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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
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).
References
Beenakker, C. Search for Majorana fermions in superconductors. Annu. Rev. of Condens. Matter Phys. 4, 113–136 (2013).
Aasen, D. et al. Milestones toward Majorana-based quantum computing. Phys. Rev. X 6, 031016 (2016).
Aguado, R. Majorana quasiparticles in condensed matter. Riv. Nuovo Cimento 40, 523–593 (2017).
Lutchyn, R. M. et al. Majorana zero modes in superconductor–semiconductor heterostructures. Nat. Rev. Mater. 3, 52–68 (2018).
Prada, E. et al. From andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires. Nat. Rev. Phys. 2, 575–594 (2020).
Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).
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).
Deng, M. T. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016).
Nichele, F. et al. Scaling of Majorana zero-bias conductance peaks. Phys. Rev. Lett. 119, 136803 (2017).
Vaitiekėnas, S. et al. Flux-induced topological superconductivity in full-shell nanowires. Science 367, eaav3392 (2020).
Albrecht, S. M. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016).
Van Heck, B., Lutchyn, R. & Glazman, L. Conductance of a proximitized nanowire in the Coulomb blockade regime. Phys. Rev. B 93, 235431 (2016).
Flensberg, K. Capacitance and conductance of dots connected by quantum point contacts. Physica B: Condens. Matter 203, 432–439 (1994).
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).
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).
Vaitiekėnas, S., Krogstrup, P. & Marcus, C. M. Anomalous metallic phase in tunable destructive superconductors. Phys. Rev. B 101, 060507 (2020).
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).
Higginbotham, A. P. et al. Parity lifetime of bound states in a proximitized semiconductor nanowire. Nat. Phys. 11, 1017–1021 (2015).
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).
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).
San-Jose, P., Cayao, J., Prada, E. & Aguado, R. Majorana bound states from exceptional points in non-topological superconductors. Sci. Rep. 6, 21427 (2016).
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).
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).
Pendharkar, M. et al. Parity-preserving and magnetic field–resilient superconductivity in InSb nanowires with sn shells. Science 372, 508–511 (2021).
Kanne, T. et al. Epitaxial Pb on InAs nanowires for quantum devices. Nat. Nanotechnol. 16, 776–781 (2021).
Whiticar, A. et al. Coherent transport through a Majorana island in an Aharonov–Bohm interferometer. Nat. Commun. 11, 3212 (2020).
het Veld, R. L. O. et al. In-plane selective area InSb–Al nanowire quantum networks. Commun. Phys. 3, 59 (2020).
Carrad, D. J. et al. Shadow epitaxy for in situ growth of generic semiconductor/superconductor hybrids. Adv. Mater. 32, 1908411 (2020).
Shen, J. et al. Parity transitions in the superconducting ground state of hybrid InSb–Al Coulomb islands. Nat. Commun. 9, 4801 (2018).
Shen, J. et al. Full-parity phase diagram of a proximitized nanowire island. Phys. Rev. B 104, 045422 (2021).
Valentini, M. et al. Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states. Science 373, 82–88 (2021).
Lee, E. J. H. et al. Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures. Nat. Nanotechnol. 9, 79–84 (2014).
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).
Krogstrup, P. et al. Epitaxy of semiconductor–superconductor nanowires. Nat. Mater. 14, 400–406 (2015).
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).
San-Jose, P. Quantica.jl: a quantum lattice simulation library in the Julia language (2021); https://doi.org/10.5281/zenodo.4762964.
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).
Author information
Authors and Affiliations
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
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.
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.
About this article
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). https://doi.org/10.1038/s41586-022-05382-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-022-05382-w
This article is cited by
Comments
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.