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
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
A.I. Buzdin, M.Y. Kupriyanov, JETP Lett. 53, 321 (1991). https://scholar.google.com.hk/scholar?hl=zh-CN &as_sdt=0
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
E.A. Demler, G. Arnold, M. Beasley, Phys. Rev. B 55, 15174 (1997). https://doi.org/10.1103/PhysRevB.55.15174
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
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
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
Z. Niu, Appl. Phys. Lett. 101, 062601 (2012). https://doi.org/10.1063/1.4743001
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
Z.P. Niu, D. Xing, Phys. Rev. Lett. 98, 057005 (2007). https://doi.org/10.1103/PhysRevLett.98.057005
B. Lv, Eur. Phys. J. B 83, 493 (2011). https://doi.org/10.1140/epjb/e2011-20044-y
A. Costa, J. Fabian, Phys. Rev. B 104, 174504 (2021). https://doi.org/10.1103/PhysRevB.104.174504
A. Mazanik, I. Bobkova, Phys. Rev. B 105, 144502 (2022). https://doi.org/10.1103/PhysRevB.105.144502
P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610 (1928). https://doi.org/10.1098/rspa.1928.0023
J.L. Mañes, F. Guinea, M.A. Vozmediano, Phys. Rev. B 75, 155424 (2007). https://doi.org/10.1103/PhysRevB.75.155424
G.W. Semenoff, Phys. Scr. 2012, 014016 (2012). https://doi.org/10.1088/0031-8949/2012/T146/014016
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
A. Bostwick, T. Ohta, T. Seyller, K. Horn, E. Rotenberg, Nat. Phys. 3, 36 (2007). https://doi.org/10.1038/nphys477
F. Bergeret, I. Tokatly, Phys. Rev. B 89, 134517 (2014). https://doi.org/10.1103/PhysRevB.89.134517
D. Beckmann, H. Weber, Hv. Löhneysen, Phys. Rev. Lett. 93, 197003 (2004). https://doi.org/10.1103/PhysRevLett.93.197003
M.F. Jakobsen, A. Brataas, A. Qaiumzadeh, Phys. Rev. Lett. 127, 017701 (2021). https://doi.org/10.1103/PhysRevLett.127.017701
A. Soori, Solid State Commun. 348, 114721 (2022). https://doi.org/10.1016/j.ssc.2022.114721
J. Linder, M. Zareyan, A. Sudbø, Phys. Rev. B 80, 014513 (2009). https://doi.org/10.1103/PhysRevB.80.014513
Y.-L. Yang, C. Bai, X.-D. Zhang, Eur. Phys. J. B 72, 217 (2009). https://doi.org/10.1140/epjb/e2009-00357-2
H. Mohammadpour, A. Asgari, Physica C 519, 124 (2015). https://doi.org/10.1016/j.physc.2015.09.002
R. Beiranvand, H. Hamzehpour, Sci. Rep. 10, 1 (2020). https://doi.org/10.1038/s41598-020-58799-6
R. Beiranvand, H. Hamzehpour, M. Alidoust, Phys. Rev. B 94, 125415 (2016). https://doi.org/10.1103/PhysRevB.94.125415
R. Beiranvand, H. Hamzehpour, M. Alidoust, Phys. Rev. B 96, 161403 (2017). https://doi.org/10.1103/PhysRevB.96.161403
D. Breunig, P. Burset, B. Trauzettel, Phys. Rev. Lett. 120, 037701 (2018). https://doi.org/10.1103/PhysRevLett.120.037701
Y. Wei, T. Liu, C. Huang, Y. Tao, F. Qi, Phys. Rev. Res. 3, 033131 (2021). https://doi.org/10.1103/PhysRevResearch.3.033131
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
T. Liu, F. Chen, Y. Tao, C. Huang, EPL 132, 37001 (2020). https://doi.org/10.1209/0295-5075/132/37001
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
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
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
B. Sachs, T. Wehling, M. Katsnelson, A. Lichtenstein, Phys. Rev. B 84, 195414 (2011). https://doi.org/10.1103/PhysRevB.84.195414
