Photon-assisted tunnelling of zero modes in a Majorana wire


Hybrid nanowires with proximity-induced superconductivity in the topological regime host Majorana zero modes at their ends. Networks of such structures can produce topologically protected qubits where the fundamental energy scale is given by the inter-pair coupling EM between the zero modes belonging to different wire segments. Here we report on the spectroscopic measurement of EM in an InAs/Al double-island device by tracking the position of the microwave-induced quasiparticle excitations using a radiofrequency charge sensor. At zero magnetic field, photon-assisted tunnelling of Cooper pairs allows us to estimate the Josephson coupling between the islands. In the presence of a magnetic field aligned along the nanowire, we observe the 1e periodic excitation spectrum resulting from a zero-energy subgap state that emerges in a magnetic field. The discrete 1e periodic excitation spectrum is consistent with the coherent hybridization of single-electron states belonging to two opposite-parity branches. The dependence of excitation frequency on detuning indicates a sizable (GHz-scale) and controllable hybridization of zero modes across the junction separating islands, a requirement for applications related to Majorana-based qubits.

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Fig. 1: Charge states of the semiconductor–superconductor double-island device for different magnetic field values.
Fig. 2: Characterization of tunnel conductance through the middle tunnel junction as a function of magnetic field parallel to the nanowire.
Fig. 3: Microwave spectroscopy at zero magnetic field.
Fig. 4: Microwave spectroscopy at B = 0.75 T.

Data availability

The data represented in the main text figures are available as source data with the online version of the paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We thank S. Upadhyay for help with fabrication. The research is supported by Microsoft Project Q and the Danish National Research Foundation. J.S. acknowledges financial support from the Werner Siemens Foundation Switzerland. P.K. acknowledges support from the European Research Commission (grant no. 716655). C.M.M. acknowledges support from the Villum Foundation.

Author information




P.K. developed and grew the InAs/Al nanowires. J.S. fabricated the devices. D.S., D.M.T.Z and J.S. performed the measurements with input from K.D.P. and C.M.M. Data were analysed by D.M.T.Z. and J.I.V., with input from D.I.P., D.S. and T.K. The theoretical model to analyse the data was developed by J.I.V., D.I.P. and T.K. The experiment was conceived by C.M.M. All authors contributed to the interpretation of the data. The manuscript was written by D.M.T.Z., D.S. and C.M.M., with contributions from J.S., J.I.V. and D.I.P. and suggestions from all authors.

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Correspondence to Charles M. Marcus.

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Supplementary Figs. 1–10 and Notes.

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van Zanten, D.M.T., Sabonis, D., Suter, J. et al. Photon-assisted tunnelling of zero modes in a Majorana wire. Nat. Phys. 16, 663–668 (2020).

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