Skip to main content
Log in

Identify the Nematic Superconductivity of Topological Superconductor Pd\(_x\)Bi\(_2\)Te\(_3\) by Angle-dependent Upper Critical Field Measurement

  • Letter
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

Odd-parity superconductivity is recognized as a key ingredient to realize topological superconductivity. In Bi2Se3-based bulk topological superconductors, the odd-parity pairing, which spontaneously breaks the threefold rotational symmetry of the crystal, leading to a subsidiary nematic order, was discovered. The nematic superconducting state can be identified by thermodynamic measurement, nuclear magnetic resonance measurement, ac-\(\chi\) measurement, magnetic torque measurement or magnetoresistance measurement. Here, the single crystal of topological superconductor Pd\(_x\)Bi2Te3 was grown. Its upper critical fields were obtained by magnetoresistance measurement in various magnetic field orientations parallel to the basal plane. The in-plane upper critical fields clearly demonstrate a twofold symmetry that break the threefold crystal symmetry. This provides experimental evidence that Pd-doped Bi2Te3 is a nematic topological superconductor similar to the Cu-, Sr-, and Nb-doped Bi2Se3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Qi, X.-L., Zhang, S.-C.: Topological insulators and superconductors. Rev Mod Phys 83(4), 1057 (2011)

    Article  ADS  Google Scholar 

  2. Sato, M., Ando, Y.: Topological superconductors: a review. Rep Prog Phys 80(7), 076501 (2017)

  3. Kitaev. Fault-tolerant quantum computation by anyons. Ann Phys 303:2 (2003)

  4. Freedman, M., Kitaev, A., Larsen, M., Wang, Z.: Topological quantum computation. Bull Amer Math Soc 40(1), 31–38 (2003)

    Article  MathSciNet  Google Scholar 

  5. Teo, J.C., Kane, C.L.: Majorana fermions and non-abelian statistics in three dimensions. Phys Rev Lett 104(4), 046401 (2010)

  6. Wang, D., Kong, L., Fan, P., Chen, H., Zhu, S., Liu, W., Cao, L., Sun, Y., Du, S., Schneeloch, J., et al.: Evidence for majorana bound states in an iron-based superconductor. Science 362(6412), 333–335 (2018)

    Article  ADS  Google Scholar 

  7. Fu, L., Kane, C.L.: Superconducting proximity effect and majorana fermions at the surface of a topological insulator. Phys Rev Lett 100(9), 096407 (2008)

  8. Mourik, V., Zuo, K., Frolov, S.M., Plissard, S., Bakkers, E.P., Kouwenhoven, L.P.: Signatures of majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336(6084), 1003–1007 (2012)

    Article  ADS  Google Scholar 

  9. Nadj-Perge, S., Drozdov, I.K., Li, J., Chen, H., Jeon, S., Seo, J., MacDonald, A.H., Bernevig, B.A., Yazdani, A.: Observation of majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346(6209), 602–607 (2014)

    Article  ADS  Google Scholar 

  10. Sun, H.-H., Zhang, K.-W., Hu, L.-H., Li, C., Wang, G.-Y., Ma, H.-Y., Xu, Z.-A., Gao, C.-L., Guan, D.-D., Li, Y.-Y., et al.: Majorana zero mode detected with spin selective andreev reflection in the vortex of a topological superconductor. Phys. Rev. Lett. 116(25), 257003 (2016)

  11. Hor, Y.S., Williams, A.J., Checkelsky, J.G., Roushan, P., Seo, J., Xu, Q., Zandbergen, H.W., Yazdani, A., Ong, N.P., Cava, R.J.: Superconductivity in Cu\(_x\)Bi\(_2\)Se\(_3\) and its implications for pairing in the undoped topological insulator. Phys Rev Lett 104(5), 057001 (2010)

  12. Matano, K., Kriener, M., Segawa, K., Ando, Y., Zheng, G.-Q.: Spin-rotation symmetry breaking in the superconducting state of Cu\(_x\)Bi\(_2\)Se\(_3\). Nat Phys 12(9), 852–854 (2016)

    Article  Google Scholar 

  13. Yonezawa, S., Tajiri, K., Nakata, S., Nagai, Y., Wang, Z., Segawa, K., Ando, Y., Maeno, Y.: Thermodynamic evidence for nematic superconductivity in Cu\(_x\)Bi\(_2\)Se\(_3\). Nat Phys 13(2), 123–126 (2017)

    Article  Google Scholar 

  14. Kawai, T., Wang, C., Kandori, Y., Honoki, Y., Matano, K., Kambe, T., Zheng, G.-Q.: Direction and symmetry transition of the vector order parameter in topological superconductors Cu\(_x\)Bi\(_2\)Se\(_3\). Nat Commun 11(1), 1–7 (2020)

