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,