The overdoped end of the cuprate phase diagram

Studying the disappearance of superconductivity at the end of the overdoped region of the cuprate phase diagram offers a different approach for investigating the interaction which is responsible for pairing in these materials. In the underdoped region this question is complicated by the presence of charge and stripe ordered phases as well as the pseudogap. In the overdoped region the situation appears simpler with only a normal phase, a superconducting phase and impurity scattering. Here, for the overdoped region, we report the results of a combined dynamic cluster approximation (DCA) and a weak Born impurity scattering calculation for a $t-t'-U$ Hubbard model. We find that a decrease in the $d$-wave pairing strength of the two-particle scattering vertex is closely coupled to changes in the momentum and frequency structure of the magnetic spin fluctuations as the system is overdoped. Treating the impurity scattering within a disordered BCS $d$-wave approximation, we see how the combined effects of the decreasing $d$-wave pairing strength and weak impurity scattering lead to the end of the $T_c$ dome.