We study the effects of nanoscale impurity structures on the local electronic structure of $d_{x^2-y^2}$-wave superconductors. We show that the interplay between the momentum dependence of the superconducting gap, the geometry of the nanostructure, and its orientation gives rise to a series of interesting quantum effects. Among these are the emergence of a zero-bias conductance peak in the superconductor’s density of states and the possibility to screen impurity resonances in nanostructures.

• Received 2 February 2006

DOI:https://doi.org/10.1103/PhysRevB.73.140502