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.

Two-fold symmetric superconductivity in few-layer NbSe2


The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice. Both the magnetoresistance and critical field exhibit this two-fold symmetry, and it also manifests deep inside the superconducting state in NbSe2/CrBr3 superconductor-magnet tunnel junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behaviour to the mixing between two closely competing pairing instabilities, namely the conventional s-wave instability typical of bulk NbSe2 and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results demonstrate the unconventional character of the pairing interaction in few-layer transition metal dichalcogenides and highlight the exotic superconductivity in this family of two-dimensional materials.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Crystal structure, device layout and characterization.
Fig. 2: Magnetoresistance and effective critical field signatures of two-fold superconducting behaviour.
Fig. 3: Differential conductance spectra under an in-plane magnetic field.
Fig. 4: Theoretical model for the two-fold anisotropic gap in NbSe2.

Data availability

Data for figures (including Supplementary figures) are available in the public repository Zenodo at Source data are provided with this paper.

Code availability

All relevant codes needed to evaluate the conclusions in the paper are available from the corresponding authors upon reasonable request.


  1. 1.

    Revolinsky, E., Lautenschlager, E. P. & Armitage, C. H. Layer structure superconductor. Solid State Commun. 1, 59–61 (1963).

    ADS  Article  Google Scholar 

  2. 2.

    Xiao, D. et al. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).

    ADS  Article  Google Scholar 

  3. 3.

    Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).

    ADS  Article  Google Scholar 

  4. 4.

    Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS2 monolayers by optical pumping. Nat. Nanotechnol. 7, 490–493 (2012).

    ADS  Article  Google Scholar 

  5. 5.

    Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS2 transistors. Science 344, 1489–1492 (2014).

    ADS  Article  Google Scholar 

  6. 6.

    Jones, A. M. et al. Spin-layer locking effects in optical orientation of exciton spin in bilayer WSe2. Nat. Phys. 10, 130–134 (2014).

    Article  Google Scholar 

  7. 7.

    Riley, J. M. et al. Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor. Nat. Phys. 10, 835–839 (2014).

    Article  Google Scholar 

  8. 8.

    Xi, X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).

    Article  Google Scholar 

  9. 9.

    Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    Article  Google Scholar 

  10. 10.

    Ugeda, M. M. et al. Characterization of collective ground states in single-layer NbSe2. Nat. Phys. 12, 92–97 (2016).

    Article  Google Scholar 

  11. 11.

    Moncton, D. E., Axe, J. D. & DiSalvo, F. J. Neutron scattering study of the charge-density wave transitions in 2H-TaSe2 and 2H-NbSe2. Phys. Rev. B 16, 801–819 (1977).

    ADS  Article  Google Scholar 

  12. 12.

    Harper, J. M. E., Geballe, T. H. & DiSalvo, F. J. Thermal properties of layered transition-metal dichalcogenides at charge-density-wave transitions. Phys. Rev. B 15, 2943–2951 (1977).

    ADS  Article  Google Scholar 

  13. 13.

    Fletcher, J. D. et al. Penetration depth study of superconducting gap structure of 2H-NbSe2. Phys. Rev. Lett. 98, 057003 (2007).

    ADS  Article  Google Scholar 

  14. 14.

    De La Barrera, S. C. et al. Tuning Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides. Nat. Commun. 9, 1427 (2018).

    ADS  Article  Google Scholar 

  15. 15.

    Clogston, A. M. Upper limit for the critical field in hard superconductors. Phys. Rev. Lett. 9, 266–267 (1962).

    ADS  Article  Google Scholar 

  16. 16.

    Chandrasekhar, B. S. A note on the maximum critical field of high-field superconductors. Appl. Phys. Lett. 1, 7–8 (1962).

    ADS  Article  Google Scholar 

  17. 17.

    Möckli, D. & Khodas, M. Magnetic-field induced s + if pairing in Ising superconductors. Phys. Rev. B 99, 180505 (2019).

    ADS  Article  Google Scholar 

  18. 18.

    Möckli, D. & Khodas, M. Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides. Phys. Rev. B 98, 144518 (2018).

    ADS  Article  Google Scholar 

  19. 19.

    Yuan, N. F. Q., Mak, K. F. & Law, K. T. Possible topological superconducting phases of MoS2. Phys. Rev. Lett. 113, 097001 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Samokhin, K. V. Symmetry and topology of two-dimensional noncentrosymmetric superconductors. Phys. Rev. B 92, 174517 (2015).