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
J. Jung, A.M. DaSilva, A.H. MacDonald, S. Adam, Nat. Commun. 6, 1 (2015). https://doi.org/10.1038/ncomms7308
M. Kindermann, B. Uchoa, D.L. Miller, Phys. Rev. B 86, 115415 (2012). https://doi.org/10.1103/PhysRevB.86.115415
P. San-Jose, A. Gutiérrez-Rubio, M. Sturla, F. Guinea, Phys. Rev. B 90, 115152 (2014). https://doi.org/10.1103/PhysRevB.90.115152
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
K. Zollner, M. Gmitra, T. Frank, J. Fabian, Phys. Rev. B 94, 155441 (2016). https://doi.org/10.1103/PhysRevB.94.155441
K. Zollner, J. Fabian, Phys. Rev. B 106, 035137 (2022). https://doi.org/10.1103/PhysRevB.106.035137
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
Z. Wang, C. Tang, R. Sachs, Y. Barlas, J. Shi, Phys. Rev. Lett. 114, 016603 (2015). https://doi.org/10.1103/PhysRevLett.114.016603
A. Dyrdał, J. Barnaś, 2D Mater 4, 034003 (2017). https://doi.org/10.1088/2053-1583/aa7bac
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
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
C. Beenakker, Phys. Rev. Lett. 97, 067007 (2006). https://doi.org/10.1103/PhysRevLett.97.067007
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
C. Beenakker, Rev. Mod. Phys. 80, 1337 (2008). https://doi.org/10.1103/RevModPhys.80.1337
P.-G. De Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, 2018)
H. Li, Phys. Rev. B 94, 075428 (2016). https://doi.org/10.1103/PhysRevB.94.075428
J. Linder, T. Yokoyama, Phys. Rev. B 89, 020504 (2014). https://doi.org/10.1103/PhysRevB.89.020504
K. Halterman, O.T. Valls, M. Alidoust, Phys. Rev. Lett. 111, 046602 (2013). https://doi.org/10.1103/PhysRevLett.111.046602
G. Blonder, M. Tinkham, T. Klapwijk, Phys. Rev. B 25, 4515 (1982). https://doi.org/10.1103/PhysRevB.25.4515
W. Zeng, R. Shen, Phys. Rev. B 104, 075436 (2021). https://doi.org/10.1103/PhysRevB.104.075436
Z.P. Niu, J. Phys.: Condens. Matter 31, 485701 (2019). https://doi.org/10.1088/1361-648X/ab351b
C. Benjamin, J.K. Pachos, Phys. Rev. B 78, 235403 (2008). https://doi.org/10.1103/PhysRevB.78.235403
W.-T. Lu, Q.-F. Sun, Phys. Rev. B 104, 045418 (2021). https://doi.org/10.1103/PhysRevB.104.045418
J. Cayssol, Phys. Rev. Lett. 100, 147001 (2008). https://doi.org/10.1103/PhysRevLett.100.147001
M. Veldhorst, A. Brinkman, Phys. Rev. Lett. 105, 107002 (2010). https://doi.org/10.1103/PhysRevLett.105.107002
W. Chen, R. Shen, L. Sheng, B. Wang, D. Xing, Phys. Rev. B 84, 115420 (2011). https://doi.org/10.1103/PhysRevB.84.115420
C. Bai, Y. Zou, W.-K. Lou, K. Chang, Phys. Rev. B 90, 195445 (2014). https://doi.org/10.1103/PhysRevB.90.195445
Y.S. Ang, L. Ang, C. Zhang, Z. Ma, Phys. Rev. B 93, 041422 (2016). https://doi.org/10.1103/PhysRevB.93.041422
W. Zeng, R. Shen, Phys. Rev. B 106, 094503 (2022). https://doi.org/10.1103/PhysRevB.106.094503
Acknowledgements
This work is supported by the National Key R &D Program of China (Grant No. 2022YFA1403601).
Author information
Authors and Affiliations
Contributions
WY: derivation of equations, numerical calculations, writing, and reviewing. WZ: writing, and reviewing. RS: writing, and reviewing.
Corresponding author
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.
About this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-023-00555-6