journal article·2025-06Open access

Enhanced Majorana stability in a three-site Kitaev chain

Alberto Bordin, Chun-Xiao Liu, Tom Dvir, Francesco Zatelli, Sebastiaan L. D. ten Haaf, David van Driel, Guanzhong Wang, Nick van Loo, Yining Zhang, Jan Cornelis Wolff, Thomas Van Caekenberghe, Ghada Badawy, Sasa Gazibegovic, Erik P. A. M. Bakkers, Michael Wimmer, Leo P. Kouwenhoven, Grzegorz P. Mazur

Nature Nanotechnology· Volume 20· Issue 6

Abstract

Abstract Majorana zero modes are non-Abelian quasiparticles predicted to emerge at the edges of topological superconductors. A one-dimensional topological superconductor can be realized with the Kitaev model—a chain of spinless fermions coupled via p-wave superconductivity and electron hopping—which becomes topological in the long-chain limit. Here we realize a three-site Kitaev chain using semiconducting quantum dots coupled by superconducting segments in a hybrid InSb/Al nanowire. We investigate the robustness of Majorana zero modes under varying coupling strengths and electrochemical potentials, comparing two- and three-site chains realized within the same device. We observe that extending the chain to three sites enhances the stability of the zero-energy modes, especially against variations in the coupling strengths. This experiment lacks superconducting phase control, yet numerical conductance simulations with phase averaging align well with our observations. Our results demonstrate the scalability of quantum-dot-based Kitaev chains and its benefits for Majorana stability.
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Research context

OpenAlex topics: Topological Materials and Phenomena · Advanced Condensed Matter Physics · Electronic and Structural Properties of Oxides

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (55)

