Skip to main content
Log in

Pairing symmetry in monolayer of orthorhombic CoSb

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Ferromagnetism and superconductivity are generally considered to be antagonistic phenomena in condensed matter physics. Here, we theoretically study the interplay between the ferromagnetic and superconducting orders in a recent discovered monolayered CoSb superconductor with an orthorhombic symmetry and net magnetization, and demonstrate the pairing symmetry of CoSb as a candidate of non-unitary superconductor with time-reversal symmetry breaking. By performing the group theory analysis and the first-principles calculations, the superconducting order parameter is suggested to be a triplet pairing with the irreducible representation of 3B2u, which displays intriguing nodal points and non-zero periodic modulation of Cooper pair spin polarization on the Fermi surface topologies. These findings not only provide a significant theoretical insight into the coexistence of superconductivity and ferromagnetism, but also reveal the exotic spin polarized Cooper pairing driven by ferromagnetic spin fluctuations in a triplet superconductor.

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.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.- Usp. 44(10S), 131 (2001)

    Article  ADS  Google Scholar 

  4. D. A. Ivanov, Non-Abelian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett. 86(2), 268 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. K. T. Law, P. A. Lee, and T. K. Ng, Majorana fermion induced resonant Andreev reflection, Phys. Rev. Lett. 103(23), 237001 (2009)

    Article  ADS  Google Scholar 

  7. J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Generic new platform for topological quantum computation using semiconductor heterostructures, Phys. Rev. Lett. 104(4), 040502 (2010)

    Article  ADS  Google Scholar 

  8. G. Xu, B. Lian, P. Tang, X. L. Qi, and S. C. Zhang, Topological superconductivity on the surface of Fe-based superconductors, Phys. Rev. Lett. 117(4), 047001 (2016)

    Article  ADS  Google Scholar 

  9. N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B61(15), 10267 (2000)

    Article  Google Scholar 

  10. G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360(2–3), 362 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  11. N. Read and G. Moore, Fractional quantum Hall effect and nonabelian statistics, Prog. Theor. Phys. Suppl. 107, 157 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  12. A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (Amsterdam) 303(1), 2 (2003)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80(3), 1083 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75(7), 076501 (2012)

    Article  ADS  Google Scholar 

  15. C. W. J. Beenakker, Search for Majorana fermions in superconductors, Annu. Rev. Condens. Matter Phys. 4(1), 113 (2013)

    Article  ADS  Google Scholar 

  16. S. R. Elliott and M. Franz, Majorana fermions in nuclear, particle, and solid-state physics, Rev. Mod. Phys. 87(1), 137 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  17. R. Aguado, Majorana quasiparticles in condensed matter, Riv. Nuovo Cim. 40, 523 (2017)

    ADS  Google Scholar 

  18. V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336(6084), 1003 (2012)

    Article  ADS  Google Scholar 

  19. M. Deng, C. Yu, G. Huang, M. Larsson, P. Caroff, and H. Xu, Anomalous zero-bias conductance peak in a Nb-InSb nanowire-Nb hybrid device, Nano Lett. 12(12), 6414 (2012)

    Article  ADS  Google Scholar 

  20. A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions, Nat. Phys. 8(12), 887 (2012)

    Article  Google Scholar 

  21. M. T. Deng, S. Vaitiekènas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, and C. M. Marcus, Majorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354(6319), 1557 (2016)

    Article  ADS  Google Scholar 

  22. H. Zhang, C. X. Liu, S. Gazibegovic, D. Xu, J. A. Logan, G. Wang, N. van Loo, J. D. S. Bommer, M. W. A. de Moor, D. Car, R. L. M. Ophet Veld, P. J. van Veld-hoven, S. Koelling, M. A. Verheijen, M. Pendharkar, D. J. Pennachio, B. Shojaei, J. Sue Lee, C. J. Palmstrøm, E. P. A. M. Bakkers, S. Das Sarma, and L. P. Kouwenhoven, Quantized Majorana conductance, Nature 556(7699), 74 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. J. P. Xu, M. X. Wang, Z. L. Liu, J. F. Ge, X. Yang, C. Liu, Z. A. Xu, D. Guan, C. L. Gao, D. Qian, Y. Liu, Q. H. Wang, F. C. Zhang, Q. K. Xue, and J. F. Jia, Experimental detection of a Majorana mode in the core of a magnetic vortex inside a topological insulator-superconductor Bi2Te3/NbSe2 heterostructure, Phys. Rev. Lett. 114(1), 017001 (2015)

