Correlation between the Hall coefficient,penetration depth,transition temperature,gap anisotropy and hole concentration in layered high-temperature superconductors

We explore the correlation between the Hall coefficient, penetration depth, transition temperature, gap anisotropy and hole concentration in a tight binding model for layered high-temperature superconductors. By adopting the BCS strategy, nearest neighbor intralayer singlet and extendeds-wave pairing cut off at the hole Fermi energy, remarkable agreement with generic experimental facts is obtained. Thus, a cylindrical hole Fermi surface and intralayer extendeds-wave singlet pairing appear to be generic features of the cuprate semiconductors. For high doping levels, however, intralayerd-wave singlet pairing appears to be the stable phase.     

Pairing symmetry in layered BiS2 compounds driven by electron-electron correlation

We investigate the pairing symmetry of layered BiS2 compomlds by assuming that electron-electron correlation is still important so that the pairing is rather short range. We lind that the extended .s-wave pairing symmetry always wins over d-wave when the pairing is confined between two short range sites up to next nearest neighbors. The pairing strength is peaked around the doping level ：r = 0.5. which is consistent with experimental observation. The extended s-wave pairing symmetry is very robust against spin orbital coupling because it is mainly determined by the structure of Fermi surfaces, Moreover. the extended s-wave pafiring can be distinguished from conventional swave pairing by measuring and comparing superconducting gaps of different Fermi surfaces.     

Superconducting instability in the large-U limit of the two-dimensional Hubbard model

We have investigated numerically the pairing instabilities of Gutzwiller wavefunctions. These are equivalent to a certain form of the resonant valence bond wavefunction. The case considered is a nearly half-filled two dimensional band with interactions given by a Hubbard model with large on-site Coulomb interactions. We find that the paramagnetic normal state is unstable tod-wave pairing but stable againsts-wave pairing. The antiferromagnetic state is marginally stable against both types of pairing. These results can be explained as an interference effect resulting in enhanced antiferromagnetic spin correlation in the paired state.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T _c mediated by the antiferromagnetic exchange and spin fluctuations.     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

Electron-doping versus hole-doping in the 2D t-t' Hubbard model

We compare the one-loop renormalization group flow to strong coupling of the electronic interactions in the two-dimensional t-t'-Hubbard model with t' = - 0.3t for band fillings smaller and larger than half-filling. Using a numerical N-patch scheme ( N = 32, ..., 96) we show that in the electron-doped case with decreasing electron density there is a rapid transition from a d _{x2 - y2}-wave superconducting regime with small characteristic energy scale to an approximate nesting regime with strong antiferromagnetic tendencies and higher energy scales. This contrasts with the hole-doped side discussed recently which exhibits a broad parameter region where the renormalization group flow suggests a truncation of the Fermi surface at the saddle points. We compare the quasiparticle scattering rates obtained from the renormalization group calculation which further emphasize the differences between the two cases. Received 19 December 2000 and Received in final form 28 February 2001     

Theoretical investigation of the superconducting gaps in the Fe-based superconductors

Based on an antiferromagnetic (AFM) spin fluctuation approximation, we study the superconducting gaps in Fe-based compound using two-band model. We find that our results are consistent with the previous work that concludes sign-reversal extended s-wave pairings between different Fermi surface sheets. The different superconducting gap magnitude around different Fermi surface sheets is probably due to the different density of states on them. This calculation can give insight to the recent angle-resolved photoemission (ARPES) experiments on these materials. To detect the phase variation of the superconducting gap over the Fermi surfaces, we propose a new method for measuring the particular wave vector phonon linewidth. In the case of the sign-reversal superconducting pairing, the linewidth shows continuities compared to the case of no phase variation.     

Extended -wave superconductivity. Flat nodes in the gap and the low-temperature asymptotic properties of high- superconductors

Remarkable anisotropic structures have been recently observed in the order parameter of the underdoped superconductor Bi₂Sr₂CaCu₂O . Such findings are strongly suggestive of deviations from a simple d _{x2 - y2} -wave picture of high- superconductivity, i.e. . In particular, flatter nodes in are observed along the directions in -space, than within this simple model for a d-wave gap. We argue that nonlinear corrections in the -dependence of near the nodes introduce new energy scales, which would lead to deviations in the predicted power-law asymptotic behaviour of several measurable quantities, at low or intermediate temperatures. We evaluate such deviations, either analytically or numerically, within the interlayer pair-tunneling model, and within yet another phenomenological model for a d-wave order parameter. We find that such deviations are expected to be of different sign in the two cases. Moreover, the doping dependence of the flatness of the gap near the nodes is also attributable to Fermi surface effects, in addition to possible screening effects modifying the in-plane pairing kernel, as recently proposed. Received 19 November 1999     

d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model

We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.     

