Pair fluctuation effects above $T_{\rm c}$

TL;DR

This paper investigates pairing phenomena above the critical temperature in a 2D attractive Hubbard model, revealing significant pair effects and altered electronic properties that challenge the traditional BCS framework.

Contribution

It demonstrates the presence of pairing effects above $T_c$ using a self-consistent $T$-matrix approach, highlighting deviations from BCS theory in the 2D Hubbard model.

Findings

10% change in $n(k)$ distribution above $k_F$

$ heta$-like behavior of phase shift at large $k$

Fermi surface not well-defined at given interaction

Abstract

We explore the occurrence of pairing effects above $T_{\rm c}$ in the 2D attractive Hubbard model. The presence of pairs above $T_{\rm c}$ goes beyond the BCS approximation, in which pair formation and condensation occur at the same temperature. Using the fully self-conserving $T$-matrix formalism, which is valid above $T_{\rm c}$, we find that (1) the distribution function, $n(k)$, shows a 10\% change of the weight from ``below'' to ``above'' $k_{\rm F}$ with respect to the free case, and (2) the phase shift, $\delta\phi(\omega,k)$, shows $\Theta$-like behavior as a function of $\omega$ for large momentum $k$ along the diagonal of the Brillouin zone. Our calculations have been carried out for an interaction of $U/t = - 4.0$ and a temperature of $T/t = 0.125$, where $t$ is the hopping matrix element between nearest neighbors. We conclude that for such an interaction value the Fermi surface is not a well-defined quantity.