Quantum critical fluctuations in disordered d-wave superconductors

TL;DR

This paper investigates how static disorder affects quantum critical fluctuations in disordered d-wave superconductors, revealing diffusive dynamics and a secondary transition influenced by impurity levels.

Contribution

It extends previous models by incorporating static disorder, showing distinct effects for id_{xy}- and is-symmetry fluctuations, including a disorder-sensitive secondary transition.

Findings

Disorder causes diffusive behavior in id_{xy}-symmetry fluctuations.

Impurity scattering can induce a secondary superconducting transition.

Critical temperature of the secondary transition is exponentially sensitive to disorder.

Abstract

Quasiparticles in the cuprates appear to be subject to anomalously strong inelastic damping mechanisms. To explain the phenomenon, Sachdev and collaborators recently proposed to couple the system to a critically fluctuating order parameter mode of either id_{xy}- or is-symmetry. Motivated by the observation that the energies relevant for the dynamics of this mode are comparable to the scattering rate induced by even moderate impurity concentrations, we here generalize the approach to the presence of static disorder. In the id-case, we find that the coupling to disorder renders the order parameter dynamics diffusive but otherwise leaves much of the phenomenology observed in the clean case intact. In contrast, the interplay of impurity scattering and order parameter fluctuations of is-symmetry entails the formation of a secondary superconductor transition, with a critical temperature exponentially sensitive to the disorder concentration.