Impurity resonant state in d-wave superconductors: in favor of a Kondo-like response

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.