Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

TL;DR

This paper maps the phase diagram of an Anderson impurity coupled to superconducting and normal leads, revealing complex spectral behaviors and zero-bias anomalies relevant for Majorana detection.

Contribution

It provides a comprehensive analysis of the Anderson model with hybrid leads, highlighting the impact of weak normal lead coupling and finite temperature effects on spectral features.

Findings

Normal lead coupling significantly affects spectral properties.

Zero-bias anomalies can occur regardless of ground state nature.

Finite temperature and magnetic field influence phase transitions.

Abstract

We determine the phase diagram of an Anderson impurity in contact with superconducting and normal-state leads for arbitrary ratio of the gap $\Delta$ to the Kondo temperature $T_K$. We observe a considerable effect of even very weak coupling to the normal lead that is usually considered as a non-perturbing tunneling probe. The numerical renormalization group results are analyzed in the context of relevant experimental scenarios such as parity crossing (doublet-singlet) quantum phase transitions induced by a gap reduction as well as novel Kondo features induced by the normal lead. We point out the important role of finite temperatures and magnetic fields. Overall, we find a very rich behavior of spectral functions with zero-bias anomalies which can emerge irrespective of whether the ground state is a doublet or a singlet. Our findings are pertinent to the tunnelling-spectroscopy experiments aiming at detecting Majorana modes in nanowires.