Anisotropic superconductivity in the two-dimensional Hubbard model

We address the problem of anisotropic superconductivity in the two-dimensional Hubbard model. The Eliashberg equations have been generalized to the case which accounts for the anisotropy of the order parameter. Strong local correlations are treated within the mean field slave boson approximation. The superconducting transition temperatureT _c is evaluated as a function of the occupation number. Our results indicate that thed-wave state is the most likely channel for superconductivity for small concentration of holes. We have also derived an approximate analytical formula forT _c valid for any value of the occupation number. In addition, the influence of strong correlations on the electron-phonon coupling function is also discussed.     

Eliashberg equations with momentum-dependent Kernels for the two-dimensional Hubbard model

We discuss the impact of the strong electron-phonon interactions on the physical properties of correlated electrons in the two-dimensional Hubbard model. An easy access to the physical properties of the superconducting state is obtained by solving the Eliashberg equations with explicit momentum-dependent kernels. In order to facilitate the numerical procedure to solve these equations, correlations are treated within the Gutzwiller approximation (i.e., mean-field-slave boson approximation). Our results strongly support the view thatd-wave symmetry is the most important feature of the superconducting state in the copper oxides. A possible extension beyond the mean field approximation is also presented.Supported by the State Committee for Scientific Research, Grant No. 283021805.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U→∞ limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

D-Wave Superconductivity and Coulomb Correlations in the Two-Dimensional Hubbard Lattice

We considered anisotropic superconductivity within the two-dimensional Hubbard model extended by pairing correlations originating from the electron–phonon interaction. To discuss the onset of superconductivity close to the insulator–metal transition, we used the Hubbard I approximation to account for the formation of the insulating gap and see the role of Coulomb correlations for superconducting pairing. It has been shown that the Hubbard I approximation reflects effective pairing interactions genuine for correlated electron systems and leads to the stabilization of the superconductivity in the d-wave channel. One may expect the cooperation of phonon-free and phonon-induced mechanism in the formation of thed-wave superconducting state.     

Interlayer Tunneling in High-Temperature Superconductors Beyond the Mean-Field Approximation

The interlayer tunneling in high-temperature superconductors has been reconsidered beyond the mean-field approximation. The modification of the quasiparticle spectrum originating from the momentum-conserving interlayer transportation of Cooper pairs has been taken into account exactly. The pronounced reduction of the superconducting transition temperature when compared to the mean-field solution can be observed. Our self-consistent Green's functions approach allows for incorporation of Coulomb correlation and gives support for the mixed s- and d-wave scenario of high-temperature superconductivity.     

s-Wave vs.d -Wave Superconductivity in the Two-Dimensional Hubbard Model

The anisotropic superconductivity has been considered in the two-dimensional Hubbard model. We allow for on and off-site intralayer Cooper pairs. Interlayer momentum-conserving Josephson tunneling which couples adjacent layers has been taken into account. The meanfield solution for the superconducting transition temperature demonstrates the competition between local Coulomb repulsion and interlayer tunneling in thes-wave channel. This competition leads to the mixedsd superconducting state at low doping. We also demonstrate thatc-phonon-assisted transitions between intra and interlayer states can effectively give rise to momentum-conserving Josephson tunneling.     

Superconductivity Within the Pair-Tunneling Model Close to the Metal-Insulator Transition

We have considered the problem of s-wave and d-wave superconductivity in the two-layer Hubbard model close to the metal-insulator transition. To mimic the formation of the insulating gap, the Coulomb correlations have been taken into account within the Hubbard I approximation. The interlayer momentum-conserving Josephson tunneling between the layers has been included on the mean-field level. We demonstrate that the interlayer tunneling may contribute to the occurrence of mixed d + s wave symmetry of the superconducting state with a dominating d-wave component at a low concentration of holes. The problem of the validity of the pair-tunneling model is also briefly discussed.     

