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arXiv:0907.0609 · Physical Review B

Optical conductivity of a doped Mott insulator: The interplay between correlation and electron-phonon interaction

G. De Filippis, V. Cataudella, Andrei S. Mishchenko, C. A. Perroni, Naoto Nagaosa

Published Nov 4, 2009• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.80.195104

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The optical conductivity (OC) of cuprates is studied theoretically in the low-density limit of the t\ensuremath-t\ensuremath′\ensuremath-Jt\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}Jt\ensuremath-t\ensuremath′\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×\else\texttimes\fi4)(4\ifmmode\times\else\texttimes\fi{}4)(4\ifmmode×\else\texttimes\fi4), 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.
We study the Cu and O spectral density of states and the optical conductivity of CuO2{}_{2}2​ planes using an effective generalized one-band Hubbard model derived from the extended three-band Hubbard model. We solve exactly a square cluster of 10 unit cells and average the results over all possible boundary conditions, which leads to smooth functions of frequency. Upon doping, the Fermi energy jumps to Zhang-Rice states which are connected to the rest of the valence band (in contrast to an isolated band in the middle of the gap). The transfer of spectral weight depends on the parameters of the original three-band model not only through the one-band effective parameters but also through the relevant matrix elements. We discuss the evolution of the gap upon doping. The optical conductivity of the doped system shows a mid-infrared peak due to intraband transitions, a pseudogap, and a high-frequency part related to interband transitions. Its shape and integrated weight up to a given frequency (including the Drude weight) agree qualitatively with experiments in the cuprates for low to moderate doping levels, but significant deviations exist for doping x>0.3x>0.3x>0.3.
An understanding of the anomalous charge dynamics in the high-Tc{T}_{c}Tc​ cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude-like part followed by a mid-infrared band. The scattering rate associated with the Drude part exhibits a linear-temperature dependence over a wide range of high temperature, while the Drude term gets progressively suppressed below a characteristic energy of magnetic origin as the system enters the pseudogap phase. The high-energy optical conductivity shows a resonancelike feature in an underdoped case and continuously evolves into a $1∕\ensuremath{\omega}$ tail at higher doping, indicating that they share the same physical origin. In particular, such a high-energy component is closely correlated with the $\ensuremath{\omega}$-peak structure of the density-density correlation function at different momenta, in systematic consistency with exact diagonalization results based on the $t\text{\ensuremath{-}}J$ model. The underlying physics is attributed to the high-energy spin-charge separation in the model, in which the ``mode coupling'' responsible for the anomalous charge properties is not between the electrons and some collective mode but rather between charge carriers, holons, and a topological gauge field controlled by spin dynamics, as the consequence of the strong short-range electron-electron Coulomb repulsion in the doped Mott insulator.
We compute the one-particle spectral function and the optical conductivity for the two-dimensional Hubbard model on a square lattice. The computational method is cellular dynamical mean-field theory in which a four-site Hubbard plaquette is embedded in a self-consistent bath. We obtain a ``kink'' feature in the dispersion of the spectral function and a mid-infrared (mid-IR) absorption peak in the optical conductivity, consistent with experimental data. Of the 256 plaquette states, only a single state which has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry contributes to the mid-IR, thereby suggesting a direct link with the pseudogap. Local correlations between doubly and singly occupied sites which lower the kinetic energy of a hole are the efficient cause of this effect.
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The real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and Nd2CuO4{\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}Nd2​CuO4​, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.
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