The intrinsic superconductor 2M-WS2 (Tc=8.8T_c = 8.8 K, the highest among natural transition metal dichalcogenides) was proposed as a stoichiometric Fu-Kane-type topological superconductor after scanning tunnelling microscopy/spectroscopy (STM/STS) revealed a non-split, zero-bias vortex-bound state, spatially highly anisotropic, coexisting with ordinary Caroli-de Gennes-Matricon bound states and interpreted as a probable anisotropic Majorana bound state (Yuan et al., Nature Physics 2019). That study left three linked questions open: (1) the zero mode's topological (Majorana) nature was not definitively confirmed, since a zero-bias peak alone can arise from trivial quasiparticle physics; (2) only a minority (approximately 25%) of imaged vortices hosted the non-split zero-energy state, and the local factors controlling this vortex-to-vortex variability were unknown; (3) a second intrinsic impurity species seen in STM remained microscopically unidentified. A later research program has strengthened the platform (ARPES confirmation of gapped, spin-momentum-locked topological surface states; theory of anisotropic full-gap s-wave pairing; disorder probes) and partially answered question (2) by discovering a coexisting stripe-like surface charge order that locally suppresses the surface Majorana state. Still open are Majorana-specific confirmation (braiding, fusion, nonlocal or spin-selective probes), a complete accounting of which vortices trap the zero mode, and the identity of the second impurity species.

Background

A Majorana bound state (MBS) or Majorana zero mode is a zero-energy quasiparticle excitation that is its own antiparticle; in two-dimensional topological superconductors such modes localize at the cores of superconducting vortices (magnetic-flux quanta piercing the superconducting condensate) and are predicted to obey non-Abelian exchange statistics, meaning that exchanging two such modes acts on a degenerate ground-state manifold in a way that depends on the order of the exchanges, the basis of proposals for topological quantum computing. In the Fu-Kane mechanism, an s-wave superconductor that gaps a set of topological surface states (surface bands with a nontrivial Z2 topology, protected against elastic backscattering by spin-momentum locking) becomes a topological superconductor, and each vortex binding such gapped surface states traps one Majorana mode. In any vortex, ordinary Caroli-de Gennes-Matricon (CdGM) bound states also form, a discrete ladder of low-energy quasiparticle levels inside the vortex core; their energy spread and spatial envelope can produce zero-bias spectral weight that mimics a Majorana mode, which is why a zero-bias tunnelling peak alone is not accepted as definitive Majorana evidence.

2M-WS2 is the monoclinic ("2M") polymorph of tungsten disulfide, a layered transition metal dichalcogenide (TMD) built from the same layers as monolayer 1T'-TMDs, long predicted to host quantum-spin-Hall-type topological bands (the two-dimensional topological-insulator bands whose spin-momentum-locked edge channels are the 3D analogue of the surface states relevant here). Unlike most Majorana candidate platforms (proximity-engineered semiconductor nanowires, topological-insulator/superconductor bilayers, or non-stoichiometric superconductors), it is an intrinsic, substitution-free stoichiometric superconductor with Tc=8.8T_c = 8.8 K, the highest among natural TMDs, and is cleavable into few-layer devices. The 2019 STM/STS study of Yuan et al. found: a U-shaped (fully gapped, nodeless) superconducting quasiparticle spectrum fit by an anisotropic gap function Δ(θ)=1.35+0.64cos⁡2θ\Delta(\theta) = 1.35 + 0.64\cos^2\theta meV; in vortex cores, a robust non-split zero-bias conductance peak coexisting with energy-split CdGM branches, attributed to a probable Majorana bound state; strong in-plane anisotropy of the zero-energy state, with exponential-decay lengths of about ξa≈13.94\xi_a \approx 13.94 nm along the crystallographic aa axis and ξb≈4.28\xi_b \approx 4.28 nm along bb, inherited from the anisotropy of the order parameter and Fermi velocity; an upper critical field Hc2H_{\mathrm{c2}} (the field above which superconductivity is destroyed) of roughly 2.6 T; and two types of intrinsic surface impurities acting as non-magnetic scatterers that produced no gap suppression or in-gap impurity states, consistent with s-wave pairing and backscattering-suppressed topological surface states.

