We present a Fermi liquid model for the overdoped and optimally doped cuprate superconductors. For the normal state, we provide an analytic demonstration, backed by self-consistent Baym-Kadanoff (BK) numerical calculations, of the linear in temperature resistivity and linear in 1/energy optical conductivity, provided the interacting Fermi liquid has strong peaks in its density of states (van-Hove singularities in 2 dimensions) near the chemical potential µ. Recent ARPES expts. by Valla et al., Science 285, 2110, and e-print cond-mat/0003407, directly support the linearity of the one-particle scattering rate everywhere in the Brillouin zone hereto obtained. We show that the origin of this linearity is the linear in energy term of the imaginary part of the carrier susceptibility. Moreover, we verify that the interactions tend to pin the van-Hove singularities close to µ. We show that the low energy dependence of the susceptibility can have a purely fermionic origin. We introduce an ansatz for the susceptibility of the carriers, which we postulate to be enhanced in an additive manner due to the weak antiferromagnetic order of the CuO2 planes. Inter alia, this ansatz may explain the appearance of the spin resonance peak (observed in neutron scattering) in the normal state of the cuprates. Further, we obtain particularly high transition temperatures Tc from our BK-Eliashberg scheme by using this ansatz: we have a d x 2 −y 2 gap with Tc > 120 o K for nearest neighbour hopping t = 250meV .

Based on an unconventional Fermi liquid model, we present several results on the optimally doped and overdoped cuprate superconductors. For the normal state, we provide an analytic demonstration, backed by self-consistent Baym-Kadanoff (BK) numerical calculations, of the linear in T resistivity and linear in 1/ǫ optical conductivity, provided the interacting Fermi liquid has strong peaks in its density of states (van-Hove singularities in 2 dimensions) near the chemical potential µ. Moreover, we find that the interactions tend to pin these strong density of states peaks close to µ. We show that the low energy dependence of χMMP has a fermionic origin. We obtain particularly high transition temperatures Tc from our BK-Eliashberg scheme by introducing an ansatz for the fermionic susceptibility of the carriers. We postulate that the latter is enhanced in an additive manner due to the weak antiferromagnetic order of the CuO2 planes. We have obtained a d x 2 −y 2 gap with Tc > 120 o K for n.n. hopping t = 250meV .The nature of the many-body state of the cuprate superconductors is a core question for the understanding of these materials [1][2][3]. In this Letter, we show that a minimum unconventional Fermi liquid model accounts in a natural, comprehensive and internally consistent manner for several normal state characteristics. The introduction of an ansatz for the susceptibility of the carriers further allows us to obtain particularly high transition temperatures T c .Our starting point is the 2-dimensional Hamiltonianc † k,σ is an electron creation operator andA o is the strength of a contact Coulomb interaction, and U o the strength of a paramagnon interaction. A small negative A o would mimic an isotropic phononic interaction.We have developed a self-consistent many-body treatment of the above Hamiltonian. We write a set of diagrams within the frame of a Baym-Kadanoff conserving approximation [4], summing bubble and ladder diagrams [5]. There is a free energy functional Φ[G] of the Green's function G, such that the self-energy Σ is given by the relation Σ = δΦ[G]/δG. We thus obtain a set of self-consistent equations for G(k, ǫ n ) and Σ(k, ǫ n ) :µ is the chemical potential and the Matsubara frequencies are ǫ n = (2n + 1)πT and ω m = 2mπT for fermions and bosons, respectively. This system of equations is solved numerically, similarly to e.g. [6][7][8][9][10][11][12]. We work with a given number M of Matsubara frequencies and a N ×N discretization of the Brillouin zone (M = 256−480 and N ≥ 64). The potential. V ex (q, ω m ) includes vertex corrections due to the internal dressing of bubbles with A o . Our potential is an extension of the fluctuation-exchange (FLEX) approximation of Bickers, Scalapino and White [6], as can easily be seen by taking. All the convolution operations are done by using the Fast Fourier Transform (FFT), in order to cut down calculation time. We use Padé approximants [13] to analytically continue our results to the real frequency axis.The numerical solution of the many-body system yields a...