Phonon-Induced Superconductivity and the Staggered Magnetic Field on a Square Lattice

We have considered phonon-induced superconductivity on a square lattice. The antiferromagnetic correlations that are present in high-temperature superconductors (HTSC) have been simulated by the staggered magnetic field. The Eliashberg equations have been generalized to account for the momentum dependent order parameter, and the superconducting transition temperature T _c has been evaluated within the strong-coupling theory. The two-dimensional band structure has explicitly been taken into account. It occurs that the results obtained for T _c when considering d-wave symmetry of the superconducting state much better reflect the experimentally observed behavior than those derived for s-wave symmetry. The isotope shift exponent has also been evaluated. One can observe that the introduction of the staggered magnetic field leads to the decrease of this quantity. Therefore, the presence of the staggered magnetic field may contribute to experimentally observed values of smaller than the BCS value of 1/2     

Effect of disordered magnetic correlations in a layered high-temperature superconductor

Using the Eliashberg equations for superconductivity in a layered high-temperature superconductor and taking into consideration the phonon-mediated electron-electron interaction and the effect of the disordered magnetic correlations, we calculated the expressions for the critical temperature. The phonon and the magnetic kernels have a logarithmic divergence in the lowfrequency limit and the critical temperature differs from the McMillan form. The effect of various parameters on the decrease of the critical temperature has been analyzed. The renormalization functionZ _ph () contains a logarithmic dependence on.     

Some potential antenna applications of high-temperature superconductors

A review of possible applications of high-temperature superconductors (HTS) to antennas and antenna feed networks is presented. The frequency range of consideration is 1 MHz to 100 GHz. Three antenna application areas seem appropriate for HTS material. (1)Electrically small antennas and their matching networks: An increase in efficiency is possible for electrically short antennas, but at the expense of bandwidth. Substantial radiated power levels (on the order of kilowatts) can be handled by the best HTS material. Substantial improvement may be realized by making only the matching network of HTS material. (2)Feed and matching networks for compact arrays with enhanced directive gain (superdirective arrays): HTS material should permit such arrays to be fabricated that have high efficiency. (3)Feed networks for millimeter-wave arrays: Low-loss feed networks using HTS microstrip transmission lines give many decibels improvement in gain.     

T c and crystal structure distortions of high-temperature superconductors

The influence of orthorhombic distortions of CuO₂ layer onT _c is considered within the framework of kinematic mechanism. The dependence of the interaction constant on orthorhombicity is calculated. It is shown that orthorhombic distortions may result in the increase ofT _c by 10% in accordance with experiment.     

Magnetic properties of high-temperature superconductors: Analysis within the framework of the impurity mechanism

The impurity mechanism proposed earlier is used to interpret the magnetic properties of hightemperature superconductors. The appearance of superconductive granules and the existence of weak bonds in grains of ceramics and in single crystals is explained. The irreversibility line is obtained and its new interpretation as the line of thresholds of appearance of infinite nonsuperconductive cluster is given. The relaxation time of the magnetic susceptibility in alternating magnetic fields is calculated. The decrease of the Meissner fraction with increase in magnetic field and decrease in doping, and other magnetic properties are explained.     

Microwave surface impedance of YBa2Cu3O7?x:S-wave versusD-wave pairing

The low temperature behavior of the microwave surface resistanceR _s and the penetration provides information on the pairing state. Fully oxygenated films with low de-resistivity in the normal state exhibit an exponential temperature dependence corresponding to values of the energy gap up to 10 meV. For oxygen deficient films a linearR _s(T) was observed, similar to single crystals. This can be explained qualitatively by induced superconductivity in the copper-oxygen chains.     

Flux-creep activation energies at the grain boundaries of Y-Ba-Cu-O superconductors in the characteristic frequency band

Measurements on the temperature and frequency dependence of the complex ac susceptibility of sintered Y_1.01Ba_1.95Cu_2.97O _x are reported. The data are used to obtain the flux-creep activation energies at the grain boundaries in the characteristic frequency band. The found nonlinear frequency dependence of these energies can be approximated differently in the low, characteristic, and high frequency bands. The relaxation frequency of thermal fluctuation of the vortex lattice (2 3×10⁴ Hz) and the surface current density (J _s=0–10 A/cm²) have been estimated.     

