Abstract
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.
Highlights
In the overdoped region of the cuprate phase diagram the normal phase exhibits properties similar to those of a strongly correlated Fermi liquid [1,2,3]
The d-wave pairing strength was shown to decrease despite the persistence of magnetic spin fluctuations in determinant quantum Monte Carlo calculations of the overdoped Hubbard model [8]
We expand on this research by studying the relation between the decrease in the pairing interaction and the magnetic fluctuations in more detail and its relation to a Lifshitz transition in the Fermi surface topology, and we examine the additional effect of impurity scattering on the decrease of Tc
Summary
In the overdoped region of the cuprate phase diagram the normal phase exhibits properties similar to those of a strongly correlated Fermi liquid [1,2,3]. Previous dynamic cluster approximation (DCA) calculations for a single-band Hubbard model have found that in the overdoped region the superconducting transition temperature Tc(x) falls as the density x of doped holes per site increases [5,6,7]. We expand on this research by studying the relation between the decrease in the pairing interaction and the magnetic fluctuations in more detail and its relation to a Lifshitz transition in the Fermi surface topology, and we examine the additional effect of impurity scattering on the decrease of Tc. In particular, we use DCA calculations [9] to study the decrease in the strength of the d-wave pairing interaction for a t-t -U Hubbard model in the overdoped regime as the hole density x increases [10]. Using the DCA results and treating the impurity scattering associated with the doping with in a disordered BCS d-wave approximation, we determine Tc(x) at the overdoped end of the phase diagram
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