    Article  Google Scholar 

  15. Liu, Z., Yao, X., Shao, J., Zuo, M., Pi, L., Tan, S., Zhang, C., Zhang, Y.: Superconductivity with topological surface state in Sr\(_x\)Bi\(_2\)Se\(_3\). J Am Chem Soc 137(33), 10512–10515 (2015)

    Article  Google Scholar 

  16. Li, Z., Wang, M., Zhang, D., Feng, N., Jiang, W., Han, C., Chen, W., Ye, M., Gao, C., Jia, J., et al.: Possible structural origin of superconductivity in Sr-doped Bi\(_2\)Se\(_3\). Phys Rev Materials 2(1), 014201 (2018)

  17. Pan, Y., Nikitin, A., Araizi, G., Huang, Y., Matsushita, Y., Naka, T., De Visser, A.: Rotational symmetry breaking in the topological superconductor Sr\(_x\)Bi\(_2\)Se\(_3\) probed by upper-critical field experiments. Sci Rep 6(1), 1–7 (2016)

    Article  Google Scholar 

  18. Han, C., Li, H., Chen, W., Zhu, F., Yao, M.-Y., Li, Z., Wang, M., Gao, B.F., Guan, D., Liu, C., et al.: Electronic structure of a superconducting topological insulator Sr-doped Bi\(_2\)Se\(_3\). Appl Phys Lett 107(17), 171602 (2015)

  19. Du, G., Shao, J., Yang, X., Du, Z., Fang, D., Wang, J., Ran, K., Wen, J., Zhang, C., Yang, H., et al.: Drive the dirac electrons into cooper pairs in Sr\(_x\)Bi\(_2\)Se\(_3\). Nat Commun 8(1), 1–9 (2017)

    Article  ADS  Google Scholar 

  20. Du, G., Li, Y., Schneeloch, J., Zhong, R., Gu, G., Yang, H., Lin, H., Wen, H.-H.: Superconductivity with two-fold symmetry in topological superconductor Sr\(_x\)Bi\(_2\)Se\(_3\). Sci China Phys Mech Astron 60(3), 037411 (2017)

  21. Qiu, Y., Sanders, K.N., Dai, J., Medvedeva, J.E., Wu, W., Ghaemi, P., Vojta, T., Hor, Y.S.:  Time reversal symmetry breaking superconductivity in topological materials. arXiv preprint arXiv:1512.03519(2015)

  22. Lawson, B., Corbae, P., Li, G., Yu, F., Asaba, T., Tinsman, C., Qiu, Y., Medvedeva, J.E., Hor, Y.S., Li, L.: Multiple fermi surfaces in superconducting Nb-doped Bi\(_2\)Se\(_3\). Phys Rev B 94(4), 041114 (2016)

  23. Asaba, T., Lawson, B., Tinsman, C., Chen, L., Corbae, P., Li, G., Qiu, Y., Hor, Y.S., Fu, L., Li, L.: Rotational symmetry breaking in a trigonal superconductor Nb-doped Bi\(_2\)Se\(_3\). Phys Rev X 7(1), 011009 (2017)

  24. Kobayashi, K., Ueno, T., Fujiwara, H., Yokoya, T., Akimitsu, J.: Unusual upper critical field behavior in Nb-doped bismuth selenides. Phys Rev B 95(18), 180503 (2017)

  25. Wang, J., Jiao, F., Zhang, D., Chang, M., Cai, L., Li, Y., Wang, C., Tan, S., Jing, Q., Liu, B., et al.: Investigate the Nb doping position and its relationship with bulk topological superconductivity in Nb\(_x\)Bi\(_2\)Se\(_3\) by X-ray photoelectron spectra. J Phys Chem Solids 137, 109208 (2020)

  26. Kevy, S.M., Lund, H.E., Wollesen, L., Dalgaard, K.J., Hsu, Y.-T., Wiedmann, S., Bianchi, M., Holt, A.J.U., Curcio, D., Biswas, D., et al.: Structural and electronic inhomogeneity of superconducting Nb-doped Bi\(_2\)Se\(_3\). Phys Rev B 103(8), 085107 (2021)

  27. Kamminga, M.E., Batuk, M., Hadermann, J., Clarke, S.J.: Misfit phase (BiSe)\(_{1.10}\) NbSe\(_2\) as the origin of superconductivity in niobium-doped bismuth selenide. Commun Mater 1(1), 1–7 (2020)

  28. Sharma, M., Rani, P., Sang, L., Wang, X., Awana, V.:  Superconductivity below 2.5 k in Nb\(_{0.25}\) Bi\(_2\)Se\(_3\) topological insulator single crystal. J Supercond Nov Magn 33(3), 565–568 (2020)

  29. Levy, N., Zhang, T., Ha, J., Sharifi, F., Talin, A.A., Kuk, Y., Stroscio, J.A.: Experimental evidence for s-wave pairing symmetry in superconducting Cu\(_x\)Bi\(_2\)Se\(_3\) single crystals using a scanning tunneling microscope. Phys Rev Lett 110(11), 117001 (2013)

