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超导体的磁性杂质效应以及其中存在的束缚态(即Yu-Shiba-Rusinov 态)一直受到较多的关注. 最近, 在实验室中, 成功发现了石墨烯类超导材料中Yu-Shiba-Rusinov 态的存在. 本文在实空间建立描述石墨烯材料超导态的有效哈密顿量, 考虑单个磁性杂质, 构造Bogoliubov-de Gennes (BdG)方程, 并对超导序参量做自洽计算, 在此基础上, 理论研究了石墨烯类超导体的磁性杂质效应. 计算结果显示, 仅当超导的配对对称性是传统的s波配对时, 能隙内会出现Yu-Shiba-Rusinov 束缚态, 束缚态的位置以及强度和杂质的磁矩有关, 且强度显示出了明显的正负非对称性, 但对于p+ip和d+id配对对称性, 则不存在能隙内的束缚态. 本文的理论计算结果一方面对实验现象做了合理解释, 另一方面指出了石墨烯和传统超导组成的异质结系统, 石墨烯层由于临近效应诱导出来的超导配对项仍然是s波配对.The magnetic impurity effects and the existence of bound states (i.e. Yu-Shiba-Rusinov states) in superconductors have been a topic of great interest. Recently, the existence of Yu-Shiba-Rusinov states in graphene-based superconducting materials has been successfully observed in the laboratory. In this work, an effective Hamiltonian in real space is established to describe the superconducting state of graphene materials by considering a single magnetic impurity. Thus the Bogoliubov-de Gennes (BdG) equation is constructed and the self-consistency calculations of the superconducting order parameter are conducted. On this basis, the effects of magnetic impurities on graphene-like superconductors are investigated theoretically. The numerical results show that the Yu-Shiba-Rusinov state can only appear in the symmetry of the superconducting pair of the traditional s-wave coupling. The position and strength of the bound state are related to the magnetic moment of the impurity, showing a notable electron-hole asymmetry. There are no bound states in the energy gap for other pairing symmetries. This theoretical calculation not only provides a reasonable explanation for experimental phenomena, but also demonstrates that the heterojunction system composed of graphene and traditional superconductors has an s-wave superconducting pairing induced by the proximity effect in the graphene layer.
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Keywords:
- graphene /
- superconductor /
- magnetic impurity /
- bound state
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图 2 (a) 平均粒子数
$ n_i $ 的空间分布; (b) 局域磁矩$ m_i $ 的空间分布Fig. 2. (a) Spatial distribution of the on-site particle number
$ n_i $ ; (b) spatial distribution of the local magnetic moment$ m_i $ .
图 3 s波配对情况下磁性杂质附近的局域电子态密度的计算结果 (a) 杂质点位置的局域电子态密度; (b) 杂质最近邻格点上的局域电子态密度
Fig. 3. Numerical results of the local density of states near the magnetic impurity site for the s-wave graphene based superconductor: (a) The local density of states at the impurity site; (b) the local density of states at the nearest neighbor site of the impurity.
图 4 d+id波和p+ip波配对情况下磁性杂质附近的局域电子态密度的计算结果 (a) d+id配对杂质点位置的局域电子态密度; (b) d+id 配对杂质最近邻格点上的局域电子态密度; (c) p+ip配对杂质点位置的局域电子态密度; (d) p+ip配对杂质最近邻格点上的局域电子态密度
Fig. 4. Numerical results of the local density of states near the magnetic impurity site for the d+id-wave and p+ip-wave graphene based superconductor: (a) The local density of states at the impurity site for the d+id pairing symmetry; (b) the local density of states at the nearest neighbor site of the impurity for the d+id pairing symmetry; (c) the local density of states at the impurity site for the p+ip pairing symmetry; (d) the local density of states at the nearest neighbor site of the impurity for the p+ip pairing symmetry.
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[1] Tonnoir C, Kimouche A, Coraux J, Magaud L, Delsol B, Gilles B, Chapelier C 2013 Phys. Rev. Lett. 111 246805
Google Scholar
[2] Ichinokura S, Sugawara K, Takayama A, Takahashi T, Hasegawa S 2016 Acs Nano 10 2761
Google Scholar
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Google Scholar
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Google Scholar
[5] Zhou H, Holleis L, Saito Y, Cohen L, Huynh W, Patterson C L, Yang F, Taniguchi T, Watanabe K, Young A F 2022 Science 375 774
Google Scholar
[6] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43
Google Scholar
[7] Cao Y, Park J M, Watanabe K, Taniguchi T, Jarillo-Herrero P 2021 Nature 595 526
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Yu L 1965 Acta Phys. Sin. 21 75
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[29] Zuo X J, An J, Gong C D 2008 Phys. Rev.B 77 144512
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[30] Zuo X J, An J, Gong C D 2008 Phys. Rev.B 77 212508
Google Scholar
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