Skip to main content
Log in

Pure equal-spin and opposite-spin crossed Andreev reflection in spin-orbit-coupled graphene

  • Regular Article - Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We theoretically investigate the nonlocal transport in the ferromagnet/s-wave superconductor/Rashba spin-orbit coupled region/ferromagnet hybrid junction composed of the gapped graphene lattices. The equal-spin crossed Andreev reflection (ECAR) and the opposite-spin crossed Andreev reflection (OCAR) can be generated separately. The ECAR dominant transport and the OCAR dominant one appear for the junction with antiparallel and parallel magnetization of two ferromagnetic leads, respectively. The pure ECAR (OCAR) is achieved not only at the Dirac point but over a large voltage range, suggesting the highly efficient nonlocal splitting of the Cooper pairs with spin-triplet (spin-singlet) pairing correlations.

Graphic abstract

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

Similar content being viewed by others

Data availability statements

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: There are no associated data available.].

References

  1. A.I. Buzdin, M.Y. Kupriyanov, JETP Lett. 53, 321 (1991). https://scholar.google.com.hk/scholar?hl=zh-CN &as_sdt=0

  2. Z. Radović, M. Ledvij, L. Dobrosavljević-Grujić, A.I. Buzdin, J.R. Clem, Phys. Rev. B 44, 759 (1991). https://doi.org/10.1103/PhysRevB.44.759

    Article  ADS  Google Scholar 

  3. E.A. Demler, G. Arnold, M. Beasley, Phys. Rev. B 55, 15174 (1997). https://doi.org/10.1103/PhysRevB.55.15174

    Article  ADS  Google Scholar 

  4. C. Visani, Z. Sefrioui, J. Tornos, C. Leon, J. Briatico, M. Bibes, A. Barthélémy, J. Santamaria, J.E. Villegas, Nat. Phys. 8, 539 (2012). https://doi.org/10.1038/nphys2318

    Article  Google Scholar 

  5. V. Pena, Z. Sefrioui, D. Arias, C. Leon, J. Santamaria, M. Varela, S. Pennycook, J. Martinez, Phys. Rev. B 69, 224502 (2004). https://doi.org/10.1103/PhysRevB.69.224502

    Article  ADS  Google Scholar 

  6. R.S. Keizer, S.T. Gönnenwein, T.M. Klapwijk, G. Miao, G. Xiao, A. Gupta, Nature 439, 825 (2006). https://doi.org/10.1038/nature04499

    Article  ADS  Google Scholar 

  7. Z. Niu, Appl. Phys. Lett. 101, 062601 (2012). https://doi.org/10.1063/1.4743001

    Article  ADS  Google Scholar 

  8. C. Feng, Z.M. Zheng, R. Shen, B. Wang, D. Xing, Phys. Rev. B 81, 224510 (2010). https://doi.org/10.1103/PhysRevB.81.224510

    Article  ADS  Google Scholar 

  9. Z.P. Niu, D. Xing, Phys. Rev. Lett. 98, 057005 (2007). https://doi.org/10.1103/PhysRevLett.98.057005

    Article  ADS  Google Scholar 

  10. B. Lv, Eur. Phys. J. B 83, 493 (2011). https://doi.org/10.1140/epjb/e2011-20044-y

    Article  ADS  Google Scholar 

  11. A. Costa, J. Fabian, Phys. Rev. B 104, 174504 (2021). https://doi.org/10.1103/PhysRevB.104.174504

    Article  ADS  Google Scholar 

  12. A. Mazanik, I. Bobkova, Phys. Rev. B 105, 144502 (2022). https://doi.org/10.1103/PhysRevB.105.144502

    Article  ADS  Google Scholar 

  13. P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610 (1928). https://doi.org/10.1098/rspa.1928.0023

    Article  ADS  Google Scholar 

  14. J.L. Mañes, F. Guinea, M.A. Vozmediano, Phys. Rev. B 75, 155424 (2007). https://doi.org/10.1103/PhysRevB.75.155424

    Article  ADS  Google Scholar 

  15. G.W. Semenoff, Phys. Scr. 2012, 014016 (2012). https://doi.org/10.1088/0031-8949/2012/T146/014016

    Article  Google Scholar 

  16. I. Pletikosić, M. Kralj, P. Pervan, R. Brako, J. Coraux, A. N’diaye, C. Busse, T. Michely, Phys. Rev. Lett. 102, 056808 (2009). https://doi.org/10.1103/PhysRevLett.102.056808

