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arXiv:1604.01808 · Physical review. B./Physical review. B

Plaquette valence bond theory of high-temperature superconductivity

Malte Harland, Mikhail I. Katsnelson, Alexander I. Lichtenstein

Published Sep 19, 2016• 32 citations
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Abstract

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 $N=2--4$ 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-${T}_{c}$ superconductors but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.

DOI
10.1103/physrevb.94.125133

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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′t,{t}^{\ensuremath{'}}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 dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-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.
We investigate the phenomenon of high-temperature superconductivity within a strong coupling perspective. The occurence is traced to a quantum critical point that is in the phase diagram of the plaquette's t; t0-Hubbard model. We develop a bottom-up approach combining several methods, i.e. exact diagonalization of an isolated plaquette, the Lanczos-method for a plaquette within a bath and cluster dynamical Mean-Field theory with continuous time quantum Monte-Carlo solver to embedd the plaquette in a lattice environment. The quantum critical point is located where the N = 2; 3; 4-sectors of the plaquette cross. This point is also found to show optimal doping. The wave order turns out to be largest at the localized-itinerant transition of the electrons. Furthermore, we present an explenation for the pseudo-gap phenomenon, that is explained by a soft mode related to local singlets of the plaquette. The theory presented here is similar to the resonating valence bond theory, but stresses the importance of local singlets.
Abstract We study the physics of high-temperature cuprate superconductors starting from the highly degenerate four-site plaquette of the t−t′−Ut-t^{\prime} -Ut−t′−U t − t ′ − U Hubbard model as a reference system. The degeneracy causes strong fluctuations when a lattice of plaquettes is constructed. We show that there is a large binding energy between holes when a set of four plaquettes is considered. The next-nearest-neighbour hopping t′t^{\prime}t′ t ′ plays a crucial role in the formation of these strongly bound electronic bipolarons whose coherence at lower temperature could be the explanation for superconductivity. A complementary approach is cluster dual fermion starting from a single degenerate plaquette, which contains the relevant short-ranged fluctuations from the beginning. It gives d-wave superconductivity as the leading instability under a reasonably broad range of parameters. The origin of the pseudogap is also discussed in terms of the coupling of degenerate plaquettes. Thus, some of the essential elements of cuprate superconductivity appear from the local plaquette physics.
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.
Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the dynamical mean field theory solution of a twofold-orbital degenerate Hubbard model with an inverted on-site Hund rule exchange, favoring local spin-singlet configurations. Close to the Mott insulator (which here is a local version of a valence bond insulator) a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of cuprates. The strongly correlated s-wave superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.
The energetics of the interplay between superconductivity and the pseudogap in high-temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. Two regimes of superconductivity are found: a weak-coupling/large-doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong-coupling regime in which superconductivity is associated with an increase in potential energy and a decrease in kinetic energy. The crossover between the two regimes is found to coincide with the boundary of the normal-state pseudogap, providing further evidence of the unconventional nature of superconductivity in the pseudogap regime. However, the absence, in the strongly correlated but nonsuperconducting state, of discernibly nonlinear response to an applied pairing field suggests that resonating valence bond physics is not the origin of the kinetic-energy driven superconductivity.
Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature Tc(d), the maximum of the condensation energy as a function of doping, the correlation between maximum Tc(D) and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.