The competition and coexistence of antiferromagnetism and <Emphasis Type="Italic">d</Emphasis>-wave superconductivity: probing coupled thermal fluctuations in a two dimensional minimal model

We consider the coexistence of antiferromagnetism and d-wave superconductivity, motivated by what one observes in the quasi-two dimensional organic salts. We study an electronic model that approximates some features of the Hubbard model, e.g., a repulsion that promotes local moments and Neel order, and an attractive intersite density–density coupling that promotes d-wave superconductivity. Staying at half-filling and a fixed attractive interaction we probe the effect of varying repulsion, using mean field theory for the ground state but retaining the full O(3) × U(1) spectrum of classical fluctuations at finite temperature. The ground state is superconducting at weak repulsion, a Neel ordered insulator at large repulsion, and a coexistence of the two orders in the intermediate regime. We observe four distinct kinds of thermal behaviour depending on the strength of repulsion. Starting with weak repulsion these are, first, a d-wave superconductor renormalised by magnetic fluctuations, second, a d-wave state transiting to an antiferromagnetic insulator and then to the normal state, third, a coexistent state transiting to the antiferromagnetic insulator and then the normal state, and, fourth, a Neel ordered insulator with weak pairing fluctuations. The low temperature state is either “nodal” or gapped, due to long range order, and the low energy spectral weight generally increases monotonically with temperature. At intermediate repulsion, however, the transition from the d-wave state to Neel antiferromagnet causes a loss of low energy weight which is gradually regained only at high temperature.     

Evidence for d-wave superconductivity in the repulsive Hubbard model

We perform numerical simulations of the Hubbard model using the projector Quantum Monte Carlo method. A novel approach for finite size scaling is discussed. We obtain evidence in favor of d-wave superconductivity in the repulsive Hubbard model. For U=4, is roughly estimated as K. Received 8 September 1998     

What is the highest Tc for phonon-mediated superconductivity?

We suggest that the high-temperature superconductivity can be attributed to the director-roles of the van Hove singularity between an electron-electron interaction and an electron-phonon interaction. The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed. In particular, the non-s-wave symmetry is predicted to have the highest T _c for superconductors.      

D-wave pairing in the two-dimensional Hubbard model with low filling

It is shown that the two-dimensional electron system of low-density, when described by the Hubbard model, is unstable towards superconductive transition in thed-wave pairing state.     

Effect of next-nearest-neighbour interaction on dx2?y2-wave superconducting phase in 2D t-J model

An exact diagonalization calculation of the t-J model on 2D square cluster has been studied for the ground state properties of HTSC. Effect of next-nearest-neighbour hopping and magnetic (both antiferromagnetic and ferromagnetic) interaction on d _x ²−y ²-wave pairing has been shown. Relative strength of the next-nearest-neighbour interaction with respect to that of near-neighbour interaction for the strongest d _x ²−y ²-wave pairing has been estimated. A schematic phase diagram is shown. It is shown that a two-sublattice model with antiferromagnetic interaction between them and a small intra-ferromagnetictype interaction in one sublattice favours d _x ²−y ²-wave superconductivity and moderate negative type NNN hopping adds flavours to this phase.     

Physical quantities for two coupled Hubbard planes and comparison with experiments on Bilayer high-Tc cuprates

For a bilayer model of the high-T_c cuprates consisting of two coupled Hubbard planes we calculate within the FLEX (fluctuation exchange) approximation the quasiparticle self-energies and dynamic spin susceptibilities. We consider a Fermi surface similar to those of the YBaCuO cuprates, an on-site Coulomb repulsion U = 6 t (where t is the intraplane hopping), and interplane hoppings t’ up to t’ = 0.7 t. For sufficiently large t'(?0.3 t) the spin susceptibility gC^? due to transitions between the bonding and antibonding states becomes much larger than the susceptibility gC⁺ for transitions within the same band. The spectral density Im gC^?(q, ω) exhibits a peak centered at the antiferromagnetic wavevector q = Q = (π, π) and at the antiparamagnon frequency ω = ω_sf. For decreasing temperature T and increasing t’ the peak becomes more and more pronounced. We calculate the Fermi lines of the bonding and antibonding bands for different t'. The superconducting transition temperature T_c for d_x ²?y²-wave pairing decreases as t' increases. Our results are in qualitative agreement with magnetic neutron scattering, magnetic resonance, and photoemission experiments on bilayer YBaCuO cuprates. They are also consistent with the results of quantum Monte Carlo simulations.     

Thermodynamics and optical conductivity of unconventional spin density waves

We consider the possibility of formation of an unconventional spin density wave (USDW) in quasi-one-dimensional electronic systems. In analogy with unconventional superconductivity, we develop a mean field theory of SDW allowing for the momentum dependent gap Δ() on the Fermi surface. Conditions for the appearance of such a low temperature phase are investigated. The excitation spectrum and basic thermodynamic properties of the model are found to be very similar to those of d-wave superconductors in spite of the different topology of their Fermi surfaces. Several correlation functions are calculated, and the frequency dependent conductivity is evaluated for various gap functions. The latter is found to reflect the maximum gap value, however with no sharp onset for absorbtion. Received 19 February 2001