Robustness of quantum critical pairing against disorder

The remarkable robustness of high-temperature superconductors against disorder remains a controversial obstacle towards the elucidation of their pairing state. Indeed, experiments report a weak suppression rate of the transition temperature $T_{c}$ with disorder, significantly smaller than the universal value predicted by extensions of the conventional theory of dirty superconductors. However, in many high-$T_{c}$ compounds, superconductivity appears near a putative magnetic quantum critical point, suggesting that quantum fluctuations, which suppress coherent electronic spectral weight, may also promote unconventional pairing. Here we investigate theoretically the impact of disorder on such a quantum critical pairing state, considering the coupling of impurities both to the low-energy electronic states and to the pairing interaction itself. We find a significant reduction in the suppression rate of $T_{c}$ with disorder near the magnetic quantum critical point, shedding new light on the nature of unconventional superconductivity in correlated materials.