Impurity effect as a probe for the pairing symmetry of graphene-based superconductors
Yuan-Qiao Li1, Tao Zhou2,3,1()
1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China 3. Guangdong–Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
We study theoretically the single impurity effect on graphene-based superconductors. Four different pairing symmetries are discussed. Sharp in-gap resonant peaks are found near the impurity site for the d+id pairing symmetry and the p+ip pairing symmetry when the chemical potential is large. As the chemical potential decreases, the in-gap states are robust for the d + id pairing symmetry while they disappear for the p + ip pairing symmetry. Such in-gap peaks are absent for the fully gapped extended s-wave pairing symmetry and the nodal f-wave pairing symmetry. The existence of the ingap resonant peaks can be explained well based on the sign-reversal of the superconducting gap along different Fermi pockets and by analyzing the denominator of the T-matrix. All of the features may be checked by the experiments, providing a useful probe for the pairing symmetry of graphene-based superconductors.
. [J]. Frontiers of Physics, 2021, 16(4): 43502.
Yuan-Qiao Li, Tao Zhou. Impurity effect as a probe for the pairing symmetry of graphene-based superconductors. Front. Phys. , 2021, 16(4): 43502.
A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81(1), 109 (2009) https://doi.org/10.1103/RevModPhys.81.109
2
K. S. Novoselov, D. V. Andreeva, W. Ren, and G. Shan, Graphene and other two-dimensional materials, Front. Phys. 14(1), 13301 (2019) https://doi.org/10.1007/s11467-018-0835-6
3
C. Tonnoir, A. Kimouche, J. Coraux, L. Magaud, B. Delsol, B. Gilles, and C. Chapelier, Induced superconductivity in graphene grown on rhenium, Phys. Rev. Lett. 111(24), 246805 (2013) https://doi.org/10.1103/PhysRevLett.111.246805
4
S. Ichinokura, K. Sugawara, A. Takayama, T. Takahashi, and S. Hasegawa, Superconducting calcium-intercalated bilayer graphene, ACS Nano 10(2), 2761 (2016) https://doi.org/10.1021/acsnano.5b07848
5
J. Chapman, Y. Su, C. A. Howard, Dmytro Kundys, A. N. Grigorenko, F. Guinea, A. K. Geim, I. V. Grigorieva, and R. R. Nair, Superconductivity in Ca-doped graphene laminates, Sci. Rep. 6(1), 23254 (2016) https://doi.org/10.1038/srep23254
6
B. M. Ludbrook, G. Levy, P. Nigge, M. Zonno, M. Schneider, D. J. Dvorak, C. N. Veenstra, S. Zhdanovich, D. Wong, P. Dosanjh, C. Straßer, A. Stohr, S. Forti, C. R. Ast, U. Starke, and A. Damascelli, Evidence for superconductivity in Li-decorated monolayer graphene, Proc. Natl. Acad. Sci. USA 112(38), 11795 (2015) https://doi.org/10.1073/pnas.1510435112
7
A. Di Bernardo, O. Millo, M. Barbone, H. Alpern, Y. Kalcheim, U. Sassi, A. K. Ott, D. De Fazio, D. Yoon, M. Amado, A. C. Ferrari, J. Linder, and J. W. A. Robinson, p-wave triggered superconductivity in singlelayer graphene on an electron-doped oxide superconductor, Nat. Commun. 8(1), 14024 (2017) https://doi.org/10.1038/ncomms14817
8
Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature 556(7699), 43 (2018) https://doi.org/10.1038/nature26160
J. Linder, A. M. Black-Schaffer, T. Yokoyama, S. Doniach, and A. Sudbø, Josephson current in graphene: Role of unconventional pairing symmetries, Phys. Rev. B 80(9), 094522 (2009) https://doi.org/10.1103/PhysRevB.80.094522
12
A. M. Black-Schaffer and S. Doniach, Possibility of measuring intrinsic electronic correlations in graphene using a d-wave contact Josephson junction, Phys. Rev. B 81(1), 014517 (2010) https://doi.org/10.1103/PhysRevB.81.014517
13
T. Ma, F. Yang, H. Yao, and H. Q. Lin, Possible triplet p+ ip superconductivity in graphene at low filling, Phys. Rev. B 90(24), 245114 (2014) https://doi.org/10.1103/PhysRevB.90.245114
14
J. P. L. Faye, P. Sahebsara, and D. Senechal, Chiral triplet superconductivity on the graphene lattice, Phys. Rev. B 92(8), 085121 (2015) https://doi.org/10.1103/PhysRevB.92.085121
R. Nandkishore, L. S. Levitov, and A. V. Chubukov, Chiral superconductivity from repulsive interactions in doped grapheme, Nat. Phys. 8(2), 158 (2012) https://doi.org/10.1038/nphys2208
