Impurity scattering in a d-wave superconductor

TL;DR

This paper investigates how impurities, both magnetic and non-magnetic, affect the transition temperature of d-wave superconductors within BCS theory, revealing that impurity scattering suppresses $T_c$ proportionally and behaves differently than traditional models.

Contribution

It provides a new analysis of impurity effects on $T_c$ in d-wave superconductors, highlighting the dependence of suppression on impurity type and scattering rates, contrasting with Abrikosov-Gor'kov theory.

Findings

$T_c$ suppression is proportional to impurity scattering rate.

Initial slope of $T_c$ suppression depends on superconductor specifics.

Magnetic impurities act similarly to non-magnetic impurities in $T_c$ suppression.

Abstract

The influence of (non-magnetic and magnetic) impurities on the transition temperature of a d-wave superconductor is studied anew within the framework of BCS theory. Pairing interaction decreases linearly with the impurity concentration. Accordingly $T_{c}$ suppression is proportional to the (potential or exchange) scattering rate, $1/\tau$, due to impurities. The initial slope versus $1/\tau$ is found to depend on the superconductor contrary to Abrikosov-Gor'kov type theory. Near the critical impurity concentration $T_{c}$ drops abruptly to zero. Because the potential scattering rate is generally much larger than the exchange scattering rate, magnetic impurities will also act as non-magnetic impurities as far as the $T_{c}$ decrease is concerned. The implication for the impurity doping effect in high $T_{c}$ superconductors is also discussed.