Show source-provided references
1. Kitaev, A. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).10.1016/S0003-4916(02)00018-0 ↗
2. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).10.1103/RevModPhys.80.1083 ↗
3. Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).10.1103/PhysRevLett.105.077001 ↗
4. Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).10.1103/PhysRevLett.105.177002 ↗
5. Prada, E. et al. From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires. Nat. Rev. Phys. 2, 575–594 (2020).10.1038/s42254-020-0228-y ↗
6. van Loo, N. et al. Electrostatic control of the proximity effect in the bulk of semiconductor–superconductor hybrids. Nat. Commun. 14, 3325 (2023).10.1038/s41467-023-39044-w ↗
7. Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).10.1126/science.1259327 ↗
8. Kezilebieke, S. et al. Topological superconductivity in a van der Waals heterostructure. Nature 588, 424–428 (2020).10.1038/s41586-020-2989-y ↗
9. Pientka, F. et al. Topological superconductivity in a planar Josephson junction. Phys. Rev. X 7, 021032 (2017).
10. Fornieri, A. et al. Evidence of topological superconductivity in planar Josephson junctions. Nature 569, 89–92 (2019).10.1038/s41586-019-1068-8 ↗
11. Ren, H. et al. Topological superconductivity in a phase-controlled Josephson junction. Nature 569, 93–98 (2019).10.1038/s41586-019-1148-9 ↗
12. Zhang, P. et al. Observation of topological superconductivity on the surface of an iron-based superconductor. Science 360, 182–186 (2018).10.1126/science.aan4596 ↗
13. Vaitiekėnas, S. et al. Flux-induced topological superconductivity in full-shell nanowires. Science 367, eaav3392 (2020).10.1126/science.aav3392 ↗
14. Banerjee, A. et al. Signatures of a topological phase transition in a planar Josephson junction. Phys. Rev. B 107, 245304 (2023).10.1103/PhysRevB.107.245304 ↗
15. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Physics-Uspekhi 44, 131–136 (2001).10.1070/1063-7869/44/10S/S29 ↗
16. Sau, J. D. & Sarma, S. D. Realizing a robust practical Majorana chain in a quantum-dot-superconductor linear array. Nat. Commun. 3, 964 (2012).10.1038/ncomms1966 ↗
17. Dvir, T. et al. Realization of a minimal Kitaev chain in coupled quantum dots. Nature 614, 445–450 (2023).10.1038/s41586-022-05585-1 ↗
18. ten Haaf, S. L. D. et al. A two-site Kitaev chain in a two-dimensional electron gas. Nature 630, 329–334 (2024).10.1038/s41586-024-07434-9 ↗
19. Leijnse, M. & Flensberg, K. Parity qubits and poor man’s Majorana bound states in double quantum dots. Phys. Rev. B 86, 134528 (2012).10.1103/PhysRevB.86.134528 ↗
20. Hofstetter, L., Csonka, S., Nygård, J. & Schönenberger, C. Cooper pair splitter realized in a two-quantum-dot y-junction. Nature 461, 960–963 (2009).10.1038/nature08432 ↗
21. Hofstetter, L. et al. Finite-bias Cooper pair splitting. Phys. Rev. Lett. 107, 136801 (2011).10.1103/PhysRevLett.107.136801 ↗
22. Herrmann, L. G. et al. Carbon nanotubes as Cooper-pair beam splitters. Phys. Rev. Lett. 104, 026801 (2010).10.1103/PhysRevLett.104.026801 ↗
23. Ranni, A., Brange, F., Mannila, E. T., Flindt, C. & Maisi, V. F. Real-time observation of Cooper pair splitting showing strong non-local correlations. Nat. Commun. 12, 6358 (2021).10.1038/s41467-021-26627-8 ↗
24. Wang, G. et al. Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires. Nature 612, 448–453 (2022).10.1038/s41586-022-05352-2 ↗
25. Wang, Q. et al. Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas. Nat. Commun. 14, 4876 (2023).10.1038/s41467-023-40551-z ↗
26. Bordin, A. et al. Crossed Andreev reflection and elastic cotunneling in three quantum dots coupled by superconductors. Phys. Rev. Lett. 132, 056602 (2024).10.1103/PhysRevLett.132.056602 ↗
27. Fulga, I. C., Haim, A., Akhmerov, A. R. & Oreg, Y. Adaptive tuning of Majorana fermions in a quantum dot chain. New J. Phys. 15, 045020 (2013).10.1088/1367-2630/15/4/045020 ↗
28. Liu, C.-X., Wang, G., Dvir, T. & Wimmer, M. Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor–superconductor nanowires. Phys. Rev. Lett. 129, 267701 (2022).10.1103/PhysRevLett.129.267701 ↗
29. Bordin, A. et al. Tunable crossed Andreev reflection and elastic cotunneling in hybrid nanowires. Phys. Rev. X 13, 031031 (2023).
