An unconventional Fermi liquid model for the optimally doped and overdoped cuprate superconductors

Abstract

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...

Quasiparticle scattering rate in overdoped superconducting cuprates

“…Our treatment shows that ω B here is nothing else but the fermionic energy w k−qo ,ǫ . The results here complement our earlier normal state results in 3,4 . ARPES experiments 10,11 have indicated that in the superconducting state, and, presumably, for ǫ → 0, the scattering rate is linear in T for k F close to the nodal directions, but otherwise saturates to a value which increases as k F approaches the vH points.…”

“…The normal state result was obtained in 3,4 . Summarizing, within the Fermi liquid Eliashberg formalism, we calculate the one-particle scattering rate in the superconducting state of overdoped cuprates.…”

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

“…From a theoretical point of view the linear-T dependence is not unexpected because already the bare two-loop diagram with unrenormalized couplings yields this behavior if the band filling is sufficiently close to the van Hove filling [20,21]. Hence it should be considered as an effect of the van Hove singularities and does not immediately imply a breakdown of the quasiparticle concept.…”

“…The lower plots are for µ = 0.04t, which is further away from half-filling. The dashed lines in the left plots show the flow of Cooper couplings at the FS, the solid lines umklapp processes in the BZ diagonal VΛ(4,4,21), VΛ(3,4,21), and VΛ(5,4,21). The dashed-dotted lines denote Cooper processes between the saddle point regions with band energies below the FS (discussed in the text).…”

Non-Fermi-liquid scattering rates and anomalous band dispersion in ferropnictides

“…[6,7]. On the other hand, there are various models to explain the strange normal state properties of unconventional superconductors, e.g., for cuprates on the basis of a van Hove scenario [8][9][10].…”