Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads

TL;DR

This paper employs the numerical renormalization group method to accurately analyze the spectral functions of the Anderson model with superconducting leads, revealing sharp near-gap peaks previously unresolved.

Contribution

It demonstrates that NRG iterations can extend to very low energies, enabling precise calculation of spectral features near the superconducting gap edge.

Findings

NRG iterations can reach energies far below the gap

Sharp peaks near the gap edge are resolved

Spectral functions show new features close to the gap

Abstract

We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows, in contrast to previous belief, that NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the superconducting gap. This allows us to calculate the impurity spectral function very accurately for frequencies near the gap edge, and to resolve, in a certain parameter regime, sharp peaks in the spectral function close to the gap edge.