Synthetic spin–orbit interaction for Majorana devices


The interplay of superconductivity with non-trivial spin textures is promising for the engineering of non-Abelian Majorana quasiparticles. Spin–orbit coupling is crucial for the topological protection of Majorana modes as it forbids other trivial excitations at low energy but is typically intrinsic to the material1,2,3,4,5,6,7. Here, we show that coupling to a magnetic texture can induce both a strong spin–orbit coupling of 1.1 meV and a Zeeman effect in a carbon nanotube. Both of these features are revealed through oscillations of superconductivity-induced subgap states under a change in the magnetic texture. Furthermore, we find a robust zero-energy state—the hallmark of devices hosting localized Majorana modes—at zero magnetic field. Our findings are generalizable to any low-dimensional conductor, and future work could include microwave spectroscopy and braiding operations, which are at the heart of modern schemes for topological quantum computation.

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Fig. 1: Hybrid superconductor–nanotube–magnetic texture set-up.
Fig. 2: Oscillations of the subgap states and synthetic spin–orbit interaction.
Fig. 3: Control experiment and phenomenology of subgap states under a magnetic field.
Fig. 4: Zero-bias peak.

Data availability

The authors declare that the main data supporting the findings of this study are available within the article (main text, methods and Supplementary information). Extra data are available from the corresponding author on reasonable request.

Code availability

The codes used in this paper are available at


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We are indebted to B. Leridon for the SQUID measurements and to K. Bouzehouane for MFM measurements. We acknowledge J. Palomo, M. Rosticher, A. Pierret and A. Denis for technical support. L.C.C. acknowledges the support from a Foundation CFM-J.P. Aguilar grant. The devices were made within the consortium Salle Blanche Paris Centre. This work is supported by ERC Starting Grant CIRQYS and grants from Région Ile de France and the ANR FunTheme.

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M.M.D. set up the experiment, and L.C.C. made the devices and carried out the measurements with the help of T.K. L.C.C. and M.M.D. performed the analysis of the data with inputs from T.K. L.C.C. and M.R.D. carried out the fabrication, measurement and analysis of the control experiment. M.M.D., J.J.V. and L.E.B. contributed through early experiments and the development of the nanofabrication process. T.C. and F.M. contributed to the experimental aspects. M.C.D. developed the data acquisition software. S.R. and A.T. developed the magnetic texture process and carried out the magnetic characterization with M.M.D. and L.C.C. M.M.D., L.C.C., M.R.D., T.K. and A.C. carried out the theory for the ABS oscillations. M.M.D. studied the tight-binding model using a framework developed by M.C.D. with theoretical insight from A.C. T.K., M.M.D., L.C.C., M.R.D. and A.C. co-wrote the manuscript with inputs from all the authors.

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Correspondence to T. Kontos.

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Supplementary Information

Supplementary Notes 1–7, Figs. 1–16 and references.

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Desjardins, M.M., Contamin, L.C., Delbecq, M.R. et al. Synthetic spin–orbit interaction for Majorana devices. Nat. Mater. 18, 1060–1064 (2019).

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