Quasi-Particle Bound States around Impurities in d-wave Superconductors

Zn and Ni impurities in the hole-doped high-temperature superconductors are known to have strong effects on thermodynamic and transport properties. A recent scanning tunneling microscope study of Zn-doped Bi2212 (Pan et al., Nature 403, 746 (2000)) has provided high-resolution images of the local density of states around non-magnetic impurities in d-wave superconductors. These pictures contain detailed information about the spinor wave functions u(r) and v(r) of bound states with energy E_0 \sim Delta/30, centered at the Zn-sites. We show that this type of wave function follows from the solutions of the Bogoliubov-de Gennes equations for d-wave superconductors.