    Article  ADS  Google Scholar 

  25. H. H. Sun, K. W. Zhang, L. H. Hu, C. Li, G. Y. Wang, H. Y. Ma, Z. A. Xu, C. L. Gao, D. D. Guan, Y. Y. Li, C. Liu, D. Qian, Y. Zhou, L. Fu, S. C. Li, F. C. Zhang, and J. F. Jia, Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor, Phys. Rev. Lett. 116(25), 257003 (2016)

    Article  ADS  Google Scholar 

  26. A. Banerjee, C. A. Bridges, J. Q. Yan, A. A. Aczel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus, and S. E. Nagler, Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet, Nat. Mater. 15(7), 733 (2016)

    Article  ADS  Google Scholar 

  27. J. X. Yin, Z. Wu, J. H. Wang, Z. Y. Ye, J. Gong, X. Y. Hou, L. Shan, A. Li, X. J. Liang, X. X. Wu, J. Li, C. S. Ting, Z. Q. Wang, J. P. Hu, P. H. Hor, H. Ding, and S. H. Pan, Observation of a robust zero-energy bound state in iron-based superconductor Fe(Te,Se), Nat. Phys. 11(7), 543 (2015)

    Article  Google Scholar 

  28. Q. Liu, C. Chen, T. Zhang, R. Peng, Y. J. Yan, C. H. P. Wen, X. Lou, Y. L. Huang, J. P. Tian, X. L. Dong, G. W. Wang, W. C. Bao, Q. H. Wang, Z. P. Yin, Z. X. Zhao, and D. L. Feng, Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe, Phys. Rev. X 8(4), 041056 (2018)

    Google Scholar 

  29. M. Chen, X. Chen, H. Yang, Z. Du, and H. H. Wen, Superconductivity with twofold symmetry in Bi2Te3/FeTe0.55Se0.45 heterostructures, Sci. Adv. 4(6), eaat1084 (2018)

    Article  ADS  Google Scholar 

  30. D. Wang, L. Kong, P. Fan, H. Chen, S. Zhu, W. Liu, L. Cao, Y. Sun, S. Du, J. Schneeloch, R. Zhong, G. Gu, L. Fu, H. Ding, and H. J. Gao, Evidence for Majorana bound states in an iron-based superconductor, Science 362(6412), 333 (2018)

    Article  ADS  Google Scholar 

  31. S. Zhu, L. Kong, L. Cao, H. Chen, S. Du, Y. Xing, W. Liu, D. Wang, C. Shen, F. Yang, J. Schneeloch, R. Zhong, G. Gu, L. Fu, Y. Y. Zhang, H. Ding, and H. J. Gao, Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor, Science 367, eaax0274 (2019)

    Google Scholar 

  32. C. Chen, K. Jiang, Y. Zhang, C. Liu, Y. Liu, Z. Wang, and J. Wang, Atomic line defects and zero-energy end states in monolayer Fe(Te,Se) high-temperature superconductors, arXiv: 2003.04539 (2020)

  33. C. Liu, C. Chen, X. Liu, Z. Wang, Y. Liu, S. Ye, Z. Q. Wang, J. P. Hu, and J. Wang, Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit, Sci. Adv. 6(13), eaax7547 (2020)

    Article  ADS  Google Scholar 

  34. M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63(2), 239 (1991)

    Article  ADS  Google Scholar 

  35. V. Kozii, J. W. F. Venderbos, and L. Fu, Three-dimensional Majorana fermions in chiral superconductors, Sci. Adv. 2(12), e1601835 (2016)

    Article  ADS  Google Scholar 

  36. V. Ambegaokar and N. D. Mermin, Thermal anomalies of 3He: Pairing in a magnetic field, Phys. Rev. Lett. 30(3), 81 (1973)