    ADS  Article  Google Scholar 

  21. 21.

    Zhou, B. T., Yuan, N. F. Q., Jiang, H. L. & Law, K. T. Ising superconductivity and Majorana fermions in transition-metal dichalcogenides. Phys. Rev. B 93, 180501 (2016).

    ADS  Article  Google Scholar 

  22. 22.

    Hsu, Y. T., Vaezi, A., Fischer, M. H. & Kim, E. A. Topological superconductivity in monolayer transition metal dichalcogenides. Nat. Commun. 8, 14985 (2017).

    ADS  Article  Google Scholar 

  23. 23.

    He, W.-Y. et al. Magnetic field driven nodal topological superconductivity in monolayer transition metal dichalcogenides. Commun. Phys. 1, 40 (2018).

    Article  Google Scholar 

  24. 24.

    Fischer, M. H., Sigrist, M. & Agterberg, D. F. Superconductivity without inversion and time-reversal symmetries. Phys. Rev. Lett. 121, 157003 (2018).

    ADS  Article  Google Scholar 

  25. 25.

    Shaffer, D., Kang, J., Burnell, F. J. & Fernandes, R. M. Crystalline nodal topological superconductivity and Bogolyubov Fermi surfaces in monolayer NbSe2. Phys. Rev. B 101, 224503 (2020).

    ADS  Article  Google Scholar 

  26. 26.

    Tsubokawa, I. On the magnetic properties of a CrBr3 single crystal. J. Phys. Soc. Jpn 15, 1664–1668 (1960).

    ADS  Article  Google Scholar 

  27. 27.

    Ghazaryan, D. et al. Magnon-assisted tunnelling in van der Waals heterostructures based on CrBr3. Nat. Electron. 1, 344–349 (2018).

    Article  Google Scholar 

  28. 28.

    Baral, D. et al. Small energy gap revealed in CrBr3 by scanning tunneling spectroscopy. Phys. Chem. Chem. Phys. 23, 3225–3232 (2021).

    Article  Google Scholar 

  29. 29.

    Kim, H. H. et al. Evolution of interlayer and intralayer magnetism in three atomically thin chromium trihalides. Proc. Natl Acad. Sci. USA 166, 11131–11136 (2019).

    ADS  Article  Google Scholar 

  30. 30.

    Zhang, Z. et al. Direct photoluminescence probing of ferromagnetism in monolayer two-dimensional CrBr3. Nano Lett. 19, 3138–3142 (2019).

    ADS  Article  Google Scholar 

  31. 31.

    Chen, W. et al. Direct observation of van der Waals stacking–dependent interlayer magnetism. Science 366, 983–987 (2019).

    ADS  Article  Google Scholar 

  32. 32.

    Dvir, T. et al. Spectroscopy of bulk and few-layer superconducting NbSe2 with van der Waals tunnel junctions. Nat. Commun. 9, 598 (2018).

    ADS  Article  Google Scholar 

  33. 33.

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

    ADS  Article  Google Scholar 

  34. 34.

    Sohn, E. et al. An unusual continuous paramagnetic-limited superconducting phase transition in 2D NbSe2. Nat. Mater. 17, 504–508 (2018).

    ADS  Article  Google Scholar 

  35. 35.

    Sheet, G., Mukhopadhyay, S. & Raychaudhuri, P. Role of critical current on the point-contact Andreev reflection spectra between a normal metal and a superconductor. Phys. Rev. B 69, 134507 (2004).

    ADS  Article  Google Scholar 

  36. 36.

    Wang, Y. L. et al. Parallel magnetic field suppresses dissipation in superconducting nanostrips. Proc. Natl Acad. Sci. USA 114, E10274–E10280 (2017).

    ADS  Article  Google Scholar 

  37. 37.

    Cho, C. et al. Distinct nodal and nematic superconducting phases in the 2D Ising superconductor NbSe2. Preprint at (2020).

  38. 38.

    Cai, X. et al. Disentangling spin–orbit coupling and local magnetism in a quasi-two-dimensional electron system. Phys. Rev. B 100, 081402(R) (2019).

    ADS  Article  Google Scholar 

  39. 39.