The same study reported two observations that define the unresolved core. First, vortices fell into two spatial-evolution classes: type A showing the non-split zero-bias peak together with splitting CdGM branches, and type B showing only splitting branches, with the non-split zero mode present in only roughly a quarter of imaged vortices; the authors suggested the occurrence might depend on local parameters such as the chemical potential. Second, of the two intrinsic impurity species, one was tentatively identified as a sulfur vacancy while the nature of the other was left undetermined (its non-magnetic character was inferred indirectly, not from a Kondo-resonance test — a Kondo resonance being the characteristic zero-bias tunnelling peak produced by a localized magnetic moment — or from a magnetic-field-dependent test). Subsequent work established by angle-resolved photoemission spectroscopy (ARPES) that 2M-WS2 hosts topological surface states that acquire a nodeless superconducting gap of magnitude comparable to the bulk gap (Li et al. 2021) with the expected spin-momentum locking (Cho et al. 2022); ab initio Migdal-Eliashberg theory (a first-principles, electron-phonon many-body treatment of superconductivity) found a single anisotropic full-gap s-wave pairing state (Lian et al. 2021); and penetration-depth and irradiation-disorder measurements constrained the pairing to a strongly anisotropic multiband s-wave state whose TcT_c is sensitive to non-magnetic disorder (Ghimire et al. 2024). Most directly, low-temperature STM later discovered a stripe-like surface charge order coexisting with superconductivity (Fan et al. 2024; Xiao et al. 2025), and showed that vortices within strongly stripe-ordered regions lack the surface Majorana state, while adjacent stripe-free layers show it; tight-binding modeling of the Fu-Kane stack indicates the surface charge order does not destroy the bulk topology but pushes the Majorana wavefunction below the surface.

Problem Statement

Establish, with evidence beyond a zero-bias tunnelling peak, whether the non-split vortex zero mode observed by STM/STS in the intrinsic topological-superconductor candidate 2M-WS2 is a genuine topological (Majorana) bound state, and determine the local material conditions under which it occurs. Concretely, the objective comprises three jointly posed sub-questions: (1) obtain complementary measurements that unambiguously distinguish the vortex Majorana zero mode from trivial zero-energy vortex-core features (evidence that cannot be reproduced by any trivial vortex-core mechanism such as a Caroli-de Gennes-Matricon ladder, a vortex-core envelope effect, or a disorder- or Kondo-induced bound state), consolidating the now-confirmed ingredients of gapped, spin-momentum-locked topological surface states and anisotropic full-gap superconductivity; (2) determine the local electronic and structural variables that control whether an individual vortex hosts the non-split zero-energy state — the 2019 study found it in only a minority (approximately 25%) of imaged vortices, and although later work identified surface stripe charge order as one factor that suppresses the surface zero mode by pushing it below the surface, a complete accounting (including the roles of chemical potential, local disorder, and charge-order strength) is lacking; and (3) identify microscopically the second intrinsic impurity species observed on the 2M-WS2 surface (the first is likely a sulfur vacancy) and test its non-magnetic character directly, so that the absence of impurity-induced in-gap states can be used as valid evidence for s-wave pairing and backscattering-protected topological surface states. (1) and (2) settle, respectively, the two-part objective above — the topological (Majorana) nature of the zero mode and the local material conditions under which it occurs — while (3) identifies the second intrinsic impurity species and tests its (non-)magnetic character, which is needed to validate the s-wave and surface-state-protection premise on which the impurity argument rests. Together, these three tasks serve the common objective of deciding whether 2M-WS2 is a robust, controllable intrinsic platform for Majorana bound states, which its layered, substitution-free, stoichiometric nature would make uniquely suitable for device architectures.

