Extended impurity potential in a ${\mathit{d}}_{x^2-y^2}$ superconductor

We investigate the role of a finite potential range of a nonmagnetic impurity for the local density of states in a $d_{x^2-y^2}$ superconductor. Impurity-induced subgap resonances are modified by the appearance of further scattering channels beyond the $s$-wave scattering limit. The structure of the local density of states (DOS) in the vicinity of the impurity is significantly enhanced and therefore improves the possibility for observing the characteristic anisotropic spatial modulation of the local DOS in a $d_{x^2-y^2}$ superconductor by scanning tunneling microscopy.