Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor

TL;DR

This paper investigates how superconductivity affects the formation and properties of magnetic moments in quantum impurities within BCS superconductors using theoretical models and Green's function techniques.

Contribution

It introduces a combined Bogoliubov transformation and Green's function approach within a self-consistent Hartree-Fock framework to analyze magnetic moment formation in superconducting environments.

Findings

Magnetic moments form under specific conditions in superconductors.

Spectral density reveals sub-gap states influenced by impurity parameters.

Comparison with normal metals highlights the impact of superconductivity.

Abstract

We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen-Cooper-Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green's function method within self-consistent Hartree-Fock Mean Field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit $|\omega|<<\Delta_{sc}$ as well as for the finite superconducting gap $\Delta_{sc}$. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further we analyze the electronic spectral density of the quantum impurity embedded in superconducting host with the finite superconducting gap to study the sub-gap states as a function of impurity parameters.