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arXiv:cond-mat/0205347 · Physical Review Letters

Pseudogaps in an Incoherent Metal

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

Published Nov 15, 2002• 47 citations
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Abstract

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.

DOI
10.1103/physrevlett.89.236402

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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.
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 $\ensuremath{\delta}.$
We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the cellular dynamical mean-field theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum-dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.
An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.
The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.
The optical conductivity of the weakly doped two-dimensional repulsive Hubbard model on the square lattice with the nearest and next-nearest hoppings is calculated within the generalized dynamical mean-field $(\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}})$ approach, which includes correlation length scale $\ensuremath{\xi}$ into the standard DMFT equations via the momentum dependent self-energy ${\ensuremath{\sum}}_{\mathbf{p}}$, with a full account of appropriate vertex corrections. This approach takes into consideration the nonlocal dynamical correlations induced, e.g., by short-ranged collective spin-density-wavelike antiferromagnetic spin fluctuations, which (at high enough temperatures) can be viewed as a quenched Gaussian random field with finite correlation length $\ensuremath{\xi}$. The DMFT effective single-impurity problem is solved by numerical renormalization group. We consider both the case of correlated metal with the bandwidth $W\ensuremath{\lesssim}U$ and that of doped Mott insulator with U⪢WU⪢WU⪢W (UUU---the value of local Hubbard interaction). The optical conductivity calculated within $\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}}$ demonstrates typical pseudogap behavior within the quasiparticle band, in qualitative agreement with experiments in copper oxide superconductors. For large values of UUU, pseudogap anomalies are effectively suppressed.
We have generalized the dynamical mean-field theory to study the doping dependence of the crossover from antiferromagnetic to short-range order modeled by an incommensurate spin density wave in the Hubbard model. The local self-energy which includes spin fluctuations gives quasiparticle weights and spectral properties in good agreement with quantum Monte Carlo and exact diagonalization data in two dimensions. The spectra at finite doping are characterized by a Mott-Hubbard ``gap'' accompanied by a pseudogap induced by the local spin order.