We calculate the quasiparticle scattering rate in the superconducting state of the overdoped cuprates, in the context of the Eliashberg formalism for a Fermi liquid with strong van Hove singularities close to the chemical potential. For a d x 2 −y 2 superconducting gap, we demonstrate analytically that the scattering rate is linear in the maximum of temperature or energy, but with different intercepts and momentum dependence, thus extending our earlier results on the normal state. We discuss our results in view of angle-resolved photoemission experiments. We also comment on the case of a s-wave gap.The nature of the carriers in the cuprates is an important question, which has been discussed and debated extensively. The availability of relevant experimental data over the years, and in particular angle-resolved photoemission (ARPES), should be helpful in the effort towards achieving a better understanding of this question.Here, we look at a characteristic one-particle property, relevant to ARPES. We obtain analytically the scattering rate in the superconducting state for a Fermi liquid with strong density of states peaks -van-Hove singularities (vHs) in 2-D -located close to the chemical potential µ. Incidentally, this model does not apply to the underdoped cuprates, as there is no indication that a Fermi liquid description is appropriate. The qualitative nature of our results does not depend on the doping level, for as long as we remain within the realm of Fermi liquid theory. Precise numerical calculations can yield the quantitative dependence of the theory on the doping etc. A review of related work in the frame of the so-called van-Hove scenario has been given in 1 . The pinning of the vHs close to µ seems to be a plausible explanation for the common characteristics of a good many cuprates, whose van-Hove singularities are located between 10-30 meV below the Fermi surface 2 , as ARPES experiments have shown. A review of some calculations yielding the pinning of the vHs close to µ appears in 3 . The present work extends our results for the normal state, obtained in 3,4 , to the superconducting state. The analysis presented below can also be done in the frame of a weak-coupling BCS-type approach. We opt for the intermediate to strong-coupling Eliashberg approach, which is relevant for the cuprates. Qualitatively, i.e. as far as power laws etc. are concerned in terms of energy and temperature, the answers are the same for the two approaches.We consider a generic dispersion appropriate for the cuprates, of the type t, t ′ , t ′′

We calculate analytically the low temperature quasi-particle scattering rate, the conductivity, and the specific heat in weakly disordered metals close to a quantum critical point, via the use of a proper fluctuation potential V (q, ω) between the quasi-particles. We obtain typical Fermi liquid results proportional to T 2 and T respectively, with prefactors which diverge as power laws of the control parameter a upon approaching the critical point. The Kadowaki-Woods ratio is shown to be independent of a (possibly times a logarithmic dependence on a) only for the case of threedimensional ferromagnetic fluctuations. Our results are consistent with experiments on the eight materials CeCoIn5,

We treat the question of the low temperature behavior of the dephasing rate of the electrons in the presence of elastic spin disorder scattering and interactions. In the frame of a self-consistent diagrammatic treatment, we obtain saturation of the dephasing rate in the limit of low temperature for magnetic scattering, in agreement with the non-interacting case. The magnitude of the dephasing rate is set by the strength of the magnetic scattering rate. We discuss the agreement of our results with relevant experiments.An important quantity in disordered electronic systems is the dephasing rate τ −1 φ . It provides a measure of the loss of coherence of the carriers, but in the two-particle channel -c.f. eq. (1) below. Decoherence arises from coulombic interactions, scattering by phonons, magnetic fluctuations etc. The saturation of the dephasing rate at low temperature T seen in numerous experiments 1-13 has attracted a vigorous interest, especially given the longstanding theoretical prediction for a vanishing τ −1 φ as the temperature T → 0. 14-21 . Previous theoretical studies 14-25 have focused on the calculation of τ −1 φ in the absence of spin-scattering disorder. The majority of these studies predict, correctly, a vanishing τ −1 φ (T → 0) . Here we determine and calculate the factors which contribute to dephasing in the presence of spin-scattering disorder. The saturation obtained allows for the consistent elucidation of this puzzle.In the presence of spin-less disorder, the cooperon (particle-particle diffusion correlator -c.f. fig. 1) is given byD is the diffusion coefficient, N F is the density of states at the Fermi level and τ −1 the total impurity scattering rate. We work in the diffusive regime ǫ F τ > 1 (h = 1), ǫ F being the Fermi energy. With spin-disorder present, the cooperon becomes spin-dependent. The relevant terms C i are shown in fig. 1. We start by giving the explicit form of these C o 0,1,2 without a dephasing rate. C o 0 acquires a finite spin-dependent term in the denominator, which is crucial for the determination of the dephasing rate -c.f. below.For the case , τ −1 S > 0, τ −1 so = 0 -with τ −1 S the magnetic impurity scattering rate and τ −1 so the spin-orbit impurity scattering rate -the cooperons are given byBased on eqs. (2), we expect a saturation of the dephasing rate. The simple diffusion pole is "cut-off" by the constant terms proportional to τ −1 S . On symmetry grounds, the spin-conserving Coulomb interaction cannot eliminate these terms.We emphasize that the impurity scattering considered is elastic, bulk-type. Interfacial impurity scattering, though similar to bulk-type, is expected to differ in detail.To calculate the dephasing rate, we write down and solve the appropriate coupled equations for all three renormalized cooperons C i (q, ω), i = 0, 1, 2. We note that usually the terms containing the factors d i and h i below are completely omitted. The equations are shown schematically in fig. 2:

