Pairing and Superconductivity from weak to strong coupling in the Attractive Hubbard model

TL;DR

This paper investigates the finite-temperature phase diagram of the attractive Hubbard model using Dynamical Mean Field Theory, revealing a first-order pairing transition, a crossover to a pseudogap phase, and the relation between superconducting and pairing instabilities.

Contribution

It provides a detailed analysis of the normal and superconducting phases, identifying the nature of the pairing transition and the pseudogap crossover in the attractive Hubbard model.

Findings

First-order pairing transition between metallic and paired phases.

Superconducting transition occurs before the pairing transition in the normal phase.

Identification of pseudogap region via observables like spin susceptibility and spectral function.

Abstract

The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the Dynamical Mean Field Theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this case we obtain a first-order pairing transition between a metallic phase and a paired phase formed by strongly coupled incoherent pairs. The transition line ends in a finite temperature critical point, but a crossover between two qualitatively different solutions still occurs at higher temperature. Comparing the superconducting and the normal phase solutions, we find that the superconducting instability always occurs before the pairing transition in the normal phase takes place, i.e., $T_c > T_{pairing}$. Nevertheless, the high-temperature phase diagram at $T > T_c$ is still characterized by a crossover from a metallic phase to a preformed pair phase. We characterize this crossover by computing different observables that can be used to identify the pseudogap region, like the spin susceptibility, the specific heat and the single-particle spectral function.