Reduced effect of impurities on the universal pairing scale in the cuprates

TL;DR

This paper investigates how non-magnetic impurities affect the pairing temperature in cuprates, finding that the pairing scale is surprisingly robust against impurities in the intermediate coupling regime, aligning well with experimental data.

Contribution

It demonstrates that the universal pairing scale in cuprates is less sensitive to impurities than previously thought, especially in the intermediate coupling regime.

Findings

Impurity scattering rate needed to suppress $T^*$ is about 4 times larger than in weak coupling.

The universal pairing scale remains robust against impurities in the analyzed regime.

Analytical reasoning supports the numerical findings.

Abstract

We consider the effect of non-magnetic impurities on the onset temperature $T^*$ for the $d-$wave pairing in spin-fluctuation scenario for the cuprates. We analyze intermediate coupling regime when the magnetic correlation length $\xi/a >1$ and the dimensionless coupling $u$ is O(1). In the clean limit, $T^* \approx 0.02 v_f/a$ in this parameter range, and weakly depends on $\xi$ and $u$. We found numerically that this universal pairing scale is also quite robust with respect to impurities: the scattering rate $\Gamma_{cr}$ needed to bring $T^*$ down to zero is about 4 times larger than in weak coupling, in good quantitative agreement with experiments. We provide analytical reasoning for this result.