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arXiv:cond-mat/0304096 · Physical review. B, Condensed matter

Pseudogaps in the t−J model: An extended dynamical mean-field theory study

Kristjan Haule, Achim Rosch, Johann Kroha, P. Wölfle

Published Oct 28, 2003• 49 citations
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Abstract

We investigate the highly incoherent regime of hole-doped two-dimensional Mott-Hubbard insulators at moderately small doping $\ensuremath{\delta}$ and temperatures $\ensuremath{\gtrsim}0.1J,$ where J is the exchange coupling. Within an extended dynamical mean-field theory of the $t\ensuremath{-}J$ model and a generalized noncrossing approximation we calculate the single-particle spectral function, the dynamical susceptibility, and thermodynamic and transport quantities. Short-ranged antiferromagnetic fluctuations lead to strongly incoherent single-particle dynamics, large entropy, and large electrical resistivity. At low doping a pseudogap is found to open up in both the single-particle and spin excitation spectra, leading to a decrease in entropy and resistivity. The Hall coefficient changes sign to positive values upon lowering the doping level and increases inversely proportional to $\ensuremath{\delta}.$

DOI
10.1103/physrevb.68.155119

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We investigate the highly incoherent regime of hole-doped two-dimensional Mott-Hubbard insulators at moderately small doping \ensuremathδ\ensuremath{\delta}\ensuremathδ and temperatures \ensuremath≳0.1J,\ensuremath{\gtrsim}0.1J,\ensuremath≳0.1J, where J is the exchange coupling. Within an extended dynamical mean-field theory of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model and a generalized noncrossing approximation we calculate the single-particle spectral function, the dynamical susceptibility, and thermodynamic and transport quantities. Short-ranged antiferromagnetic fluctuations lead to strongly incoherent single-particle dynamics, large entropy, and large electrical resistivity. At low doping a pseudogap is found to open up in both the single-particle and spin excitation spectra, leading to a decrease in entropy and resistivity. The Hall coefficient changes sign to positive values upon lowering the doping level and increases inversely proportional to \ensuremathδ.\ensuremath{\delta}.\ensuremathδ.
How are the properties of a metal changed by strong inelastic scattering? We investigate this question within the two-dimensional t-J model using extended dynamical mean field theory and a generalized noncrossing approximation. Short-ranged antiferromagnetic fluctuations lead to a strongly incoherent single particle dynamics, large entropy, and resistance. Close to the Mott transition at low hole doping a pseudogap opens, accompanied by a drop in resistivity and an increase in the Hall constant for both lower temperatures T and doping levels. The behavior obtained bears surprising similarity to properties of the cuprates.
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We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ (UUU---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.
Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.
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The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto $2\ifmmode\times\else\texttimes\fi{}2$ clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ${\ensuremath{\Sigma}}_{X}$ associated with $X=(\ensuremath{\pi},0)$ is shown to develop a collective mode above EF{E}_{F}EF​, whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value ${\ensuremath{\delta}}_{c}$, and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above EF{E}_{F}EF​ and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that ${\ensuremath{\delta}}_{c}\ensuremath{\approx}0.15\dots{}0.20$ for various system parameters. For electron doping, the collective mode of ${\ensuremath{\Sigma}}_{X}(\ensuremath{\omega})$ and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below EF{E}_{F}EF​. The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.