Inductive microwave response of Yu-Shiba-Rusinov states

TL;DR

This paper investigates how Yu-Shiba-Rusinov states influence the microwave response of phase-biased Josephson junctions with magnetic impurities, revealing the interaction-driven 0-pi transition through inductive admittance analysis.

Contribution

It models the microwave response of a magnetic impurity in a Josephson junction using three approaches, highlighting the interaction-induced 0-pi transition in the inductive response.

Findings

Yu-Shiba-Rusinov states affect sub-gap absorption and inductance.

The 0-pi transition causes a discontinuity in the inductive response.

All models capture the interaction-driven 0-pi transition.

Abstract

We calculate the frequency-dependent admittance of a phase-biased Josephson junction spanning a magnetic impurity or a spinful Coulomb-blockaded quantum dot. The local magnetic moment gives rise to Yu-Shiba-Rusinov bound states, which govern the sub-gap absorption as well as the inductive response. We model the system by a superconducting spin-polarized exchange-cotunnel junction and calculate the linear current response to an AC bias voltage, including its dependence on phase bias as well as particle-hole, and source-drain coupling asymmetry. The corresponding inductive admittance is analyzed and compared to results of a zero-bandwidth, as well as an infinite-gap approximation to the superconducting Anderson model. All three approaches capture the interaction-induced $0-\pi$ transition, which is reflected as a discontinuity in the adiabatic inductive response.