conductivity in thet-Jmodel: Slave-boson, large-Ntechnique

Yunkyu Bang, Gabriel Kotliar

Published Oct 1, 1993• 12 citations
Publisher

Abstract

We study the real part of the optical conductivity in the t-J model using the slave-boson technique and the large-N expansion to the next-to-leading order in 1/N. The conductivity falls off at a slower rate than predicted by the Drude theory due to the coupling to the low-energy spin excitation. The absorptions from the mid-infrared (MIR) range to higher frequency (\ensuremath{\sim}1 eV) arise from the incoherent motion of the charge carrier. We compare our results to finite-cluster exact-diagonalization studies and to experimental studies in the copper oxide system.

DOI
10.1103/physrevb.48.9898

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We study the real part of the optical conductivity in the t-J model using the slave-boson technique and the large-N expansion to the next-to-leading order in 1/N. The conductivity falls off at a slower rate than predicted by the Drude theory due to the coupling to the low-energy spin excitation. The absorptions from the mid-infrared (MIR) range to higher frequency (\ensuremath{\sim}1 eV) arise from the incoherent motion of the charge carrier. We compare our results to finite-cluster exact-diagonalization studies and to experimental studies in the copper oxide system.
The optical conductivity for the Hubbard and t-J models is calculated numerically by use of a Lanczos algorithm. One- and two-dimensional systems of up to 16 sites with periodic and open boundary conditions are examined for the t-J model, as well as Hubbard-model systems of up to 9 sites. In the one-dimensional case, the low-frequency part of the conductivity away from half filling is shown to consist almost entirely of a single \ensuremath{\delta} function (Drude peak) even for J of the order of t. This is a direct consequence of the decoupling of charge and spin in one dimension. In two dimensions there is an additional broad absorption band above the Drude peak, consistent with the experimentally observed midinfrared band in the copper oxide superconductors. The importance of vertex corrections is demonstrated by comparing the exact conductivity with the convolution integral of the exact single-particle Green's function.
The optical conductivity of the one-band Hubbard model is calculated using the ``dynamical cluster approximation'' implementation of dynamical mean-field theory for parameters appropriate to high-temperature copper-oxide superconductors. The calculation includes vertex corrections and the result demonstrates their importance. At densities of one electron per site, an insulating state is found with gap value and above-gap absorption consistent with measurements. As carriers are added the above-gap conductivity rapidly weakens and a three component structure emerges, with a low-frequency ``Drude'' peak, a mid-infrared absorption, and a remnant of the insulating gap. The mid-infrared feature obtained at intermediate dopings is shown to arise from a pseudogap structure in the density of states. On further doping the conductivity evolves to the Drude peak plus weakly frequency dependent tail structure expected for less strongly correlated metals.
The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.
The optical conductivity, \ensuremath{\sigma}(\ensuremath{\omega}), of the two-dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane dc resistivity, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$, is also evalauted. We find that at large U/t and temperature T, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$ is approximately linear with temperature. We also observed that \ensuremath{\sigma}(\ensuremath{\omega}) displays charge excitations, a midinfrared (MIR) band, and a Drude peak. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than 1/${\mathrm{\ensuremath{\omega}}}^{2}$ at energies smaller than the insulator gap near half filling.
The optical conductivity (OC) of cuprates is studied theoretically in the low-density limit of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model taking into account the hole-lattice coupling. By developing a limited phonon basis exact diagonalization method capable of treating the lattice of largest size ever considered $(4\ifmmode\times\else\texttimes\fi{}4)$, we are able to discern the fine features of the mid-infrared (MIR) part of the OC revealing a three-peak structure. The two lowest peaks are observed in experiments and the highest one is tacitly resolved in moderately doped cuprates. Comparison of OC with the results of semianalytic approaches and detailed analysis of the calculated isotope effect indicate that the middle-energy MIR peak is of mostly magnetic origin while the lowest MIR band originates from the scattering of holes by phonons.
Exact finite-lattice results for the optical conductivity of Hubbard models near half-filling are compared with recent experimental data for the dopant- and photoinduced mid-infrared absorption of cuprate high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials. An as yet unobserved photoinduced absorption feature in the 4--6 eV range is predicted.