Local lattice instability and ionic transport in high-temperature superconductors

Ionic transport, a characteristic feature of superionic conductors, is analyzed microscopically for the RBa₂Cu₃O{7-Σ} (R = rare earth) high-temperature superconductors. The electronic correlation effects are considered to be responsible for the formation of a local double-well potential for apical oxygen, which in its turn results in a decrease of the activation energy for interstitial chain oxygen defects. The behavior of the double well upon reduction of the oxygen content is discussed and its possible manifestation in the low-frequency dynamical response is considered.     

Orbital-dependent effects of electron correlations in microscopic models for iron-based superconductors

The bad metal behavior in the normal state of the iron-based superconductors suggests an intimate connection between the superconductivity and a proximity to a Mott transition. At the same time, there is strong evidence for the multiorbital nature of the electronic excitations. It is then important to understand the orbital-dependent effects of electron correlations. In this paper we review the recent theoretical progresses on the metal-to-insulator transition in multiorbital models for the iron-based superconductors. These include studies of models that contain at least the 3d xy and 3d xz/yz models, using a slave-spin technique. For commensurate filling corresponding to that of the parent iron pnictides and chalcogenideds, a Mott transition generally exists in all these models. Near the Mott transition, a strongly correlated metal exhibiting bad metal features and strong orbital selectivity is stabilized due to the interplay of Hund’s coupling and orbital-degeneracy breaking. Particularly for the alkaline iron selenides, the ordered vacancies effectively reduce the kinetic energy, thereby pushing the system further into the Mott-insulating regime; in the metallic state, there exists an orbital-selective Mott phase in which the iron 3d xy orbital is Mott localized while the other 3d orbitals are still itinerant. An overall phase diagram for the alkaline iron selenides has been proposed, in which the orbital-selective Mott phase connects between the superconducting phase and the Mott-insulating parent state.     

Stripe correlations of spins and holes in cuprate superconductors

It is argued that the stripe order of spins and holes found in La_2–x Sr _x NiO₄+ is a useful model for spin and charge correlations in La_2–x Sr _x CuO₄. A direct connection with the cuprates is now established by neutron diffraction evidence for stripe order in La_1.6–x Nd_0.4Sr _x CuO₄ withx=0.12. The experimental work has stimulated new theoretical ideas.It is a pleasure to acknowledge my collaborators, especially J. D. Axe, D. J. Buttrey, N. Ichikawa, J. E. Lorenzo, Y. Nakamura, V. Sachan, B. J. Sternlieb, P. Wochner, and S. Uchida. Work at Brookhaven is supported by the Division of Materials Sciences, U.S. Department of Energy, under Contrast No. DE-AC02-76CH00016.     

Normal state of short coherence length superconductors: Qualitative differences between spin and charge correlations

The temperature scaleT* at which the amplitude of the order parameter is formed is in general much higher than theT _c at which phase coherence is established in short coherence length superconductors. Using quantum Monte Carlo simulations for the attractive Hubbard model we show that for a degenerate 2D system the spin and charge responses show qualitatively different behavior in the normal state in the temperature rangeT _c <T<T*. We find that _s is stronglyT-dependent whiledn/d is independent ofT. A pseudo-gap develops in the one-particle density of states and leads to anomalous behavior of the NMR relaxation rate 1/T ₁ T _s (T) characteristic of spin gap behavior in the high-T _c materials.     

Self-Consistent Calculation of the Self-Trapping Barrier for a Hole in the CuO2 Plane

We study the behavior of an extra hole added to the ground state of the antiferromagnetically ordered CuO₂ plane. Both the Cu--O hybridization and the O--O transfer are taken into account. As has been shown previously (V. Hizhnyakov and E. Sigmund, Physica C 156, 655 [1988]), the energetically most favorable situation is given when a localized state is formed in which the antiferromagnetic order is locally destroyed and a small ferromagnetic cluster is built up. We show that due to the increase of the magnetic energy induced by the spin–flip process (E _s0.15 eV), the localized and the metastable free-hole states are separated by a barrier of energy (E _b0.05 eV), which can reveal itself in various kinetic phenomena.