  30. Chen, M., Chen, X., Yang, H., Du, Z., Wen, H.-H.: Superconductivity with twofold symmetry in Bi\(_2\)Te\(_3\)/FeTe\(_{0. 55}\)Se\(_{0. 45}\) heterostructures. Sci Adv 4(6), eaat1084 (2018)

  31. Fu, L.: Odd-parity topological superconductor with nematic order: Application to Cu\(_x\)Bi\(_2\)Se\(_3\). Phys Rev B 90(100509(R)), 1  (2014)

  32. Vojta, M.: Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity. Adv Phys 58(6), 699 (2009)

    Article  ADS  Google Scholar 

  33. Komiya, S., Ando, Y., Segawa, K., Lavrov, A.N.: Electrical Resistivity Anisotropy from Self-Organized One Dimensionality in High-Temperature Superconductors. Phys Rev Lett 88(13), 137005 (2002)

  34. Kasahara, S., Shi, H.J., Hashimoto, K., Tonegawa, S., Mizukami, Y., Shibauchi, T., Sugimoto, K., Fukuda, T., Terashima, T., Nevidomskyy, A.H., Matsuda, Y.: Electronic nematicity above the structural and superconducting transition in BaFe\(_2\)(As\(_{1-x}\)P\(_x\))\(_2\). Nature 486, 382  (2012)

  35. Fernandes, R.M., Chubukov, A.S.J.: What drives nematic order in iron-based superconductors? Nat Phys 10, 97 (2014)

    Article  Google Scholar 

  36. Borzis, R.A., Grigeraj, S.A., Farrell, J., Perry, R.S., Listers, S.J.S., Leed, S.L., Tennanty D.A., Maeno, Y., Mackenzie, A.P.: Formation of a nematic fluid at high fields in Sr\(_3\)Ru\(_2\)O\(_7\). Science 315, 214 (2007)

  37. Yonezawa, S.: Nematic superconductivity in doped Bi\(_2\)Se\(_3\) topological superconductors. Condens Matter 4, 2 (2019)

    Article  Google Scholar 

  38. Venderbos, J.W., Kozii, V., Fu, L.: Identification of nematic superconductivity from the upper critical field. Phys Rev B 94(9), 094522 (2016)

  39. Shen, J., He, W.-Y., Yuan, N.F.Q., Huang, Z., Cho, C.-W., Lee, S.H., San Hor, Y., Law, K.T., Lortz, R. Nematic topological superconducting phase in Nb-doped Bi\(_2\)Se\(_3\). npj Quantum Mater 2(1), 1–7 (2017)

  40. Wan, S., Gu, Q., Li, H., Yang, H., Schneeloch, J., Zhong, R., Gu, G., Wen, H.-H.: Twofold symmetry of proximity-induced superconductivity in Bi\(_2\)Te\(_3\)/Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8+\delta }\) heterostructures revealed by scanning tunneling microscopy. Phys Rev B 101(22), 220503 (2020)

  41. Hor, Y.S., Checkelsky, J.G., Qu, D., Ong, N., Cava, R.J.: Superconductivity and non-metallicity induced by doping the topological insulators Bi\(_2\)Se\(_3\) and Bi\(_2\)Te\(_3\). J Phys Chem Solids 72(5), 572–576 (2011)

    Article  ADS  Google Scholar 

  42. Singh, Y., et al.: The ht and pt phase diagram of the superconducting phase in Pd: Bi\(_2\)Te\(_3\). J Supercond Nov Magn 29(8), 1975–1979 (2016)

    Article  Google Scholar 

  43. Sharma, M., Sang, L., Rani, P., Wang, X., Awana, V. Bulk superconductivity below 6 k in PdBi\(_2\)Te\(_3\) topological single crystal. J Supercond Nov Magn 1–5 (2020)

  44. Hamill, A., Heischmidt, B., Sohn, E., Shaffer, D., Tsai, K.-T., Zhang, X., Xi, X., Suslov, A., Berger, H., Forró, L., et al. Unexpected two-fold symmetric superconductivity in few-layer NbSe\(_2\). arXiv preprint arXiv:2004.02999 (2020)

Download references

Funding

This work was supported by National Natural Science Foundation of China (Nos. 11804194), Natural Science Foundation of Shandong Province, China (Nos. ZR2016AQ08).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Qiang Jing or Bo Liu.

Additional information

Publisher’s Note

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

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 447 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Jiao, F., Tian, Q. et al. Identify the Nematic Superconductivity of Topological Superconductor Pd\(_x\)Bi\(_2\)Te\(_3\) by Angle-dependent Upper Critical Field Measurement. J Supercond Nov Magn 34, 3045–3052 (2021). https://doi.org/10.1007/s10948-021-06055-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-021-06055-x

Keywords

Navigation