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Physica C Superconductivity

Polaron theory of mid infrared conductivity: an exact cluster solution

A. S. Alexandrov, V. V. Kabanov, D.K. Ray

Published Dec 1, 1994• 0 citations
Publisher
DOI
10.1016/0921-4534(94)92403-1

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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 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 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.