Impurity-Induced Virtual Bound States in d-Wave Superconductors

TL;DR

This paper demonstrates that strong impurities in d-wave superconductors create bound or virtual bound quasiparticle states within the energy gap, explaining experimental NMR observations and analyzing impurity band formation.

Contribution

It provides explicit wave functions for impurity-induced states and examines the transition to impurity bands in d-wave superconductors.

Findings

Impurities induce bound and virtual bound states inside the superconducting gap.

The wave functions decay exponentially with angle-dependent range.

Impurity concentration leads to the formation of an impurity band, analyzed via the Mott criterion.

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 concentration of impurities in a $d$-wave superconductor, we reexamine the growth of these states into an impurity band, and discuss the Mott criterion for this band.