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Physical review. B, Condensed matter

Fluctuation effects of the superconducting order parameter in a strongly correlated system

S. Hirooka, Yasuo Hamakawa

Published Feb 1, 1990• 1 citation
Publisher

Abstract

Effects of fluctuation of the superconducting order parameter in a Hubbard model are investigated in the functional-integral formalism. It is shown in the framework of the Gaussian approximation that the critical temperature is drastically reduced owing to the large fluctuations of the order parameter which originate in the strong electron correlations.

DOI
10.1103/physrevb.41.1979

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Effects of fluctuation of the superconducting order parameter in a Hubbard model are investigated in the functional-integral formalism. It is shown in the framework of the Gaussian approximation that the critical temperature is drastically reduced owing to the large fluctuations of the order parameter which originate in the strong electron correlations.
The effect of spin-fluctuation scattering processes on the region of the superconducting phase in the strongly correlated electrons (Hubbard fermions) has been investigated by the diagram technique for Hubbard operators. It is shown that spin fluctuations in the one-loop approximation for the − t' − t − J*- model taking into account long-range hoppings and three-center interactions are reflected by components of the strength operator. In this approximation for the d-type symmetry of the order parameter for the superconducting phase a system of infinite integral equations has been derived. Obtained dependencies of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and dynamical spin-fluctuation processes leads to strong renormalization of the superconducting phase region. It was shown that these processes essentially modify distribution functions of Hubbard fermions in normal phase.
In this work we study the superconductivity within an attractive two-dimensional one-band Hubbard model. We consider a d-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use the Green’s function method to obtain the order parameter Δ and the superconducting critical temperature Tc. The results show that for fixed values of the superconducting attractive potential U(U<0), the gap increases for low temperatures but diminishes abruptly as the temperature increases. The effect of pressure is discussed, varying the next-nearest-neighbor hopping t2, yielding a change in Tc, and also in Δ0, and a tendency to suppress the superconductivity.
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. We briefly discuss a formulation for the superconducting transition temperature in the present approximation.
We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction Vij{\mathit{V}}_{\mathit{ij}}Vij​. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of Tc{\mathit{T}}_{\mathit{c}}Tc​ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.
We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized preformed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number $Z\ensuremath{\gg}1$ of similar neighboring pairs. We derived integral equations for the probability distribution $P(\mathrm{\ensuremath{\Delta}})$ of local superconducting order parameter $\mathrm{\ensuremath{\Delta}}(\mathbit{r})$ and analyzed their solutions in the limit of small dimensionless Cooper coupling constant $\ensuremath{\lambda}\ensuremath{\ll}1$. The shape of the order-parameter distribution is found to depend crucially upon the effective number of nearest neighbors ${Z}_{\text{eff}}=2{\ensuremath{\nu}}_{0}{\mathrm{\ensuremath{\Delta}}}_{0}Z$, with ${\ensuremath{\nu}}_{0}$ being the single-particle density of states at the Fermi level. The solution we provide is valid both at large and small Zeff{Z}_{\text{eff}}Zeff​; the latter case is nontrivial as the function $P(\mathrm{\ensuremath{\Delta}})$ is heavily non-Gaussian. One of our key findings is the discovery of a broad range of parameters where the distribution function $P(\mathrm{\ensuremath{\Delta}})$ is non-Gaussian but also noncritical (in the sense of superconductor-insulator transition criticality). The analytic results are supplemented by numerical data and good agreement between them is observed.
The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction UminU_{min}Umin​ is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature TcT_cTc​ shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.