Fate of disorder-induced inhomogeneities in strongly correlated d-wave superconductors

We analyze the complex interplay of the strong correlations and
impurities in a high temperature superconductor and show that both the
nature and degree of the inhomogeneities change drastically due to
strong correlations. While both the strong electronic repulsions and
disorder contribute to the nanoscale inhomogeneity in the population
of charge-carriers, we find them to compete with each other leading to
a relatively smooth variation of the local density. Our
self-consistent calculations prohibit the formation of distinct
superconducting-`islands'. The reorganization of the spatial
structures makes these superconductors surprisingly insensitive to the
impurities. We also conclude that the underlying one-particle normal
states reshape in a rich manner, such that the superconductor formed
by pairing these states experiences a weaker but spatially correlated
effective disorder. Such a route to superconductivity makes it
tempting to extend Anderson's theorem to the correlated d-wave
superconductors.