Spin-rotation symmetry breaking in the superconducting state of CuxBi2Se3


Spontaneous symmetry breaking is an important concept for understanding physics ranging from the elementary particles to states of matter. For example, the superconducting state breaks global gauge symmetry, and unconventional superconductors can break further symmetries. In particular, spin-rotational symmetry is expected to be broken in spin-triplet superconductors. However, experimental evidence for such symmetry breaking has not been conclusively obtained so far in any candidate compounds. Here, using 77Se nuclear magnetic resonance measurements, we show that spin-rotation symmetry is spontaneously broken in the hexagonal plane of the electron-doped topological insulator Cu0.3Bi2Se3 below the superconducting transition temperature Tc = 3.4 K. Our results not only establish spin-triplet superconductivity in this compound, but may also serve to lay a foundation for the research of topological superconductivity.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: The NMR spectra of Cu0.3Bi2Se3 with the magnetic field applied in the hexagonal plane.
Figure 2: Temperature dependence of the Knight shift with the magnetic field in the plane and along the c axis.
Figure 3: Angle dependence of the Knight shift reduction below Tc.


  1. 1

    Tsuei, C. C. & Kirtley, J. R. Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000).

    Article  ADS  Google Scholar 

  2. 2

    Matano, K. et al. Spin-singlet superconductivity with multiple gaps in PrFeAsO0.89F0.11 . Europhys. Lett. 83, 57001 (2008).

    Article  ADS  Google Scholar 

  3. 3

    Leggett, A. J. A theoretical description of the new phases of liquid 3He. Rev. Mod. Phys. 47, 331–414 (1975).

    Article  ADS  Google Scholar 

  4. 4

    Tilley, D. R. & Tilley, J. Superfluidity and Superconductivity 3rd edn (IOP, 1990).

    Google Scholar 

  5. 5

    Joynt, R. & Taillefer, L. The superconducting phases of UPt3 . Rev. Mod. Phys. 74, 235–294 (2002).

    Article  ADS  Google Scholar 

  6. 6

    Mackenzie, A. P. & Maeno, Y. The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003).

    Article  ADS  Google Scholar 

  7. 7

    Tou, H. et al. Nonunitary spin-triplet superconductivity in UPt3: evidence from 195Pt knight shift study. Phy. Rev. Lett. 80, 3129–3132 (1998).

    Article  ADS  Google Scholar 

  8. 8

    Ishida, K. et al. Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift. Nature 396, 658–660 (1998).

    Article  ADS  Google Scholar 

  9. 9

    Maeno, Y., Kittaka, S., Nomura, T., Yonezawa, S. & Ishida, K. Evaluation of spin-triplet superconductivity in Sr2RuO4 . J. Phys. Soc. Jpn 81, 011009 (2012).

    Article  ADS  Google Scholar 

  10. 10

    Machida, K. & Ichioka, M. Magnetic field dependence of low-temperature specific heat in Sr2RuO4 . Phys. Rev. B 77, 184515 (2008).

    Article  ADS  Google Scholar 

  11. 11

    Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    Article  ADS  Google Scholar 

  12. 12

    Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  Google Scholar 

  13. 13

    Ando, Y. & Fu, L. Topological crystalline insulators and topological superconductors: from concepts to materials. Annu. Rev. Condens. Matter Phys. 6, 361–381 (2015).

    Article  ADS  Google Scholar 

  14. 14

    Zhang, H. J. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009).

    Article  ADS  Google Scholar 

  15. 15

    Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).

    Article  ADS  Google Scholar 

  16. 16

    Hor, Y. S. et al. Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator. Phys. Rev. Lett. 104, 057001 (2010).

    Article  ADS  Google Scholar 

  17. 17

    Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3 . Phys. Rev. Lett. 105, 097001 (2010).

    Article  ADS  Google Scholar 

  18. 18

    Wan, X. & Savrasov, S. Y. Tuning a band insulator into an exotic superconductor. Nature Commun. 5, 4144 (2013).

    Article  ADS  Google Scholar 

  19. 19

    Brydon, P. M. R., Das Sarma, S., Hui, H.-Y. & Sau, J. D. Odd-parity superconductivity from phonon-mediated pairing: application to CuxBi2Se3 . Phys. Rev. B 90, 184512 (2014).

