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# Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions

## Abstract

The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates, providing a highly scalable and in situ variation of the device properties. In addition, semiconductors with large g-factor and spin–orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as φ0 Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gate-tunable, high transmission probabilities up to 0.9, which is required for gate-tunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spin-split pair of ABS and observe symmetry-broken ABS, a direct consequence of the spin–orbit coupling in the semiconductor.

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van Woerkom, D. J. et al. Microwave Spectroscopy of Spinful Andreev Bound States in Ballistic Semiconductor Josephson Junctions (QuTech, 2017); http://doi.org/b6xg

## Acknowledgements

The authors thank L. Bretheau, Ç. Ö. Girit, L. DiCarlo, M. P. Nowak and A. R. Akhmerov for fruitful discussions, and R. van Gulik, T. Kriváchy, A. Bruno, N. de Jong, J. D. Watson, M. C. Cassidy, R. N. Schouten and T. S. Jespersen for assistance with fabrication and experiments. This work has been supported by the Danish National Research Foundation, the Villum Foundation, the Dutch Organization for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO) by a Veni grant, Microsoft Corporation Station Q and a Synergy Grant of the European Research Council. B.v.H. was supported by ONR Grant Q00704. L.I.G. and J.I.V. acknowledge the support by NSF Grant DMR-1603243.

## Author information

Authors

### Contributions

D.J.v.W., A.P. and D.B. performed the experiments. B.v.H., J.I.V. and L.I.G. developed the theory to analyse the data. P.K. and J.N. contributed to the nanowire growth. D.J.v.W., A.P. and D.B. fabricated the samples. L.P.K. and A.G. designed and supervised the experiments. D.J.v.W., B.v.H., L.P.K. and A.G. analysed the data. The manuscript has been prepared with contributions from all the authors.

### Corresponding author

Correspondence to Attila Geresdi.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 2207 kb)

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van Woerkom, D., Proutski, A., van Heck, B. et al. Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions. Nature Phys 13, 876–881 (2017). https://doi.org/10.1038/nphys4150

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