Abstract
Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the (\(1\bar{1}0\))-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of the magnetic field and expands the types of MZM available for tuning topological states.
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Data availability
The data supporting the findings of this study are presented within the paper and Supplementary Information. Source data are provided with this paper. Additional data are available from the corresponding authors upon reasonable request.
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The code for this paper is available from the corresponding authors upon reasonable request.
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Acknowledgements
We acknowledge financial support from the Ministry of Science and Technology of China (Grant Nos. 2019YFA0308600, 2021YFA1401500 and 2020YFA0309000), the National Natural Science Foundation of China (Grant Nos. 11861161003, 12104293, 92365302, 22325203, 92265105, 92065201, 12074247 and 12174252), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000), the Science and Technology Commission of Shanghai Municipality (Grant Nos. 19JC1412701, 2019SHZDZX01 and 20QA1405100), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302500) and the China National Postdoctoral Program for Innovative Talents (Grant No. BX2021185). Y.Z., C.W. and J.L. also acknowledge financial support from the Hong Kong Research Grants Council (Projects No. N_HKUST626/18, 26302118 and 16305019). The theoretical simulations were conducted at the Hefei Advanced Computing Center.
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Y.L., J.L. and J.J. supervised the research. H.Y. and T.L. performed the experiments with the help of B.X., W.Z. and Z.Y. C.Y.W. and Y.Z. performed the simulations. D.G., S.W., H.Z., C.L., L.F., J.L., Y.L. and J.J. analysed the results. Y.L., J.L. and J.J. wrote the manuscript with contributions from all authors.
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Liu, T., Wan, C.Y., Yang, H. et al. Signatures of hybridization of multiple Majorana zero modes in a vortex. Nature 633, 71–76 (2024). https://doi.org/10.1038/s41586-024-07857-4
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DOI: https://doi.org/10.1038/s41586-024-07857-4
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