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Enhancement of the critical temperature in cuprate superconductors by inhomogeneous doping

We use a renormalized mean field theory to investigate the superconducting properties of underdoped cuprates embedded with overdoped or metallic regions that carry excess dopants. The overdoped regions are considered, within two different models, first as stripes of mesoscopic size larger than the coherence length and then as point impurities. In the former case we compute the temperature dependent superfluid stiffness by solving Bogoliubov de Gennes equations within the slave boson mean field theory. We average over stripes of different orientations to obtain an isotropic result. To compute the superfluid stiffness in the model with point impurities we resort to a diagrammatic expansion in the impurity concentration (to first order) and their strength (up to second order). We find analytic expressions for the disorder averaged superfluid stiffness and the critical temperature. For both types of inhomogeneity we find increased superfluid stiffness, and for a wide range of doping enhancement of Tc relative to a homogeneously underdoped system. Remarkably, in the case of microscopic impurities we find that the maximal Tc can be significantly increased compared to Tc at optimal doping of a pure system.