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# Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures

## Abstract

The physics and operating principles of hybrid superconductor–semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

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## Acknowledgements

This work was supported by the European Research Council (ERC Grant agreement no. 280043-HybridNano) and by the Agence Nationale de la Recherche (ANR-08-JCJC-0010). R.A. acknowledges support from the Spanish Ministry of Economy and Innovation through grants FIS2009-08744 and FIS2012-33521. The authors thank J-D. Pillet for useful discussions.

## Author information

Authors

### Contributions

E.J.H.L. and S.D.F. conceived the experiment. X.J. grew the semiconductor NWs under C.M.L.'s supervision. E.J.H.L. fabricated the devices and performed all the measurements under S.D.F.'s supervision. R.A. performed the Hartree–Fock calculations, and M.H. carried out the analytical study of the level-repulsion effect. E.J.H.L., S.D.F., R.A. and M.H. analysed and interpreted the results. All authors co-wrote the manuscript.

### Corresponding author

Correspondence to Silvano De Franceschi.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 1239 kb)

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Lee, E., Jiang, X., Houzet, M. et al. Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures. Nature Nanotech 9, 79–84 (2014). https://doi.org/10.1038/nnano.2013.267

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