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Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks

Abstract

Hybrid semiconductor–superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes1,2,3,4,5. However, multiple claims of Majorana detection, based on either tunnelling6,7,8,9,10 or Coulomb blockade (CB) spectroscopy11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even–odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.

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Fig. 1: Experimental protocol for combining tunnelling and Coulomb spectroscopy on the same device.
Fig. 2: Even–odd modulation and its tunability.
Fig. 3: Numerical simulation of the single-particle LDOS and conductance (dI/dV) in full-shell nanowires.
Fig. 4: Conductance in LP lobes when increasing the measurement sensitivity or barrier transparency.

Data availability

All experimental data included in this work and related to this work but not explicitly shown in the paper are available via the zenodo repository at https://zenodo.org/record/7404229#.Y4-MR3bMJaQ.

Code availability

Code used for the data analysis,microscopy analysis data and the codes used for the numerical simulation can also be found at the zenodo repository (https://zenodo.org/record/7404229#.Y4-MR3bMJaQ).

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Acknowledgements

We thank P. Krogstrup for providing us with the NW materials. We thank A. Higginbotham, E. J. H. Lee, C. Marcus and S. Vaitiekėnas for helpful discussions and G. Steffensen for his input on the diffusive Little-Parks theory. This research was supported by the Scientific Service Units of ISTA through resources provided by the MIBA Machine Shop and the nanofabrication facility; the NOMIS Foundation; the CSIC Interdisciplinary Thematic Platform (PTI+) on Quantum Technologies (PTI-QTEP+). A.H. acknowledges support from H2020-MSCA-IF-2018/844511. ICN2 also acknowledges funding from Generalitat de Catalunya 2017 SGR 327. ICN2 is supported by the Severo Ochoa Program from Spanish MINECO (Grant no. SEV-2017-0706) and is funded by the CERCA Programme/Generalitat de Catalunya. Part of the present work has been performed in the framework of Universitat Autònoma de Barcelona Materials Science PhD programme. Authors acknowledge the use of instrumentation as well as the technical advice provided by the National Facility ELECMI ICTS, node ‘Laboratorio de Microscopías Avanzadas’ at University of Zaragoza. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 823717-ESTEEM3. This study was supported by MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1) and Generalitat de Catalunya. This research is part of the CSIC programme for the Spanish Recovery, Transformation and Resilience Plan funded by the Recovery and Resilience Facility of the European Union, established by the Regulation (EU) 2020/2094. We thank support from Grant PGC2018-097018-BI00, project FlagERA TOPOGRAPH (PCI2018-093026) and project NANOGEN (PID2020-116093RB-C43), funded by MCIN/AEI/10.13039/501100011033/ and by ‘ERDF A way of making Europe’, by the European Union. M. Botifoll acknowledges support from SUR Generalitat de Catalunya and the EU Social Fund (project ref. 2020 FI 00103).

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Authors and Affiliations

Authors

Contributions

M.V., M. Borovkov and G.K. designed the experiment. M.V. and M. Borovkov fabricated the devices, performed the measurements and analyzed the data under the supervision of G.K. A.H. and G.K. performed precharacterization measurements on island devices. S.M.-S., M. Botifoll and J.A. performed the HAADF STEM and EELS measurements. E.P., R.A. and P.S.-J. provided theory support during and after the measurements, and developed the theoretical framework and models to analyze the experiment. E.P. and P.S.-J. performed the numerical simulations. M.V., M. Borovkov, E.P., R.A., P.S.-J. and G.K. contributed to discussions and the preparation of the manuscript with input from the rest of the authors.

Corresponding authors

Correspondence to Marco Valentini, Pablo San-Jose or Georgios Katsaros.

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Nature thanks Andrey Antipov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Behaviour of partial-shell devices.

(a) Zero bias dI/dV as a function of Visl and B for configuration pA1. (b) Plot showing the Coulomb peak spacing extracted from a. In the inset, a high-angle annular dark-field scanning transmission electron microscopy image of a partial-shell device is shown. The white area is the InAs core and the Al, shown in grey, does not cover all the facets but only the upper part of the wire. The scale bar corresponds to 20 nm. (c) (top) dI/dV as a function of V and B for device pA with one junction in the open regime and the other tuned in the weak coupling regime. The tunnelling spectroscopy does not reveal a ZBP and/or subgap states. (bottom) Zero bias dI/dV vs B. The purple curve in the inset shows that the conductance background grows with B. (d) Plot showing E0 vs. B for different configurations of the partial-shell device pA, i.e. pA1, pA2, PA3 and pA4.

Supplementary information

Supplementary Information

This file contains Supplementary Figs. 1–44, Supplementary Measurements and Theory, and Supplementary Tables 1–14.

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Valentini, M., Borovkov, M., Prada, E. et al. Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks. Nature 612, 442–447 (2022). https://doi.org/10.1038/s41586-022-05382-w

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