Pairing symmetry in monolayer of orthorhombic CoSb
Tian-Zhong Yuan, Mu-Yuan Zou, Wen-Tao Jin, Xin-Yuan Wei, Xu-Guang Xu, Wei Li
Pairing symmetry in monolayer of orthorhombic CoSb
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.
superconductivity / ferromagnetism / non-unitary pair
[1] |
X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)
CrossRef
ADS
Google scholar
|
[2] |
M. Sato and Y. Ando, Topological superconductors: A review, Rep. Prog. Phys. 80(7), 076501 (2017)
CrossRef
ADS
Google scholar
|
[3] |
A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.- Usp. 44(10S), 131 (2001)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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. B 61(15), 10267 (2000)
CrossRef
ADS
Google scholar
|
[10] |
G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360(2–3), 362 (1991)
CrossRef
ADS
Google scholar
|
[11] |
N. Read and G. Moore, Fractional quantum Hall effect and nonabelian statistics, Prog. Theor. Phys. Suppl. 107, 157 (1992)
CrossRef
ADS
Google scholar
|
[12] |
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (Amsterdam) 303(1), 2 (2003)
CrossRef
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)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[15] |
C. W. J. Beenakker, Search for Majorana fermions in superconductors, Annu. Rev. Condens. Matter Phys. 4(1), 113 (2013)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[17] |
R. Aguado, Majorana quasiparticles in condensed matter, Riv. Nuovo Cim. 40, 523 (2017)
|
[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)
CrossRef
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)
CrossRef
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)
CrossRef
ADS
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)
CrossRef
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. Op het Veld, P. J. van Veldhoven, 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)
|
[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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
ADS
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)
CrossRef
ADS
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)
CrossRef
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)
CrossRef
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)
CrossRef
ADS
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)
CrossRef
ADS
Google scholar
|
[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 twodimensional limit, Sci. Adv. 6(13), eaax7547 (2020)
CrossRef
ADS
Google scholar
|
[34] |
M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63(2), 239 (1991)
CrossRef
ADS
Google scholar
|
[35] |
V. Kozii, J. W. F. Venderbos, and L. Fu, Threedimensional Majorana fermions in chiral superconductors, Sci. Adv. 2(12), e1601835 (2016)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[37] |
A. J. Leggett, A theoretical description of the new phases of liquid He3, Rev. Mod. Phys. 47(2), 331 (1975)
CrossRef
ADS
Google scholar
|
[38] |
J. C. Wheatley, Experimental properties of superfluid 3He, Rev. Mod. Phys. 47(2), 415 (1975)
CrossRef
ADS
Google scholar
|
[39] |
T. Ohmi and K. Machida, Nonunitary superconducting state in UPt3, Phys. Rev. Lett. 71(4), 625 (1993)
CrossRef
ADS
Google scholar
|
[40] |
J. A. Sauls, The order parameter for the superconducting phases of UPt3, Adv. Phys. 43(1), 113 (1994)
CrossRef
ADS
Google scholar
|
[41] |
H. Tou, Y. Kitaoka, K. Ishida, K. Asayama, N. Kimura, Y. Ōnuki, E. Yamamoto, Y. Haga, and K. Maezawa, Nonunitary spin-triplet superconductivity in UPt3: Evidence from 195Pt Knight shift study, Phys. Rev. Lett. 80(14), 3129 (1998)
CrossRef
ADS
Google scholar
|
[42] |
R. Joynt and L. Taillefer, The superconducting phases of UPt3, Rev. Mod. Phys. 74(1), 235 (2002)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[48] |
J. F. Annett, Symmetry of the order parameter for high-temperature superconductivity, Adv. Phys. 39(2), 83 (1990)
CrossRef
ADS
Google scholar
|
[49] |
V. P. Mineev, Superconducting states in ferromagnetic metals, Phys. Rev. B 66(13), 134504 (2002)
CrossRef
ADS
Google scholar
|
[50] |
K. V. Samokhin and M. B. Walker, Order parameter symmetry in ferromagnetic superconductors, Phys. Rev. B 66(17), 174501 (2002)
CrossRef
ADS
Google scholar
|
[51] |
D. J. Singh and L. Nordstrom, Planewaves, Pseudopotentials, and the LAPW Method, 2nd Ed., Springer-Verlag, Berlin, 2006
|
[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
|
[53] |
J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[55] |
J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals, J. Phys. Chem. Solids 10(2-3), 87 (1959)
CrossRef
ADS
Google scholar
|
[56] |
W. Ding, J. Zeng, W. Qin, P. Cui, and Z. Zhang, Exploringhigh transition temperature superconductivity in a freestanding or SrTiO3-supported CoSb monolayer, Phys. Rev. Lett. 124(2), 027002 (2020)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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)
CrossRef
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(Fe0.75Ru0.25)2As2, Phys. Rev. B 100, 060406(R) (2019)
CrossRef
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)
CrossRef
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
CrossRef
ADS
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)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[67] |
K. Hattori and H. Tsunetsugu, p-wave superconductivity near a transverse saturation field, Phys. Rev. B 87(6), 064501 (2013)
CrossRef
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)
CrossRef
ADS
Google scholar
|
[69] |
C. Kallin and J. Berlinsky, Chiral superconductors, Rep. Prog. Phys. 79(5), 054502 (2016)
CrossRef
ADS
Google scholar
|
/
〈 | 〉 |