Impurity-induced virtual bound states in<i>d</i>-wave superconductors

Abstract

It is shown that a single, strongly scattering impurity produces a bound or a virtual-bound quasiparticle state inside the gap in a d-wave superconductor. The explicit form of the bound-state wave function is found to decay exponentially with angle-dependent range. These states provide a natural explanation of the second Cu NMR rate arising from the sites close to Zn impurities in the cuprates. Finally, for finite density of impurities in a d-wave superconductor, we re-examine the growth of these states into an impurity band, and discuss the Mott criterion for the metal-insulator transition in this band.