Yu-Shiba-Rusinov states in phase-biased S-QD-S junctions

TL;DR

This paper investigates how phase differences influence Yu-Shiba-Rusinov states in a spinful quantum dot coupled to superconductors, revealing phase-dependent states, zero-energy crossings, and conductance resonances.

Contribution

It provides a detailed analysis of phase effects on YSR states in Coulomb-blockaded quantum dots, including the emergence of additional states and conductance features.

Findings

Phase difference induces an additional YSR state.

Zero-energy crossings occur twice within odd occupancy valleys.

Resonant conductance peaks of magnitude 4e^2/h are observed.

Abstract

We study the effects of a phase difference on Yu-Shiba-Rusinov (YSR) states in a spinful Coulomb-blockaded quantum dot contacted by a superconducting loop. In the limit where charging energy is larger than the superconducting gap, we determine the subgap excitation spectrum, the corresponding supercurrent, and the differential conductance as measured by a normal-metal tunnel probe. In absence of a phase difference only one linear combination of the superconductor lead electrons couples to the spin, which gives a single YSR state. With finite phase difference, however, it is effectively a two-channel scattering problem and therefore an additional state emerges from the gap edge. The energy of the phase-dependent YSR states depend on the gate voltage and one state can cross zero energy twice inside the valley with odd occupancy. These crossings are shifted by the phase difference towards the charge degeneracy points, corresponding to larger exchange couplings. Moreover, the zero-energy crossings give rise to resonant peaks in the differential conductance with magnitude $4e^2/h$. Finally, we demonstrate that the quantum fluctuations of the dot spin do not alter qualitatively any of the results.