Comment on ``BCS to Bose-Einstein crossover phase diagram at zero temperature for a d_{x^2-y^2} order parameter superconductor: Dependence on the tight-binding structure''

TL;DR

This paper challenges previous claims by showing that in a 2D attractive Hubbard model with d-wave pairing, a non-pairing region does not exist, and the gap remains finite for all non-zero densities and couplings.

Contribution

It provides analytical and numerical evidence that contradicts earlier work, demonstrating continuous pairing without non-pairing regions in the phase diagram.

Findings

No non-pairing region in the phase diagram.

Finite gap at T=0 for all non-zero densities and couplings.

Contradicts previous claims of a non-pairing region.

Abstract

The work by Soares et al. [Phys. Rev. B 65, 174506 (2002)] investigates the BCS-BE crossover for d-wave pairing in the 2-dimensional attractive Hubbard model. Contrary to their claims, we found that a non-pairing region does not exist in the density vs coupling phase diagram. The gap parameter at T=0, as obtained by solving analytically as well as numerically the BCS equations, is in fact finite for any non-zero density and coupling, even in the weak-coupling regime.