Destruction of Superconductivity by Impurities in the Attractive Hubbard Model

TL;DR

This study investigates how non-interacting impurities affect superconductivity in the attractive Hubbard model, finding a critical impurity concentration that destroys long-range order while local pairing persists.

Contribution

It demonstrates that a specific fraction of impurities can eliminate superconducting order without destroying local pairing correlations.

Findings

Critical impurity fraction for destroying superconductivity is about 30%.

Superconducting order is suppressed independently of filling within a certain range.

Two-peak structure in specific heat persists despite impurity-induced suppression of long-range order.

Abstract

We study the effect of U=0 impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of $f_{\rm crit} \approx 0.30$ of the sites results in the destruction of off-diagonal long range order in the ground state. This critical fraction is roughly independent of filling in the range $0.75 < \rho < 1.00$, although our data suggest that $f_{\rm crit}$ might be somewhat larger below half-filling than at $\rho=1$. We also find that the two peak structure in the specific heat is present at $f$ both below and above the value which destroys long range pairing order. It is expected that the high $T$ peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low temperature peak.