17
M. L. Kiesel, C. Platt, W. Hanke, D. A. Abanin, and R. Thomale, Competing many-body instabilities and unconventional superconductivity in grapheme, Phys. Rev. B 86(2), R020507 (2012) https://doi.org/10.1103/PhysRevB.86.020507
18
R. Nandkishore, R. Thomale, and A. V. Chubukov, Superconductivity from weak repulsion in hexagonal lattice systems, Phys. Rev. B 89(14), 144501 (2014) https://doi.org/10.1103/PhysRevB.89.144501
19
L. Y. Xiao, S. L. Yu, W. Wang, Z. J. Yao, and J. X. Li, Possible singlet and triplet superconductivity on honeycomb lattice, Europhys. Lett. 115(2), 27008 (2016) https://doi.org/10.1209/0295-5075/115/27008
20
M. V. Hosseini and M. Zareyan, Model of an exotic chiral superconducting phase in a graphene bilayer, Phys. Rev. Lett. 108(14), 147001 (2012) https://doi.org/10.1103/PhysRevLett.108.147001
21
J. L. Lado and J. Fernandez-Rossier, Unconventional Yu–Shiba–Rusinov states in hydrogenated grapheme, 2D Mater. 3(2), 025001 (2016) https://doi.org/10.1088/2053-1583/3/2/025001
22
T. Huang, L. Zhang, and T. Ma, Antiferromagnetically ordered Mott insulator and d+ id superconductivity in twisted bilayer graphene: A quantum Monte Carlo study, Sci. Bull. (Beijing) 64(5), 310 (2019) https://doi.org/10.1016/j.scib.2019.01.026
23
W. Chen, Y. Chu, T. Huang, and T. Ma, Metal-insulator transition and dominant d+ id pairing symmetry in twisted bilayer graphene, Phys. Rev. B 101(15), 155413 (2020) https://doi.org/10.1103/PhysRevB.101.155413
24
C. X. Zhao and J. F. Jia, Stanene: A good platform for topological insulator and topological superconductor, Front. Phys. 15(5), 53201 (2020) https://doi.org/10.1007/s11467-020-0965-5
A. V. Balatsky, I. Vekhter, and J. X. Zhu, Impurityinduced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78(2), 373 (2006) https://doi.org/10.1103/RevModPhys.78.373
27
D. G. Zhang, Nonmagnetic impurity resonances as a signature of sign-reversal pairing in FeAs-based superconductors, Phys. Rev. Lett. 103(18), 186402 (2009) https://doi.org/10.1103/PhysRevLett.103.186402
28
W. F. Tsai, Y. Y. Zhang, C. Fang, and J. P. Hu, Impurityinduced bound states in iron-based superconductors with s-wave cos(kx) · cos(ky) pairing symmetry, Phys. Rev. B 80(6), 064513 (2009) https://doi.org/10.1103/PhysRevB.80.064513
29
D. D. Wang, B. Liu, M. Liu, Y. F. Yang, and S. P. Feng, Impurity-induced bound states as a signature of pairing symmetry in multiband superconducting CeCu2Si2, Front. Phys. 14(1), 13501 (2019) https://doi.org/10.1007/s11467-018-0852-5
30
F. M. D. Pellegrino, G. G. N. Angilella, and R. Pucci, Pairing symmetry of superconducting graphene, Eur. Phys. J. B 76(3), 469 (2010) https://doi.org/10.1140/epjb/e2010-00228-9
31
T. O. Wehling, H. P. Dahal, A. I. Lichtenstein, and A. V. Balatsky, Local impurity effects in superconducting graphene, Phys. Rev. B 78(3), 035414 (2008) https://doi.org/10.1103/PhysRevB.78.035414
32
O. A. Awoga and A. M. Black-Schaffer, Probing unconventional superconductivity in proximitized graphene by impurity scattering, Phys. Rev. B 97(21), 214515 (2018) https://doi.org/10.1103/PhysRevB.97.214515
33
E. W. Hudson, S. H. Pan, A. K. Gupta, K.-W. Ng, and J. C. Davis, Atomic-scale quasi-particle scattering resonances in Bi2Sr2CaCu2O8+δ, Science 285(5424), 88 (1999) https://doi.org/10.1126/science.285.5424.88
N. Andrenacci, G. G. N. Angilella, H. Beck, and R. Pucci, Linear response theory around a localized impurity in the pseudogap regime of an anisotropic superconductor: Precursor pairing versus d-density-wave scenario, Phys. Rev. B 70(2), 024507 (2004) https://doi.org/10.1103/PhysRevB.70.024507
P. Rosenzweig, H. Karakachian, D. Marchenko, K. Küster, and U. Starke, Overdoping graphene beyond the van hove singularity, Phys. Rev. Lett. 125(17), 176403 (2020) https://doi.org/10.1103/PhysRevLett.125.176403
38
T. Löthman and A. M. Black-Schaffer, Defects in the d+ id-wave superconducting state in heavily doped graphene, Phys. Rev. B 90(22), 224504 (2014) https://doi.org/10.1103/PhysRevB.90.224504