30. Zatelli, F. et al. Robust poor man’s Majorana zero modes using Yu–Shiba–Rusinov states. Nat. Commun. 15, 7933 (2024).10.1038/s41467-024-52066-2 ↗
31. Tinkham, M. Introduction to Superconductivity (Courier Corporation, 2004).
32. Tsintzis, A., Souto, R. S. & Leijnse, M. Creating and detecting poor man’s Majorana bound states in interacting quantum dots. Phys. Rev. B 106, L201404 (2022).10.1103/PhysRevB.106.L201404 ↗
33. Liu, C.-X. et al. Enhancing the excitation gap of a quantum-dot-based Kitaev chain. Commun. Phys. 7, 235 (2024).10.1038/s42005-024-01715-5 ↗
34. Luethi, M., Legg, H. F., Loss, D. & Klinovaja, J. From perfect to imperfect poor man’s Majoranas in minimal Kitaev chains. Phys. Rev. B 110, 245412 (2024).10.1103/PhysRevB.110.245412 ↗
35. Knapp, C. et al. The nature and correction of diabatic errors in anyon braiding. Phys. Rev. X 6, 041003 (2016).
36. Araya Day, I., Miles, S., Kerstens, H. K., Varjas, D. & Akhmerov, A. R. Pymablock: an algorithm and a package for quasi-degenerate perturbation theory. SciPost Phys. Codebases, 50 (2025).10.21468/SciPostPhysCodeb.50 ↗
37. Tsintzis, A., Souto, R. S., Flensberg, K., Danon, J. & Leijnse, M. Majorana qubits and non-Abelian physics in quantum dot-based minimal Kitaev chains. PRX Quantum 5, 010323 (2024).10.1103/PRXQuantum.5.010323 ↗
38. Pino, D. M., Souto, R. S. & Aguado, R. Minimal Kitaev-transmon qubit based on double quantum dots. Phys. Rev. B 109, 075101 (2024).10.1103/PhysRevB.109.075101 ↗
39. Spethmann, M., Bosco, S., Hofmann, A., Klinovaja, J. & Loss, D. High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits. Phys. Rev. B 109, 085303 (2024).10.1103/PhysRevB.109.085303 ↗
40. Pan, H., Sarma, S. D. & Liu, C.-X. Rabi and Ramsey oscillations of a Majorana qubit in a quantum dot-superconductor array. Phys. Rev. B 111, 075416 (2025).10.1103/PhysRevB.111.075416 ↗
41. Kanne, T. et al. Epitaxial Pb on InAs nanowires for quantum devices. Nat. Nanotechnol. 16, 776–781 (2021).10.1038/s41565-021-00900-9 ↗
42. Pendharkar, M. et al. Parity-preserving and magnetic field-resilient superconductivity in InSb nanowires with Sn shells. Science 372, 508–511 (2021).10.1126/science.aba5211 ↗
43. Mazur, G. P. et al. Spin mixing enhanced proximity effect in aluminum based superconductor–semiconductor hybrids. Adv. Mater. 34, 2202034 (2022).10.1002/adma.202202034 ↗
44. Heedt, S. et al. Shadow-wall lithography of ballistic superconductor–semiconductor quantum devices. Nat. Commun. 12, 4914 (2021).10.1038/s41467-021-25100-w ↗
45. de Moor, M. Quantum Transport in Nanowire Networks. PhD thesis, Delft University of Technology (2019).
46. Schouten, R. N. QT designed instrumentation. https://qtwork.tudelft.nl/~schouten/ivvi/index-ivvi.htm (2025).
47. Schouten, R. N. M1h, Current Measurement, fast readout. https://qtwork.tudelft.nl/~schouten/ivvi/doc-mod/docm1h.htm (2025).
48. Wang, Q., Zhang, Y., Karwal, S. & Goswami, S. Spatial dependence of local density of states in semiconductor–superconductor hybrids. Nano Lett. 24, 13558–13563 (2024).10.1021/acs.nanolett.4c03108 ↗
49. Bennebroek Evertsz’, F. Supercurrent Modulation by Andreev Bound States in a Quantum Dot Josephson Junction. Master’s thesis, Delft University of Technology (2023).
50. Bordin, A. et al. Impact of Andreev bound states within the leads of a quantum dot Josephson junction. Phys. Rev. X 15, 011046 (2025).
51. Martinez, E. A. et al. Measurement circuit effects in three-terminal electrical transport measurements. Preprint at https://doi.org/10.48550/arXiv.2104.02671 (2021).10.48550/arXiv.2104.02671 ↗
52. Scarlino, P. et al. In situ tuning of the electric-dipole strength of a double-dot charge qubit: charge-noise protection and ultrastrong coupling. Phys. Rev. X 12, 031004 (2022).
53. Boross, P. & Pályi, A. Braiding-based quantum control of a Majorana qubit built from quantum dots. Phys. Rev. B 109, 125410 (2024).10.1103/PhysRevB.109.125410 ↗
54. Bordin, A. Enhanced Majorana stability in a three-site Kitaev chain (version 2). Zenodo https://doi.org/10.5281/zenodo.13891286 (2025).10.5281/zenodo.13891286 ↗
55. Bozkurt, A. M. et al. Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry. Preprint at https://doi.org/10.48550/arXiv.2405.14940 (2024).10.48550/arXiv.2405.14940 ↗