We study superconductivity in multilayer copper oxides, in the frame of a realistic microscopic formulation. Solving the full temperature dependent BCS gap equations, we obtain a maximum in the transition temperature Tc for M=3 or 4 CuO2 layers in the unit cell for appropriate values of the interlayer tunneling (negative pair tunneling), and via the consideration of the doping imbalance between the inner and outer layers. This is the ubiquitous experimental result for Ca intercalated copper oxides, as opposed to other intercalating elements. Further, using a restricted set of parameters, we obtain an exact fit of Tc(M=1-4) for five different Ca intercalated homologuous copper oxide families.

At low temperature and for finite spin scattering in a weakly disordered metal, for a certain value, predicted from our theory, of the material-dependent paramagnon interaction, the total conductivity becomes highly sensitive to the orbital effects of a finite magnetic field. As a consequence, positive giant magnetoresistance and giant corrections to the Hall coefficient arise. We obtain very good agreement between this theory and recent positive giant magnetoresistance experiments, while making specific material-dependent predictions.Recently, there has been a plethora of both experimental and theoretical investigations of giant magnetoresistance (GMR) in metallic systems [1]. In most cases experimentally observed so far, increasing the magnetic field H from zero causes the resistance to decrease to a fraction of its zero field value. This behavior persists for temperatures ranging from zero to well above room temperature. However, in the experiment of Tsui, Uher and Flynn[2] the observed GMR differs drastically from the usually observed GMR in four ways. 1) The effect only exists at low temperature T , with the magnetoresistance correction reaching ∼ 35% of the zero field value for H ∼ 6T, but vanishing completely above 60 o K for H ≤ 6T. 2) GMR is anisotropic with regards to the direction of the field H, 3) it is not connected to the magnetization and does not saturate with increasing H, for fields as big as at least 8T, and 4) it is positive, i.e. it increases with H. Save for the giant magnitude of the effect, the four characteristics above can be explained in the frame of the metallic weakly disordered regime ǫ F τ ≫ 1, where ǫ F is the Fermi energy and τ the elastic scattering time arising from disorder [3,4]. In this regime, the conductivity corrections, due to disorder induced diffusion and to electron-electron interactions, are of order σ o /(ǫ F τ ) r , where σ o is the Drude term and r = 1, 2 for d = 2, 3 space dimensions.We thereby propose a novel mechanism for giant corrections to the transport quantities, including GMR, due to the presence of paramagnons in a weakly disordered metal. At low temperature and for finite impurity spin scattering, for a certain value, predicted from our theory, of the material-dependent paramagnon interaction, the total conductivity becomes highly sensitive to the orbital effects [3] of a finite magnetic field. This is attributed to certain microscopic processes, otherwise negligibly small, which can be enhanced by a resonance factor, emanating from the spin-density channel. Thus an experimental signature like the one observed by Tsui et al.[2] is obtained. As we explain below, the samples used in ref.[2] contain the ingredients necessary for the appearance of GMR, in accordance with our theory.We begin by considering a constant paramagnon interaction A o acting only between particles of opposite spin and given bywhere Φ is dimensionless and positive, and N F is the density of states at the Fermi level.In the presence of weak disorder, which includes spin scatt...

In a previous report, we introduced a new fermionic variational wavefunction, suitable for interacting multi-species systems and sustaining superfluidity. This wavefunction contains a new quantum index. Here we introduce a spin triplet version of this wavefunction, with parallel spin pairs only. We also present a single fermion species wavefunction, which may be relevant for the problem of the BCS to BEC transition.