Quasiparticle bound states around impurities in dx2-y2-wave superconductors

Zn and Ni impurities in the holt-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 [S. H. Pan ei nl.. Nature (London) 403, 746 (2000)] has provided high-resolution images of the local density of states around nonmagnetic impurities in d(x2-y2)-wave superconductors. These pictures contain detailed information about the spinor wave functions u(r) and nu(r) of bound states with energy E-0 similar to 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(x2-y2)-wave superconductors.