  The understanding of disorder has profoundly influenced the development of
condensed matter physics, explaining such fundamental effects as, for example,
the transition from ballistic to diffusive propagation, and the presence of
quantized steps in the quantum Hall effect. For superconductors, the response
to disorder reveals crucial information about the internal gap symmetries of
the condensate, and thereby the pairing mechanism itself. The destruction of
superconductivity by disorder is traditionally described by Abrikosov-Gor'kov
(AG) theory, which however ignores spatial modulations and ceases to be valid
when impurities interfere, and interactions become important. Here we study the
effects of disorder on unconventional superconductors in the presence of
correlations, and explore a completely different disorder paradigm dominated by
strong deviations from standard AG theory due to generation of local bound
states and cooperative impurity behavior driven by Coulomb interactions.
Specifically we explain under which circumstances magnetic disorder acts as a
strong poison destroying high-Tc superconductivity at the sub-1% level, and
when non-magnetic disorder, counter-intuitively, hardly affects the
unconventional superconducting state while concomitantly inducing an
inhomogeneous full-volume magnetic phase. Recent experimental studies of
Fe-based superconductors have discovered that such unusual disorder behavior
seem to be indeed present in those systems.
