Quantum Critical Fluctuations in Disorderedd-Wave Superconductors

Abstract

To explain the strong quasiparticle damping in the cuprates, Sachdev and collaborators proposed to couple the system to a critically fluctuating $i{d}_{xy}$- or $is$-order parameter mode. Here we generalize the approach to the presence of static disorder. In the $id$ case, the order parameter dynamics becomes diffusive, but otherwise much of the phenomenology of the clean case remains intact. In contrast, the interplay of disorder and $is$-order parameter fluctuations leads to a secondary superconductor transition, with a critical temperature exponentially sensitive to the impurity concentration.