    Article  ADS  Google Scholar 

  37. A. J. Leggett, A theoretical description of the new phases of liquid He3, Rev. Mod. Phys. 47(2), 331 (1975)

    Article  ADS  Google Scholar 

  38. J. C. Wheatley, Experimental properties of superfluid 3He, Rev. Mod. Phys. 47(2), 415 (1975)

    Article  ADS  Google Scholar 

  39. T. Ohmi and K. Machida, Nonunitary superconducting state in UPt3, Phys. Rev. Lett. 71(4), 625 (1993)

    Article  ADS  Google Scholar 

  40. J. A. Sauls, The order parameter for the superconducting phases of UPt3, Adv. Phys. 43(1), 113 (1994)

    Article  ADS  Google Scholar 

  41. H. Tou, Y. Kitaoka, K. Ishida, K. Asayama, N. Kimura, Y. Ōnuki, E. Yamamoto, Y. Haga, and K. Maezawa, Non-unitary spin-triplet superconductivity in UPt3: Evidence from 195Pt Knight shift study, Phys. Rev. Lett. 80(14), 3129 (1998)

    Article  ADS  Google Scholar 

  42. R. Joynt and L. Taillefer, The superconducting phases of UPt3, Rev. Mod. Phys. 74(1), 235 (2002)

    Article  ADS  Google Scholar 

  43. A. D. Hillier, J. Quintanilla, and R. Cywinski, Evidence for time-reversal symmetry breaking in the noncentrosymmetric superconductor LaNiC2, Phys. Rev. Lett. 102(11), 117007 (2009)

    Article  ADS  Google Scholar 

  44. J. Quintanilla, A. D. Hillier, J. F. Annett, and R. Cywinski, Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor LaNiC2, Phys. Rev. B 82(17), 174511 (2010)

    Article  ADS  Google Scholar 

  45. A. D. Hillier, J. Quintanilla, B. Mazidian, J. F. Annett, and R. Cywinski, Nonunitary triplet pairing in the centrosymmetric superconductor LaNiGa2, Phys. Rev. Lett. 109(9), 097001 (2012)

    Article  ADS  Google Scholar 

  46. S. K. Ghosh, G. Csire, P. Whittlesea, J. F. Annett, M. Gradhand, B. Újfalussy, and J. Quintanilla, Quantitative theory of triplet pairing in the unconventional superconductor LaNiGa2, Phys. Rev. B 101, 100506(R) (2020)

    Article  ADS  Google Scholar 

  47. C. Ding, G. Gong, Y. Liu, F. Zheng, Z. Zhang, H. Yang, Z. Li, Y. Xing, J. Ge, K. He, W. Li, P. Zhang, J. Wang, L. Wang, and Q. K. Xue, Signature of superconductivity in orthorhombic CoSb monolayer films on SrTiO3(001), ACS Nano 13(9), 10434 (2019)

    Article  Google Scholar 

  48. J. F. Annett, Symmetry of the order parameter for high-temperature superconductivity, Adv. Phys. 39(2), 83 (1990)

    Article  ADS  Google Scholar 

  49. V. P. Mineev, Superconducting states in ferromagnetic metals, Phys. Rev. B 66(13), 134504 (2002)

    Article  ADS  Google Scholar 

  50. K. V. Samokhin and M. B. Walker, Order parameter symmetry in ferromagnetic superconductors, Phys. Rev. B 66(17), 174501 (2002)

    Article  ADS  Google Scholar 

  51. D. J. Singh and L. Nordstrom, Planewaves, Pseudopotentials, and the LAPW Method, 2nd Ed., Springer-Verlag, Berlin, 2006

    Google Scholar 

  52. P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, in: WIEN2K, An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties, edited by K. Schwarz, Technical University Wien, Austria, 2001

    Google Scholar 

  53. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)

    Article  ADS  Google Scholar 

  54. W. Li, X. Y. Wei, J. X. Zhu, C. S. Ting, and Y. Chen, Pressure-induced topological quantum phase transition in Sb2Se3, Phys. Rev. B 89(3), 035101 (2014)

    Article  ADS  Google Scholar 

  55. J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals, J. Phys. Chem. Solids 10(2–3), 87 (1959)

    Article  ADS  Google Scholar 

  56. W. Ding, J. Zeng, W. Qin, P. Cui, and Z. Zhang, Exploring high transition temperature superconductivity in a freestanding or SrTiO3-supported CoSb monolayer, Phys. Rev. Lett. 124(2), 027002 (2020)

