We present a theoretical framework for understanding the behavior of the normal and superconducting states of overdoped cuprate high temperature superconductors in the vicinity of the doping-tuned quantum superconductor-to-metal transition. The key ingredients on which we focus are d-wave pairing, a flat antinodal dispersion, and disorder. Even for homogeneous disorder, these lead to effectively granular superconducting correlations and a superconducting transition temperature determined in large part by the superfluid stiffness rather than the pairing scale.

Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped t-J models on the finite-width square lattice (doped hole densities δ=1/12 and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Ground-state correlations are found to be nearly identical for the "doped quantum spin liquid"and "doped valence bond crystal."Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any "competing"charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless d-wave superconducting ground state in the 2D limit.