Subgap states in superconducting islands

L. Pavešič,1,2 R. Žitko1,2

1Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

2Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

The local magnetic moment of an interacting quantum dot can be screened by a Bogoliubov quasiparticle from a nearby superconductor. This gives rise to a long lived discrete spin singlet state inside the superconducting gap, known as the Yu-Shiba-Rusinov (YSR) state.

We study the nature of the subgap states in a quantum dot coupled to one or two superconducting islands. These are described by a number conserving Richardson model of superconductivity, which allows us to account for the charging energy of the superconducting islands. For charging energy comparable to the superconducting gap, the subgap states are stabilized by a combination of Kondo exchange screening and charge redistribution driven by the Coulomb interaction. The model predictions match experimental results very well.

There are two singlet subgap states in the case of a quantum dot embedded between two superconducting channels, corresponding to the formation of a YSR singlet in each channel. The system can be tuned to a regime where the subgap states can be put into a superposition and coherently manipulated by electronic pulses. Such a qubit could be implemented using known technology.

In the doublet spin sector we investigate the overscreened state. Overscreening in normal state systems leads to a fixed point in the renormalization flow with non Fermi liquid properties, while for superconducting islands it emerges as a doublet subgap state with curious spin properties.

1. L. Pavešič et al., arXiv:2101.10168
2. J. C. Estrada Saldaña et al., arXiv:2101.10794
3. L. Pavešič, R. Žitko, arXiv:2110.13881

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