Superconducting properties of the attractive Hubbard model

TL;DR

This paper develops a self-consistent theoretical framework for understanding superconductivity in the attractive Hubbard model, revealing complex spectral features and the BCS to intermediate coupling crossover.

Contribution

It extends the T-matrix formalism to the superconducting state and numerically solves the equations, uncovering four-peak spectral functions and real-space bound states.

Findings

Spectral functions exhibit four peaks in the intermediate coupling regime.

Peak in self-energy linked to formation of real-space bound states.

Crossover from BCS to intermediate coupling analyzed via spectral densities.

Abstract

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.