Disorder effect on the superfluid density and the origin of the pseudogap end point in the cuprate superconductors

Abstract

A major puzzle in the study of the cuprate superconductivity is the origin of the pseudogap end point. Intriguingly, such a critical doping is also where the superfluid density of the system reaches its maximum. A non-monotonic doping dependence of the superfluid density is rather unusual since the Drude weight of the cuprate system is found to increase monotonically with the doping concentration. It is generally believed that such a peculiar behavior should be attributed to both the strongly correlated nature of the cuprate system and the disorder effect. In this work, we develop a variational theory for the zero temperature superfluid density of the disordered $t-J$ model. This is achieved in two steps. First, we perform an unrestricted variational optimization of an RVB variational ground state for the disordered $t-J$ model. Second, we construct the variational state that describes the paramagnetic current response on such an RVB state. The zero temperature superfluid density $ρ_{s}(0)$ is then extracted from the curvature of the variational ground state energy of the system as a function of the external electromagnetic field. We find that $ρ_{s}(0)$ computed in this way is remarkably robust against the disorder effect. More specifically, we find that $ρ_{s}(0)$ is a monotonically increasing function of doping concentration $x$ and scales linearly with the total optical weight. This is consistent with the observation in the underdoped cuprates but is strongly at odd with the behavior in the overdoped cuprates. The strong contrast between the disorder effect in the underdoped and the overdoped regime lends strong support to our previous proposal that there exist a Mott transition between a doped-Mott-insulating metal in the underdoped regime and a fermi-liquid-like metal in the overdoped regime around the pseudogap end point.