Ground State and Spectral Properties of a Quantum Impurity in d-Wave Superconductors

TL;DR

This paper investigates the behavior of magnetic impurities in d-wave superconductors, revealing how the impurity's ground state and spectral features change with hybridization, and relates findings to experimental observations.

Contribution

The study extends the variational approach to analyze impurity states in d-wave superconductors, identifying a critical hybridization for local moment screening and characterizing spectral features in different phases.

Findings

Local moment is screened above a critical hybridization value.

A Kondo resonance appears above the Fermi level in the singlet phase.

A low-energy spectral peak below the Fermi level exists in the doublet phase.

Abstract

The variational approach of Gunnarsson and Sch\"onhammer to the Anderson impurity model is generalized to study d-wave superconductors in the presence of dilute spin-1/2 impurities. We show that the local moment is screened when the hybridization exceeds a nonzero critical value at which the ground state changes from a spin doublet to a spin singlet. The electron spectral functions are calculated in both phases. We find that while a Kondo resonance develops above the Fermi level in the singlet phase, the spectral function exhibits a low-energy spectral peak below the Fermi level in the spin doublet phase. The origin of such a ``virtual Kondo resonance'' is the existence of low-lying collective excitations in the spin-singlet sector. We discuss our results in connection to recent spectroscopic experiments on Zn doped high-T$_c$ superconductors.