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arXiv:0709.0019 · Physical Review B

Strongly correlated superconductivity: A plaquette dynamical mean-field theory study

Kristjan Haule, Gabriel Kotliar

Published Sep 13, 2007• 199 citations
arXivHTMLPDF

Abstract

We use cluster dynamical mean-field theory to study the simplest models of correlated electrons, the Hubbard model and the $t\text{\ensuremath{-}}J$ model. We use a plaquette embedded in a medium as a reference frame to compute and interpret the physical properties of these models. We study various observables such as electronic lifetimes, one electron spectra, optical conductivities, superconducting stiffness, and the spin response in both the normal and the superconducting state in terms of correlation functions of the embedded cluster. We find that the shortest electron lifetime occurs near optimal doping where the superconducting critical temperature is maximal. A second critical doping connected to the change of topology of the Fermi surface is also identified. The mean-field theory provides a simple physical picture of three doping regimes, the underdoped, the overdoped, and the optimally doped regime, in terms of the physics of the quantum plaquette impurity model. We compare the plaquette dynamical mean-field theory results with earlier resonating valence bond mean-field theories, noting the improved description of the momentum space anisotropy of the normal state properties and the doping dependence of the coefficient of the linear temperature dependence of the superfluid density in the superconducting state.

DOI
10.1103/physrevb.76.104509

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We use cluster dynamical mean-field theory to study the simplest models of correlated electrons, the Hubbard model and the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. We use a plaquette embedded in a medium as a reference frame to compute and interpret the physical properties of these models. We study various observables such as electronic lifetimes, one electron spectra, optical conductivities, superconducting stiffness, and the spin response in both the normal and the superconducting state in terms of correlation functions of the embedded cluster. We find that the shortest electron lifetime occurs near optimal doping where the superconducting critical temperature is maximal. A second critical doping connected to the change of topology of the Fermi surface is also identified. The mean-field theory provides a simple physical picture of three doping regimes, the underdoped, the overdoped, and the optimally doped regime, in terms of the physics of the quantum plaquette impurity model. We compare the plaquette dynamical mean-field theory results with earlier resonating valence bond mean-field theories, noting the improved description of the momentum space anisotropy of the normal state properties and the doping dependence of the coefficient of the linear temperature dependence of the superfluid density in the superconducting state.
Doping a Mott insulator gives rise to unconventional superconducting correlations. Here we address the interplay between ddd-wave superconductivity and Mott physics using the two-dimensional Hubbard model with cellular dynamical mean-field theory on a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette. Our approach is to study superconducting correlations from the perspective of a cluster quantum impurity model embedded in a self-consistent bath. At the level of the cluster, we calculate the probabilities of the possible cluster electrons configurations. Upon condensation, we find an increased probability that cluster electrons occupy a four-electron singlet configuration, enabling us to identify this type of short-range spin correlation as key to superconducting pairing. The increased probability of this four-electron singlet comes at the expense of a reduced probability of a four-electron triplet with no significant probability redistribution of fluctuations of charges. This allows us to establish that superconductivity at the level of the cluster primarily involves a reorganization of short-range spin correlations rather than charge correlations. We gain information about the bath by studying the spectral weight of the hybridization function. Upon condensation, we find a transfer of spectral weight leading to the opening of a superconducting gap. We use these insights to interpret the signatures of superconducting correlations in the density of states of the system and in the zero-frequency spin susceptibility.
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We present a strong-coupling approach to the theory of high-temperature superconductivity based on the observation of a quantum critical point in the plaquette within the $t,{t}^{\ensuremath{'}}$ Hubbard model. The crossing of ground-state energies in the N=2−−4N=2--4N=2−−4 sectors occurs for parameters close to the optimal doping. The theory predicts the maximum of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave order parameter at the border between localized and itinerant electron behaviors and gives a natural explanation for the pseudogap formation via the soft-fermion mode related to local singlet states of the plaquette in the environment. Our approach follows the general line of resonating valence-bond theory stressing a crucial role of singlets in the physics of high-Tc{T}_{c}Tc​ superconductors but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.
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In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard ddd-wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the properties presented above in the doping dependence of the Hall resistivity, measured in magnetotransport experiments.