    Article  ADS  Google Scholar 

  17. A. Bostwick, T. Ohta, T. Seyller, K. Horn, E. Rotenberg, Nat. Phys. 3, 36 (2007). https://doi.org/10.1038/nphys477

    Article  Google Scholar 

  18. F. Bergeret, I. Tokatly, Phys. Rev. B 89, 134517 (2014). https://doi.org/10.1103/PhysRevB.89.134517

    Article  ADS  Google Scholar 

  19. D. Beckmann, H. Weber, Hv. Löhneysen, Phys. Rev. Lett. 93, 197003 (2004). https://doi.org/10.1103/PhysRevLett.93.197003

    Article  ADS  Google Scholar 

  20. M.F. Jakobsen, A. Brataas, A. Qaiumzadeh, Phys. Rev. Lett. 127, 017701 (2021). https://doi.org/10.1103/PhysRevLett.127.017701

    Article  ADS  Google Scholar 

  21. A. Soori, Solid State Commun. 348, 114721 (2022). https://doi.org/10.1016/j.ssc.2022.114721

    Article  Google Scholar 

  22. J. Linder, M. Zareyan, A. Sudbø, Phys. Rev. B 80, 014513 (2009). https://doi.org/10.1103/PhysRevB.80.014513

    Article  ADS  Google Scholar 

  23. Y.-L. Yang, C. Bai, X.-D. Zhang, Eur. Phys. J. B 72, 217 (2009). https://doi.org/10.1140/epjb/e2009-00357-2

    Article  ADS  Google Scholar 

  24. H. Mohammadpour, A. Asgari, Physica C 519, 124 (2015). https://doi.org/10.1016/j.physc.2015.09.002

    Article  ADS  Google Scholar 

  25. R. Beiranvand, H. Hamzehpour, Sci. Rep. 10, 1 (2020). https://doi.org/10.1038/s41598-020-58799-6

    Article  Google Scholar 

  26. R. Beiranvand, H. Hamzehpour, M. Alidoust, Phys. Rev. B 94, 125415 (2016). https://doi.org/10.1103/PhysRevB.94.125415

    Article  ADS  Google Scholar 

  27. R. Beiranvand, H. Hamzehpour, M. Alidoust, Phys. Rev. B 96, 161403 (2017). https://doi.org/10.1103/PhysRevB.96.161403

    Article  ADS  Google Scholar 

  28. D. Breunig, P. Burset, B. Trauzettel, Phys. Rev. Lett. 120, 037701 (2018). https://doi.org/10.1103/PhysRevLett.120.037701

    Article  ADS  Google Scholar 

  29. Y. Wei, T. Liu, C. Huang, Y. Tao, F. Qi, Phys. Rev. Res. 3, 033131 (2021). https://doi.org/10.1103/PhysRevResearch.3.033131

    Article  Google Scholar 

  30. Z. Tao, F. Chen, L. Zhou, B. Li, Y. Tao, J. Wang, J. Phys.: Condens. Matter 30, 225302 (2018). https://doi.org/10.1088/1361-648X/aabdfd

    Article  ADS  Google Scholar 

  31. T. Liu, F. Chen, Y. Tao, C. Huang, EPL 132, 37001 (2020). https://doi.org/10.1209/0295-5075/132/37001

    Article  Google Scholar 

  32. G. Wang, T. Dvir, G.P. Mazur, C.-X. Liu, N. van Loo, S.L. Ten Haaf, A. Bordin, S. Gazibegovic, G. Badawy, E.P. Bakkers et al., Nature (2022). https://doi.org/10.1038/s41586-022-05352-2

