The Attractive Hubbard Model in 2D: Is it capable of describing a pseudogap and preformed pairs?

TL;DR

This study investigates whether the 2D attractive Hubbard model can explain pseudogap phenomena and preformed pairs in cuprate superconductors by analyzing self-consistent calculations of pair lifetimes and scattering rates.

Contribution

It demonstrates that self-consistent calculations of the 2D attractive Hubbard model can reproduce key features of pseudogap physics, including finite pair lifetimes and linear temperature-dependent scattering rates.

Findings

Finite pair lifetimes due to pair interactions

Linear temperature dependence of quasiparticle scattering rate

Suppression of Bose-condensation instability in self-consistent approach

Abstract

Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences seem to be related to pre-transitional features appearing at temperatures above T$_c$. The observation of a pseudogap, e.g. in ARPES experiments, is a familiar example of this physics. One potential explanation for this behaviour involves preformed pairs with finite lifetimes existing in the normal state above T$_c$. In this way two characteristic temperatures can be established. A higher one T$^*$ at which pairs begin to form and the actual T$_c$ at which a phase-coherent superconducting phase is established. In order to test these ideas we have investigated the negative U Hubbard model in two dimensions in the fully self-consistent ladder approximation at low electron densities. In the non self-consistent version of this theory the system always shows an instability towards Bose-condensation of infinite lifetime pairs. In contrast to this, pairs obtain a finite lifetime due to pair-pair interaction and the sharp two-particle bound state is strongly lifetime broadened when self-consistency is applied. A quasi-particle scattering rate which varies linearly with temperature is also found. The fully self-consistent calculation we were able to perform using a ${\bf {\vec k}}$--averaged approximation in which the self-energy loses its ${\bf {\vec k}}$-dispersion due to a ${\bf {\vec k}}$-average. This approximation is found to preserve the essential physics.