    Matano, K., Kriener, M., Segawa, K., Ando, Y. & Zheng, G. Q. Spin–rotation symmetry breaking in the superconducting state of CuxBi2Se3. Nat. Phys. 12, 852–854 (2016).

    Article  Google Scholar 

  40. 40.

    Fernandes, R. M. & Millis, A. J. Nematicity as a probe of superconducting pairing in iron-based superconductors. Phys. Rev. Lett. 111, 127001 (2013).

    ADS  Article  Google Scholar 

  41. 41.

    Kang, J., Kemper, A. F. & Fernandes, R. M. Manipulation of gap nodes by uniaxial strain in iron-based superconductors. Phys. Rev. Lett. 113, 217001 (2014).

    ADS  Article  Google Scholar 

  42. 42.

    Venderbos, J. W. F., Kozii, V. & Fu, L. Identification of nematic superconductivity from the upper critical field. Phys. Rev. B 94, 094522 (2016).

    ADS  Article  Google Scholar 

  43. 43.

    Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).

    Article  Google Scholar 

  44. 44.

    Bing, D. et al. Optical contrast for identifying the thickness of two-dimensional materials. Opt. Commun. 406, 128–138 (2018).

    ADS  Article  Google Scholar 

  45. 45.

    Novoselov, K. S. et al. Electric field in atomically thin carbon films. Science 306, 666–669 (2004).

    ADS  Article  Google Scholar 

Download references


We thank E.-A. Kim for useful discussions. B.H. and A.H. thank D. Graf and S. Maier for their discussions and support related to work done at the National High Magnetic Field Laboratory. Special thanks also go to Z. Jiang for all of the support associated with the Physical Property Measurement System at UMN. The work at the University of Minnesota (UMN) was supported primarily by the National Science Foundation through the University of Minnesota MRSEC, under Awards DMR-2011401 and DMR-1420013 (iSuperSeed). Portions of the UMN work were conducted in the Minnesota Nano Center, which is supported by the National Science Foundation through the National Nano Coordinated Infrastructure Network (NNCI) under award no. ECCS-1542202. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative agreement no. DMR-1644779 and the State of Florida. The research at Cornell was supported by the Office of Naval Research (ONR) under award no. N00014-18-1-2368 for the tunnelling measurements, and the National Science Foundation (NSF) under award no. DMR-1807810 for the fabrication of tunnel junctions. The work in Lausanne was supported by the Swiss National Science Foundation. K.F.M. also acknowledges support from a David and Lucille Packard Fellowship.

Author information




B.H., A.H., V.S.P. and K.W. designed the magnetoresistance and effective critical field experiments. B.H. performed the transport measurements at UMN with support from A.H. and K.-T.T. B.H. and A.H. performed the measurements at the NHMFL with support from A.S. B.H. analysed the data with support from A.H. under the supervision of V.S.P. and K.W. A.H., K.-T.T. and X.Z. fabricated the magneto-transport heterostructures with support from B.H., under the supervision of K.W. Analytical modelling was performed by D.S., R.M.F. and F.J.B., who also contributed to the interpretation of the results. E.S., X.X., J.S. and K.F.M. designed the junction experiments. E.S. and X.X. fabricated and measured the junctions under the supervision of J.S. and K.F.M. E.S. analysed the junction data under the supervision of J.S. and K.F.M., with input from V.S.P. and R.M.F. H.B. and L.F. grew the bulk NbSe2 samples for tunnel junction studies. B.H., A.H., E.S., D.S., V.S.P. and R.M.F. co-wrote the manuscript. All authors discussed the results and provided comments on the manuscript.

Corresponding authors

Correspondence to Ke Wang or Vlad S. Pribiag.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Hadar Steinberg, Carsten Timm and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–11, Discussion and Table 12.

Supplementary Data

Fig. 1.2 data, Fig. 1.3 data, Fig. 2 data, Fig. 3 data, Fig. 4 data, Fig. 5 data, Fig. 6 data, Fig. 7 data, Fig. 8 data, Fig. 11.1 data and Fig. 11.2 data.

Source data

Source Data Fig. 1

Unprocessed images and source data.

Source Data Fig. 2

Source data.

Source Data Fig. 3

Source data.

Source Data Fig. 4

Source data.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hamill, A., Heischmidt, B., Sohn, E. et al. Two-fold symmetric superconductivity in few-layer NbSe2. Nat. Phys. 17, 949–954 (2021).

Download citation

Further reading


Quick links