    Article  Google Scholar 

  33. S.Y. Zhou, G.-H. Gweon, A. Fedorov, d First PN, W. De Heer, D.-H. Lee, F. Guinea, A. Castro Neto, Nat. Mater. 6, 770 (2007). https://doi.org/10.1038/nmat2003

    Article  ADS  Google Scholar 

  34. F. Varchon, R. Feng, J. Hass, X. Li, B.N. Nguyen, C. Naud, P. Mallet, J.-Y. Veuillen, C. Berger, E.H. Conrad et al., Phys. Rev. Lett. 99, 126805 (2007). https://doi.org/10.1103/PhysRevLett.99.126805

    Article  ADS  Google Scholar 

  35. B. Sachs, T. Wehling, M. Katsnelson, A. Lichtenstein, Phys. Rev. B 84, 195414 (2011). https://doi.org/10.1103/PhysRevB.84.195414

    Article  ADS  Google Scholar 

  36. B. Hunt, J.D. Sanchez-Yamagishi, A.F. Young, M. Yankowitz, B.J. LeRoy, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero et al., Science 340, 1427 (2013). https://doi.org/10.1126/science.1237240

    Article  ADS  Google Scholar 

  37. J. Jung, A.M. DaSilva, A.H. MacDonald, S. Adam, Nat. Commun. 6, 1 (2015). https://doi.org/10.1038/ncomms7308

    Article  Google Scholar 

  38. M. Kindermann, B. Uchoa, D.L. Miller, Phys. Rev. B 86, 115415 (2012). https://doi.org/10.1103/PhysRevB.86.115415

    Article  ADS  Google Scholar 

  39. P. San-Jose, A. Gutiérrez-Rubio, M. Sturla, F. Guinea, Phys. Rev. B 90, 115152 (2014). https://doi.org/10.1103/PhysRevB.90.115152

    Article  ADS  Google Scholar 

  40. G. Casiano-Jiménez, C. Ortega-López, J.A. Rodríguez-Martínez, M.G. Moreno-Armenta, M.J. Espitia-Rico, Coatings 12, 237 (2022). https://doi.org/10.3390/coatings12020237

    Article  Google Scholar 

  41. K. Zollner, M. Gmitra, T. Frank, J. Fabian, Phys. Rev. B 94, 155441 (2016). https://doi.org/10.1103/PhysRevB.94.155441

    Article  ADS  Google Scholar 

  42. K. Zollner, J. Fabian, Phys. Rev. B 106, 035137 (2022). https://doi.org/10.1103/PhysRevB.106.035137

    Article  ADS  Google Scholar 

  43. P. Wei, S. Lee, F. Lemaitre, L. Pinel, D. Cutaia, W. Cha, F. Katmis, Y. Zhu, D. Heiman, J. Hone et al., Nat. Mater. 15, 711 (2016). https://doi.org/10.1038/nmat4603

    Article  ADS  Google Scholar 

  44. Z. Wang, C. Tang, R. Sachs, Y. Barlas, J. Shi, Phys. Rev. Lett. 114, 016603 (2015). https://doi.org/10.1103/PhysRevLett.114.016603

    Article  ADS  Google Scholar 

  45. A. Dyrdał, J. Barnaś, 2D Mater 4, 034003 (2017). https://doi.org/10.1088/2053-1583/aa7bac

    Article  Google Scholar 

  46. A. Avsar, J.Y. Tan, T. Taychatanapat, J. Balakrishnan, G. Koon, Y. Yeo, J. Lahiri, A. Carvalho, A. Rodin, E.O. Farrell et al., Nat. Commun. 5, 1 (2014). https://doi.org/10.1038/ncomms5875

    Article  Google Scholar 

  47. T. Wakamura, F. Reale, P. Palczynski, S. Guéron, C. Mattevi, H. Bouchiat, Phys. Rev. Lett. 120, 106802 (2018). https://doi.org/10.1103/PhysRevLett.120.106802

