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Journal of Experimental and Theoretical Physics

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

Valerii Vladimirovich Val'kov, Dmitrii Mikhailovich Dzebisashvili

Published Mar 1, 2005• 28 citations
Publisher

Abstract

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H (3)) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H (3) and magnetic fluctuations at n>n 1 (n 1 ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d x 2−y 2 type.

DOI
10.1134/1.1901772

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The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H (3)) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H (3) and magnetic fluctuations at n>n 1 (n 1 ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d x 2−y 2 type.
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.
We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity, which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase T_{c}.
A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite ${\mathit{t}}^{\ensuremath{'}}$ and at ${\mathit{t}}^{\ensuremath{'}}$=0 but for two totally different physical reasons. When ${\mathit{t}}^{\ensuremath{'}}$=0, it is induced by antiferromagnetic correlations while at ${\mathit{t}}^{\ensuremath{'}}$=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.
The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature Tc is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. Tc increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. Tc is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of Tc is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively.
The interplay of magnetic and superconducting fluctuations in two-dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization-group (fRG) approach. While the fRG flow has to be stopped at a certain minimal temperature TRGmin{T}_{\text{RG}}^{\text{min}}TRGmin​, we study temperature dependence of magnetic and superconducting susceptibilities below TRGmin{T}_{\text{RG}}^{\text{min}}TRGmin​ to obtain the crossover temperatures to the regime with strong magnetic and superconducting fluctuations. Near half filling we obtain the largest crossover temperature, corresponding to a regime with strong commensurate magnetic fluctuations, which is replaced by a regime with strong incommensurate fluctuations further away from half filling. With further decreasing density the system undergoes quantum phase transition from incommensurate to paramagnetic phase. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the magnetic quantum-critical point is found almost linear in temperature.
An interplay between the superconductivity and spin density wave (SDW) is studied from the perturbative point of view based on the two dimensional Hubbard model. It is shown that the d-pairing superconductivity is induced by spin fluctuations near the SDW boundary. The superconducting transition temperature ( T c ) is found to be remarkably suppressed by the renormalization through the electron self-energy, and to be sensitive to the band parameters due to nesting of the Fermi surface and the presence of the van Hove singularity as well as to the Fermi energy and the on-site interaction. As a consequence T c is enhanced by the next-nearest-neighbour hopping integral. The relation between the present result and experiments of high T c superconductors is discussed.