References

  1. Yuan, Y., Pan, J., Wang, X., Fang, Y., Song, C., Wang, L., He, K., Ma, X., Zhang, H., Huang, F., Li, W. & Xue, Q.-K. Evidence of anisotropic Majorana bound states in 2M-WS2. Nature Physics 15, 1046-1051 (2019). DOI: 10.1038/s41567-019-0576-7, https://doi.org/10.1038/s41567-019-0576-7.
  2. Li, Y. W., Zheng, H. J., Fang, Y. Q., Zhang, D. Q., Chen, Y. J., Chen, C., Liang, A. J., Shi, W. J., Pei, D., Xu, L. X., Liu, S., Pan, J., Lu, D. H., Hashimoto, M., Barinov, A., Jung, S. W., Cacho, C., Wang, M. X., He, Y., Fu, L., Zhang, H. J., Huang, F. Q., Yang, L. X., Liu, Z. K. & Chen, Y. L. Observation of topological superconductivity in a stoichiometric transition metal dichalcogenide 2M-WS2. Nature Communications 12, 2874 (2021). DOI: 10.1038/s41467-021-23076-1, https://doi.org/10.1038/s41467-021-23076-1
  3. Cho, S., Huh, S., Fang, Y., Hua, C., Bai, H., Jiang, Z., Liu, Z., Liu, J., Chen, Z., Fukushima, Y., Harasawa, A., Kawaguchi, K., Shin, S., Kondo, T., Lu, Y., Mu, G., Huang, F. & Shen, D. Direct Observation of the Topological Surface State in the Topological Superconductor 2M-WS2. Nano Letters 22, 8827-8834 (2022). DOI: 10.1021/acs.nanolett.2c02372, https://doi.org/10.1021/acs.nanolett.2c02372
  4. Lian, C.-S., Si, C. & Duan, W. Anisotropic Full-Gap Superconductivity in 2M-WS2 Topological Metal with Intrinsic Proximity Effect. Nano Letters 21, 709-715 (2021). DOI: 10.1021/acs.nanolett.0c04357, https://doi.org/10.1021/acs.nanolett.0c04357
  5. Zhang, E., Xie, Y.-M., Fang, Y., Zhang, J., Xu, X., Zou, Y.-C., Leng, P., Gao, X.-J., Zhang, Y., Ai, L., Zhang, Y., Jia, Z., Liu, S., Yan, J., Zhao, W., Haigh, S. J., Kou, X., Yang, J., Huang, F., Law, K. T., Xiu, F. & Dong, S. Spin-orbit-parity coupled superconductivity in atomically thin 2M-WS2. Nature Physics 19, 106-113 (2023; published online 14 November 2022). DOI: 10.1038/s41567-022-01812-8, https://doi.org/10.1038/s41567-022-01812-8
  6. Ghimire, S., Joshi, K. R., Konczykowski, M., Grasset, R., Datta, A., Tanatar, M. A., Berube, D., Xu, S.-Y., Fang, Y., Huang, F., Orth, P. P., Scheurer, M. S. & Prozorov, R. Anisotropic multiband superconductivity in 2M-WS2 probed by controlled disorder. Physical Review Research 6, 013124 (2024). DOI: 10.1103/PhysRevResearch.6.013124, https://doi.org/10.1103/PhysRevResearch.6.013124
  7. Fan, X., Sun, X.-Q., Zhu, P., Fang, Y., Ju, Y., Yuan, Y., Yan, J., Huang, F., Hughes, T. L., Tang, P., Xue, Q.-K. & Li, W. Stripe charge order and its interaction with Majorana bound states in 2M-WS2 topological superconductors. National Science Review 12, nwae312 (2024). DOI: 10.1093/nsr/nwae312, https://doi.org/10.1093/nsr/nwae312 (preprint, under the title 'Stripe charge order driven manipulation of Majorana bound states in 2M-WS2 topological superconductor': arXiv:2308.16101, https://arxiv.org/abs/2308.16101)
  8. Xiao, K., Guo, Y., Fu, D., Fang, Y., Hu, Y., Yan, J., Peng, Y., Wang, Y., Ju, Y., Tang, P., Wan, X., Huang, F., Xue, Q.-K. & Li, W. Lattice-decoupled rotatable stripe-like charge order within the strange metal phase of 2M-WS2. Proceedings of the National Academy of Sciences 122, e2513493122 (2025). DOI: 10.1073/pnas.2513493122, https://doi.org/10.1073/pnas.2513493122
  9. Su, S., Xue, Q. & Li, W. Majorana zero modes, lattice-decoupled charge order, and their interactions in 2M-WS2. Science China Physics, Mechanics & Astronomy 56, 280005 (2026). DOI: 10.1360/sspma-2026-0028, https://doi.org/10.1360/sspma-2026-0028
  10. Fang, D., Yang, H. & Wen, H.-H. Scanning tunneling spectroscopy study on the vortex-core state in superconductors. Science China Physics, Mechanics & Astronomy 53, 127404 (2023). DOI: 10.1360/sspma-2023-0278, https://doi.org/10.1360/sspma-2023-0278
  11. Marra, P., Inotani, D., Mizushima, T. & Nitta, M. Majorana modes in striped two-dimensional inhomogeneous topological superconductors. npj Quantum Materials 9, 59 (2024). DOI: 10.1038/s41535-024-00672-0, https://doi.org/10.1038/s41535-024-00672-0
  12. Ding, Z., Zhang, C., Zhang, S., Zhu, X., Qin, W., Cui, P. & Zhang, Z. Coexistence and Interconversion of Multiple-Order Majorana Modes in Topological Superconductor Films with Varying Thickness. arXiv:2609.24311 (2026). DOI: 10.48550/arXiv.2609.24311, https://arxiv.org/abs/2609.24311