Quasiparticle lifetime behaviour in a simplified self-consistent T-matrix treatment of the attractive Hubbard model in 2D

Abstract

The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly with the inverse temperature, consistent with experiment. Keywords: attractive Hubbard model; quasiparticle propertiesNumerous recent experiments (e.g., neutrons, ARPES, optical, NMR) have shown that in the high T c cuprate superconductors a so-called pseudogap is present [1]. This has led to proposals that electron pairs form at temperatures well above the superconducting transition temperature. However, possibly due to phase fluctuations, a macroscopic phase coherent wave function is not formed, so superconductivity is not encountered [2].This physics motivates our study of the attractive Hubbard model. The Hamiltonian for this system iswhere the lattice sites of a 2-D square lattice are labeled by {i}, the lattice fermion operators are denoted by c i,σ , and neighbouring sites are represented by ij . For any nonzero | U |, two-particle bound states appear, and are physically related to a pair of electrons lowering the system's energy when they exist on the same lattice site. This is certainly the simplest example of a model Hamiltonian which allows for one to study the interactions between such electron pairs. Further, using a Gorkov derivation of the Ginzburg-Landau equations for an s-wave superconductor, one can show that for the values of | U | /W that we are considering, W = 8t being the (noninteracting) bandwidth, this model also reproduces the short coherence lengths of the Cooper pairs found in the high T c cuprate superconductors [3].We employ the Brueckner Hartree-Fock theory to solve the Bethe-Salpeter equation for the 2D attractive Hubbard model in the ladder approximation [4], reliable for this model at low electron (or hole) densities. This affords us the opportunity to investigate the influence of preformed pairs with arbitrary lifetimes on the normal state properties. Haussmann has argued [5] that when one solves this model in this approximation self consistently, one will include pair-pair interactions. These interactions will be, in first order, of a repulsive nature between different pairs.

Unconventional temperature dependence of the cuprate excitation spectrum

“…More recently, Pieri et al [14] considered pair fluctuations in the t-matrix framework, but again no dip in the zero temperature spectra was clearly demonstrated. In a related paper involving pair fluctuations [15], a repulsive p-1 arXiv:1607.00851v1 [cond-mat.supr-con] 4 Jul 2016 pair-pair interaction was inferred, like in our model, but an explicit calculation of the density of states was not reported. To the contrary, our model gives for the first time the low-temperature peak-dip-hump feature and the full temperature dependence of the QP spectra up to T * .…”

Universal spectral signatures in pnictides and cuprates: the role of quasiparticle-pair coupling

“…The small coherence length, ξ pair ∼ a few nanometers, and poor charge screening are typical properties of high-T c and pseudogap phenomena. Many authors have considered non-Fermi liquid behavior of the 'normal' state in such correlated systems [63][64][65][66][67][68][69][70][71][72][73][74][75]. However, the direct observation [56,78,79] using angle-resolved photoemission (ARPES) of the collapsing Fermi surface into Fermi arcs in the nodal-direction is strong evidence in favor of the precursor-pairing scenario.…”