Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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


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.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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

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 (


  1. Beenakker, C. Search for Majorana fermions in superconductors. Annu. Rev. of Condens. Matter Phys. 4, 113–136 (2013).

    Article  ADS  CAS  Google Scholar 

  2. Aasen, D. et al. Milestones toward Majorana-based quantum computing. Phys. Rev. X 6, 031016 (2016).

    Google Scholar 

  3. Aguado, R. Majorana quasiparticles in condensed matter. Riv. Nuovo Cimento 40, 523–593 (2017).

    CAS  Google Scholar 

  4. Lutchyn, R. M. et al. Majorana zero modes in superconductor–semiconductor heterostructures. Nat. Rev. Mater. 3, 52–68 (2018).

    Article  ADS  CAS  Google Scholar 

  5. Prada, E. et al. From andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires. Nat. Rev. Phys. 2, 575–594 (2020).

    Article  CAS  Google Scholar 

  6. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    Article  ADS  CAS  Google Scholar 

  7. Das, A. et al. Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 8, 887–895 (2012).

    Article  CAS  Google Scholar 

  8. Deng, M. T. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016).

    Article  ADS  CAS  Google Scholar 

  9. Nichele, F. et al. Scaling of Majorana zero-bias conductance peaks. Phys. Rev. Lett. 119, 136803 (2017).

    Article  ADS  Google Scholar 

  10. Vaitiekėnas, S. et al. Flux-induced topological superconductivity in full-shell nanowires. Science 367, eaav3392 (2020).

    Article  Google Scholar 

  11. Albrecht, S. M. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016).

    Article  ADS  CAS  Google Scholar 

  12. Van Heck, B., Lutchyn, R. & Glazman, L. Conductance of a proximitized nanowire in the Coulomb blockade regime. Phys. Rev. B 93, 235431 (2016).

    Article  ADS  Google Scholar 

  13. Flensberg, K. Capacitance and conductance of dots connected by quantum point contacts. Physica B: Condens. Matter 203, 432–439 (1994).

    Article  ADS  CAS  Google Scholar 

  14. Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunneling regimes in superconducting microconstrictions: excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 4515–4532 (1982).

    Article  ADS  CAS  Google Scholar 

  15. Little, W. A. & Parks, R. D. Observation of quantum periodicity in the transition temperature of a superconducting cylinder. Phys. Rev. Lett. 9, 9–12 (1962).

    Article  ADS  Google Scholar 

  16. Vaitiekėnas, S., Krogstrup, P. & Marcus, C. M. Anomalous metallic phase in tunable destructive superconductors. Phys. Rev. B 101, 060507 (2020).

    Article  ADS  Google Scholar 

  17. Tuominen, M. T., Hergenrother, J. M., Tighe, T. S. & Tinkham, M. Experimental evidence for parity-based 2e periodicity in a superconducting single-electron tunneling transistor. Phys. Rev. Lett. 69, 1997–2000 (1992).

    Article  ADS  CAS  Google Scholar 

  18. Higginbotham, A. P. et al. Parity lifetime of bound states in a proximitized semiconductor nanowire. Nat. Phys. 11, 1017–1021 (2015).

    Article  CAS  Google Scholar 

  19. Hekking, F. W. J., Glazman, L. I., Matveev, K. A. & Shekhter, R. I. Coulomb blockade of two-electron tunneling. Phys. Rev. Lett. 70, 4138–4141 (1993).

    Article  ADS  CAS  Google Scholar 

  20. Hansen, E. B., Danon, J. & Flensberg, K. Probing electron-hole components of subgap states in Coulomb blockaded Majorana islands. Phys. Rev. B 97, 041411 (2018).

    Article  ADS  CAS  Google Scholar 

  21. San-Jose, P., Cayao, J., Prada, E. & Aguado, R. Majorana bound states from exceptional points in non-topological superconductors. Sci. Rep. 6, 21427 (2016).

    Article  ADS  CAS  Google Scholar 

  22. Avila, J., Peñaranda, F., Prada, E., San-Jose, P. & Aguado, R. Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy. Commun. Phys. 2, 133 (2019).

    Article  Google Scholar 

  23. Setiawan, F., Liu, C.-X., Sau, J. D. & Das Sarma, S. Electron temperature and tunnel coupling dependence of zero-bias and almost-zero-bias conductance peaks in majorana nanowires. Phys. Rev. B 96, 184520 (2017).

    Article  ADS  Google Scholar 

  24. Pendharkar, M. et al. Parity-preserving and magnetic field–resilient superconductivity in InSb nanowires with sn shells. Science 372, 508–511 (2021).

    Article  ADS  CAS  Google Scholar 

  25. Kanne, T. et al. Epitaxial Pb on InAs nanowires for quantum devices. Nat. Nanotechnol. 16, 776–781 (2021).

    Article  ADS  CAS  Google Scholar 

  26. Whiticar, A. et al. Coherent transport through a Majorana island in an Aharonov–Bohm interferometer. Nat. Commun. 11, 3212 (2020).

    Article  ADS  CAS  Google Scholar 

  27. het Veld, R. L. O. et al. In-plane selective area InSb–Al nanowire quantum networks. Commun. Phys. 3, 59 (2020).

    Article  Google Scholar 

  28. Carrad, D. J. et al. Shadow epitaxy for in situ growth of generic semiconductor/superconductor hybrids. Adv. Mater. 32, 1908411 (2020).

    Article  CAS  Google Scholar 

  29. Shen, J. et al. Parity transitions in the superconducting ground state of hybrid InSb–Al Coulomb islands. Nat. Commun. 9, 4801 (2018).

    Article  ADS  Google Scholar 

  30. Shen, J. et al. Full-parity phase diagram of a proximitized nanowire island. Phys. Rev. B 104, 045422 (2021).

    Article  ADS  CAS  Google Scholar 

  31. Valentini, M. et al. Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states. Science 373, 82–88 (2021).

    Article  ADS  MathSciNet  CAS  MATH  Google Scholar 

  32. Lee, E. J. H. et al. Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures. Nat. Nanotechnol. 9, 79–84 (2014).

    Article  ADS  CAS  Google Scholar 

  33. Peñaranda, F., Aguado, R., San-Jose, P. & Prada, E. Even-odd effect and Majorana states in full-shell nanowires. Phys. Rev. Res. 2, 023171 (2020).

    Article  Google Scholar 

  34. Krogstrup, P. et al. Epitaxy of semiconductor–superconductor nanowires. Nat. Mater. 14, 400–406 (2015).

    Article  ADS  CAS  Google Scholar 

  35. Yu, B., Yuan, Y., Song, J. & Taur, Y. A two-dimensional analytical solution for short-channel effects in nanowire mosfets. IEEE Trans. Electron. Devices 56, 2357–2362 (2009).

    Article  Google Scholar 

  36. San-Jose, P. Quantica.jl: a quantum lattice simulation library in the Julia language (2021);

Download references


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).

Author information

Authors and Affiliations



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.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Peer Review File

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Valentini, M., Borovkov, M., Prada, E. et al. Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks. Nature 612, 442–447 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing