Comment on "Evolution from BCS Superconductivity to Bose-Einstein Condensation: Role of the Parameter $k_{\rm F} \xi$ in Interpreting the Experimental Plot by Uemura et al.''}

TL;DR

This paper critiques the applicability of the Nozières and Schmitt-Rink approach to the BCS-BEC crossover in high-temperature cuprates, demonstrating its limitations with a self-consistent T-matrix formalism in two dimensions.

Contribution

The authors provide a self-consistent T-matrix analysis showing the NSR approach's unphysical results in 2D, challenging previous assumptions about its validity across coupling regimes.

Findings

NSR approach yields unphysical results in 2D.

Self-consistent T-matrix formalism provides more accurate insights.

Critique of the universal validity of the NSR relation between $T_c$ and $T_F$.

Abstract

The problem of crossover from BCS to Bose-Einstein condensation has recently attracted considerable interest owing to the discovery of high-$T_{\rm c}$ cuprates. Their short coherence length, $\xi$, places these materials in the interesting region between BCS and Bose-Einstein condensation. In the paper of F. Pistolesi and G.C. Strinati (Phys. Rev. B {\bf 49}, 6356 (1994)), the Nozi\`eres and Schmitt-Rink approach (NSR) is taken, which is valid for the weak coupling regime. They derive a relation between $T_{\rm c}$ and $T_{\rm F}$, which they insist is valid for any coupling strength. We present arguments that their assumptions are incorrect by using our fully self-consistent T-matrix formalism in two dimensions, and show that the NSR approach produces unphysical results in this case.