  We investigate the impurity resonant state induced by non-magnetic impurities
in d-wave cuprate superconductors in two different impurity models: (i) in a
pure potential scattering model within the T-matrix approach and (ii) in a
Bose-Fermi Kondo model within the large-N formalism. We modify the
superconducting host to resemble the nanoscale electronic inhomogeneities seen
in the scanning tunneling microscopy (STM) spectra (i.e., the small- and
large-gap domains) and study how this influences the impurity resonance. In the
pure potential scattering model the resonant state is found to be a rather
robust feature appearing in all host domains. On the other hand, in the
Kondo-like model the impurity resonance can appear in the small-gap regions of
the host and be completely suppressed in the large-gap regions; this is in
agreement with the STM experimental data for Zn-doped BSCCO. Our results imply
that the Kondo spin dynamics of the impurity moment is the origin of the
impurity resonant state in d-wave superconductors, rather than the pure
potential scattering.