    Article  ADS  Google Scholar 

  57. M. Y. Zou, J. N. Chu, H. Zhang, T. Z. Yuan, P. Cheng, W. T. Jin, D. Jiang, X. G. Xu, W. J. Yu, Z. H. An, X. Y. Wei, G. Mu, and W. Li, Evidence the ferromagnetic order on CoSb layer of LaCoSb2, Phys. Rev. B 101(15), 155138 (2020)

    Article  ADS  Google Scholar 

  58. W. Li, J. X. Zhu, Y. Chen, and C. S. Ting, First-principles calculations of the electronic structure of iron-pnictide EuFe2(As,P)2 superconductors: Evidence for antiferromagnetic spin order, Phys. Rev. B 86(15), 155119 (2012)

    Article  ADS  Google Scholar 

  59. X. G. Xu and W. Li, Electronic and magnetic structures of ternary iron telluride KFe2Te2, Front. Phys. 10(4), 107403 (2015)

    Article  ADS  Google Scholar 

  60. D. J. Singh, Electronic structure and doping in BaFe2As2 and LiFeAs: Density functional calculations, Phys. Rev. B 78(9), 094511 (2008)

    Article  ADS  Google Scholar 

  61. W. C. Huang, W. Li, and X. Liu, Exotic ferromagnetism in the two-dimensional quantum materials C3N, Front. Phys. 13(2), 137104 (2018)

    Article  ADS  Google Scholar 

  62. Z. Zhou, W. T. Jin, W. Li, S. Nandi, B. Ouladdiaf, Z. Yan, X. Wei, X. Xu, W. H. Jiao, N. Qureshi, Y. Xiao, Y. Su, G. H. Cao, and Th. Brückel, Universal critical behavior in the ferromagnetic superconductor Eu(Fe0.75Ruo.25)2As2, Phys. Rev. B 100, 060406(R) (2019)

    Article  ADS  Google Scholar 

  63. J. B. Goodenough, Theory of the role of covalence in the perovskite-type manganites [La,M(II)]MnO3, Phys. Rev. 100(2), 564 (1955)

    Article  ADS  Google Scholar 

  64. S. Maekawa, T. Tohyama, S. E. Barnes, S. Ishihara, W. Koshibae, and G. Khaliullin, Physics of Transition Metal Oxides, Berlin Heidelberg: Springer-Verlag, 2004

    Book  Google Scholar 

  65. W. Li, Z. Liu, Y. S. Wu, and Y. Chen, Exotic fractional topological states in a two-dimensional organometallic material, Phys. Rev. B 89(12), 125411 (2014)

    Article  ADS  Google Scholar 

  66. W. Li, J. Li, J. X. Zhu, Y. Chen, and C. S. Ting, Pairing symmetry in the iron-pnictide superconductor KFe2As2, EPL 99(5), 57006 (2012)

    Article  ADS  Google Scholar 

  67. K. Hattori and H. Tsunetsugu, p-wave superconductivity near a transverse saturation field, Phys. Rev. B 87(6), 064501 (2013)

    Article  ADS  Google Scholar 

  68. Y. Tada, S. Takayoshi, and S. Fujimoto, Magnetism and superconductivity in ferromagnetic heavy-fermion system UCoGe under in-plane magnetic fields, Phys. Rev. B 93(17), 174512 (2016)

    Article  ADS  Google Scholar 

  69. C. Kallin and J. Berlinsky, Chiral superconductors, Rep. Prog. Phys. 79(5), 054502 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11927807) and the Natural Science Foundation of Shanghai of China (Grant Nos. 19ZR1402600 and 20DZ1100604). W. L. also acknowledges the startup funding from Fudan University.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Xu-Guang Xu or Wei Li.

Additional information

arXiv: 2004.10200. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-020-1040-y.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, TZ., Zou, MY., Jin, WT. et al. Pairing symmetry in monolayer of orthorhombic CoSb. Front. Phys. 16, 43500 (2021). https://doi.org/10.1007/s11467-020-1040-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-020-1040-y

Keywords

Navigation