A Fermi liquid model for the overdoped and optimally doped cuprate superconductors: scattering rate, susceptibility, spin resonance peak and superconducting transition

Abstract

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 .

Observation of non-Fermi liquid behavior in hole-dopedLiFe1−xVxAs

“…The observation of a NFL behavior without quantum critical point in both Co-doped and V-doped LiFeAs is consistent with a recent theoretical study emphasizing on the impact of nesting on the temperature evolution of the electrical conductivity [24]. We caution though that the linear resistivity in the cuprates was previously derived in the context of a FL with a large density-of-states (like a van Hove singularity) near E F [25,26], a condition that also applies to Fe-based superconductors near good nesting conditions. As shown in Fig.…”

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.…”

“…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.…”

“…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.…”