    Article  ADS  Google Scholar 

  48. C. Beenakker, Phys. Rev. Lett. 97, 067007 (2006). https://doi.org/10.1103/PhysRevLett.97.067007

    Article  ADS  Google Scholar 

  49. H.B. Heersche, P. Jarillo-Herrero, J.B. Oostinga, L.M. Vandersypen, A.F. Morpurgo, Solid State Commun. 143, 72 (2007). https://doi.org/10.1016/j.ssc.2007.02.044

    Article  ADS  Google Scholar 

  50. C. Beenakker, Rev. Mod. Phys. 80, 1337 (2008). https://doi.org/10.1103/RevModPhys.80.1337

    Article  ADS  Google Scholar 

  51. P.-G. De Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, 2018)

    Book  MATH  Google Scholar 

  52. H. Li, Phys. Rev. B 94, 075428 (2016). https://doi.org/10.1103/PhysRevB.94.075428

    Article  ADS  Google Scholar 

  53. J. Linder, T. Yokoyama, Phys. Rev. B 89, 020504 (2014). https://doi.org/10.1103/PhysRevB.89.020504

    Article  ADS  Google Scholar 

  54. K. Halterman, O.T. Valls, M. Alidoust, Phys. Rev. Lett. 111, 046602 (2013). https://doi.org/10.1103/PhysRevLett.111.046602

    Article  ADS  Google Scholar 

  55. G. Blonder, M. Tinkham, T. Klapwijk, Phys. Rev. B 25, 4515 (1982). https://doi.org/10.1103/PhysRevB.25.4515

  56. W. Zeng, R. Shen, Phys. Rev. B 104, 075436 (2021). https://doi.org/10.1103/PhysRevB.104.075436

    Article  ADS  Google Scholar 

  57. Z.P. Niu, J. Phys.: Condens. Matter 31, 485701 (2019). https://doi.org/10.1088/1361-648X/ab351b

    Article  Google Scholar 

  58. C. Benjamin, J.K. Pachos, Phys. Rev. B 78, 235403 (2008). https://doi.org/10.1103/PhysRevB.78.235403

    Article  ADS  Google Scholar 

  59. W.-T. Lu, Q.-F. Sun, Phys. Rev. B 104, 045418 (2021). https://doi.org/10.1103/PhysRevB.104.045418

    Article  ADS  Google Scholar 

  60. J. Cayssol, Phys. Rev. Lett. 100, 147001 (2008). https://doi.org/10.1103/PhysRevLett.100.147001

    Article  ADS  Google Scholar 

  61. M. Veldhorst, A. Brinkman, Phys. Rev. Lett. 105, 107002 (2010). https://doi.org/10.1103/PhysRevLett.105.107002

    Article  ADS  Google Scholar 

  62. W. Chen, R. Shen, L. Sheng, B. Wang, D. Xing, Phys. Rev. B 84, 115420 (2011). https://doi.org/10.1103/PhysRevB.84.115420

    Article  ADS  Google Scholar 

  63. C. Bai, Y. Zou, W.-K. Lou, K. Chang, Phys. Rev. B 90, 195445 (2014). https://doi.org/10.1103/PhysRevB.90.195445

    Article  ADS  Google Scholar 

  64. Y.S. Ang, L. Ang, C. Zhang, Z. Ma, Phys. Rev. B 93, 041422 (2016). https://doi.org/10.1103/PhysRevB.93.041422

    Article  ADS  Google Scholar 

  65. W. Zeng, R. Shen, Phys. Rev. B 106, 094503 (2022). https://doi.org/10.1103/PhysRevB.106.094503

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Key R &D Program of China (Grant No. 2022YFA1403601).

Author information

Authors and Affiliations

Authors

Contributions

WY: derivation of equations, numerical calculations, writing, and reviewing. WZ: writing, and reviewing. RS: writing, and reviewing.

Corresponding author

Correspondence to R. Shen.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, W., Zeng, W. & Shen, R. Pure equal-spin and opposite-spin crossed Andreev reflection in spin-orbit-coupled graphene. Eur. Phys. J. B 96, 83 (2023). https://doi.org/10.1140/epjb/s10051-023-00555-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-023-00555-6

Navigation