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arXiv:cond-mat/0312561 · AIP conference proceedings

Charge dynamics of t-J model and anomalous bond-stretching phonons in cuprates

Peter Horsch

Published Jan 1, 2003• 0 citations
arXivHTMLPDF

Abstract

The density response of a doped Mott‐Hubbard insulator is discussed starting from the t‐J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q, ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin‐charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q, ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δt related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π, 0) direction, describes the strong renormalization and anomalous damping of the highest bond‐stretching phonons in La2−xSrxCuO4.

DOI
10.1063/1.1639577

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The density response of a doped Mott‐Hubbard insulator is discussed starting from the t‐J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q, ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin‐charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q, ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δt related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π, 0) direction, describes the strong renormalization and anomalous damping of the highest bond‐stretching phonons in La2−xSrxCuO4.
The density response function $N(\mathrm{q}, \ensuremath{\omega})$ of the two-dimensional $t\ensuremath{-}J$ model is studied starting from a mixed-gauge formulation of the slave-boson approach. Our results for $N(\mathrm{q}, \ensuremath{\omega})$ are in remarkable agreement with exact diagonalization studies, and provide a natural explanation of the anomalous features in the density response in terms of the spin-polaron nature of the charge carriers. In particular, we have identified unexplained low-energy structures in the diagonalization data as arising from the coherent polaron motion of holes in a spin liquid.
The effects of the electron-phonon interaction on charge and spin dynamics are studied for the one-dimensional two-band Hubbard model by the exact diagonalization method. The parameters of the model are chosen to represent a hole-doped Cu-O system. Local charge fluctuations induced by phonons are expressed in terms of microscopic current and polarization, and it is shown that the dynamic charge transfer is strongly dependent on the phonon wave vector when the system is doped with holes. The dynamic magnetic structure factor is also found to be significantly modified by lattice distortion. In particular the lowest-energy spin excitations are greatly softened, indicating significant spin-phonon coupling. It is shown that the optical response is significantly modified as well due to coupling with the lattice over an energy range far exceeding the phonon energy. These results demonstrate the unconventional nature of the electron-phonon coupling in the strongly correlated electron systems. Its possible implications to the pairing mechanism in the cuprates are discussed.
Momentum and doping dependence of the static charge susceptibility $\ensuremath{\chi}(\mathbf{q})$ in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model is investigated. Correlations lead to a strongly momentum-dependent renormalization of $\ensuremath{\chi}(\mathbf{q})$. The charge susceptibility near the $(\ensuremath{\pi},\ensuremath{\pi})$ region of the Brillouin zone is strongly suppressed as the hole density $\ensuremath{\delta}$ is decreased. However, contrary to naive expectations, $\ensuremath{\chi}(\mathbf{q})$ around $\mathbf{q}=(\ensuremath{\pi},0)$ and $(0,\ensuremath{\pi})$ remains large and practically unchanged at $\ensuremath{\delta}\ensuremath{\sim}0.1--0.5$. This effect is consistent with a tendency towards low-energy charge fluctuations with the wave vectors along the $\ensuremath{\Gamma}\text{\ensuremath{-}}X$ direction, reported in earlier studies. Our main finding is that the above trends are amplified by JJJ-driven pairing effects, indicating that the pseudogap formation may promote the charge inhomogeneity. The next-nearest hopping ${t}^{\ensuremath{'}}$ leads to weakening of the above momentum-selective renormalizations of $\ensuremath{\chi}(\mathbf{q})$. We analyze the effects of long-range Coulomb interaction, taking into account a layered structure of cuprates. As an application, the results are discussed in the context of bond-stretching phonon softening in hole-doped cuprates. In particular, a peculiar doping and momentum dependence of the electron-phonon coupling constant is found.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
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.
The momentum dispersion of the peak structure of the single-particle spectral weight A(p,\ensuremath{\omega}) of the two-dimensional Hubbard model is discussed. Using results obtained from Monte Carlo simulations on lattices up to 12\ifmmode\times\else\texttimes\fi{}12 in size, we determine the low-lying quasiparticle dispersion relation. This dispersion relation is anomalously flat near the (\ensuremath{\pi},0) and (0,\ensuremath{\pi}) points of the Brillouin zone, similar to the results of recent angular resolved photoemission measurements of the hole-doped cuprates. We argue that the generic nature of the quasiparticle dispersion relation observed in these materials arises from the strong Coulomb interaction and reflects the hole-spin correlations rather than the one-electron interactions which customarily determine the band structure.