    Article  ADS  Google Scholar 

  20. 20

    Sasaki, S. et al. Topological Superconductivity in CuxBi2Se3 . Phys. Rev. Lett. 107, 217001 (2011).

    Article  ADS  Google Scholar 

  21. 21

    Levy, N. et al. Experimental evidence for s-wave pairing symmetry in superconducting CuxBi2Se3 single crystals using a scanning tunneling microscope. Phys. Rev. Lett. 110, 117001 (2013).

    Article  ADS  Google Scholar 

  22. 22

    Bay, T. V. et al. CuxBi2Se3 under high pressure. Phys. Rev. Lett. 108, 057001 (2012).

    Article  ADS  Google Scholar 

  23. 23

    Mizushima, K., Yamakage, A., Sato, M. & Tanaka, Y. Dirac-fermion-induced parity mixing in superconducting topological insulators. Phys. Rev. B 90, 184516 (2014).

    Article  ADS  Google Scholar 

  24. 24

    Balian, R. & Werthamer, N. R. Superconductivity with Pairs in a relative p wave. Phys. Rev. 131, 1553–1564 (1963).

    Article  ADS  Google Scholar 

  25. 25

    Strand, J. D. et al. The transition between real and complex superconducting order parameter phases in UPt3 . Science 328, 1368–1369 (2010).

    Article  ADS  Google Scholar 

  26. 26

    Hashimoto, T., Yada, K., Yamakage, A., Sato, M. & Tanaka, Y. Bulk electronic state of superconducting topological insulator. J. Phys. Soc. Jpn 82, 044704 (2013).

    Article  ADS  Google Scholar 

  27. 27

    Zocher, B. & Rosenow, B. Surface states and local spin susceptibility in doped three-dimensional topological insulators with odd-parity superconducting pairing symmetry. Phys. Rev. B 87, 155138 (2013).

    Article  ADS  Google Scholar 

  28. 28

    Appel, J. Spin-orbit coupling and the knight shift in nontransition-metal superconductors. Phys. Rev. 139, A1536 (1965).

    Article  ADS  Google Scholar 

  29. 29

    Zheng, G.-q. et al. Delocalized quasiparticles in the vortex state of an overdoped high-Tc superconductor probed by 63Cu NMR. Phys. Rev. Lett. 88, 077003 (2002).

    Article  ADS  Google Scholar 

  30. 30

    Kriener, M., Segawa, K., Ren, Z., Sasaki, S. & Ando, Y. Bulk superconducting phase with a full energy gap in the doped topological insulator CuxBi2Se3 . Phys. Rev. Lett. 106, 127004 (2011).

    Article  ADS  Google Scholar 

Download references


We thank A. Yamakage, M. Sato, L. Fu, Y. Tanaka, K. Mizushima, Y. Yanase, K. Miyake, Y. Maeno, J. P. Hu, T. Xiang and J. A. Sauls for helpful discussion, and Y. S. Hor, F. Iwase, S. Maeda and K. Ueshima for participation in the initial stage of this work. This work was supported in part by MEXT research grants (Innovative area ‘Topological Quantum Phenomena’, No. 22103004 and ‘Topological Materials Science’, No. 15H05852), JSPS grants (nos. 24540320, 25220708, 25800197, 15K05140 and 16H04016), AFOSR (AOARD 124038) and by the CAS (grant No. XDB07020200).

Author information




G.-q.Z. conceived the project. M.K. and K.S. synthesized and characterized the electrochemically intercalated single crystals under the supervision of Y.A. K.M. and G.-q.Z. performed NMR measurements. G.-q.Z. integrated different pieces of the work and wrote the manuscript with inputs from all co-authors. All authors discussed the results and interpretation.

Corresponding author

Correspondence to Guo-qing Zheng.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1700 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Matano, K., Kriener, M., Segawa, K. et al. Spin-rotation symmetry breaking in the superconducting state of CuxBi2Se3. Nature Phys 12, 852–854 (2016). https://doi.org/10.1038/nphys3781

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing