Abstract
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.
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X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)
M. Sato and Y. Ando, Topological superconductors: A review, Rep. Prog. Phys. 80(7), 076501 (2017)
A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.- Usp. 44(10S), 131 (2001)
D. A. Ivanov, Non-Abelian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett. 86(2), 268 (2001)
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)
K. T. Law, P. A. Lee, and T. K. Ng, Majorana fermion induced resonant Andreev reflection, Phys. Rev. Lett. 103(23), 237001 (2009)
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)
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)
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. B61(15), 10267 (2000)
G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360(2–3), 362 (1991)
N. Read and G. Moore, Fractional quantum Hall effect and nonabelian statistics, Prog. Theor. Phys. Suppl. 107, 157 (1992)
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (Amsterdam) 303(1), 2 (2003)
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)
J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75(7), 076501 (2012)
C. W. J. Beenakker, Search for Majorana fermions in superconductors, Annu. Rev. Condens. Matter Phys. 4(1), 113 (2013)
S. R. Elliott and M. Franz, Majorana fermions in nuclear, particle, and solid-state physics, Rev. Mod. Phys. 87(1), 137 (2015)
R. Aguado, Majorana quasiparticles in condensed matter, Riv. Nuovo Cim. 40, 523 (2017)
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)
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)
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)
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)
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. Ophet Veld, P. J. van Veld-hoven, 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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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 two-dimensional limit, Sci. Adv. 6(13), eaax7547 (2020)
M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63(2), 239 (1991)
V. Kozii, J. W. F. Venderbos, and L. Fu, Three-dimensional Majorana fermions in chiral superconductors, Sci. Adv. 2(12), e1601835 (2016)
V. Ambegaokar and N. D. Mermin, Thermal anomalies of 3He: Pairing in a magnetic field, Phys. Rev. Lett. 30(3), 81 (1973)
A. J. Leggett, A theoretical description of the new phases of liquid He3, Rev. Mod. Phys. 47(2), 331 (1975)
J. C. Wheatley, Experimental properties of superfluid 3He, Rev. Mod. Phys. 47(2), 415 (1975)
T. Ohmi and K. Machida, Nonunitary superconducting state in UPt3, Phys. Rev. Lett. 71(4), 625 (1993)
J. A. Sauls, The order parameter for the superconducting phases of UPt3, Adv. Phys. 43(1), 113 (1994)
H. Tou, Y. Kitaoka, K. Ishida, K. Asayama, N. Kimura, Y. Ōnuki, E. Yamamoto, Y. Haga, and K. Maezawa, Non-unitary spin-triplet superconductivity in UPt3: Evidence from 195Pt Knight shift study, Phys. Rev. Lett. 80(14), 3129 (1998)
R. Joynt and L. Taillefer, The superconducting phases of UPt3, Rev. Mod. Phys. 74(1), 235 (2002)
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)
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)
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)
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)
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)
J. F. Annett, Symmetry of the order parameter for high-temperature superconductivity, Adv. Phys. 39(2), 83 (1990)
V. P. Mineev, Superconducting states in ferromagnetic metals, Phys. Rev. B 66(13), 134504 (2002)
K. V. Samokhin and M. B. Walker, Order parameter symmetry in ferromagnetic superconductors, Phys. Rev. B 66(17), 174501 (2002)
D. J. Singh and L. Nordstrom, Planewaves, Pseudopotentials, and the LAPW Method, 2nd Ed., Springer-Verlag, Berlin, 2006
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
J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)
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)
J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals, J. Phys. Chem. Solids 10(2–3), 87 (1959)
W. Ding, J. Zeng, W. Qin, P. Cui, and Z. Zhang, Exploring high transition temperature superconductivity in a freestanding or SrTiO3-supported CoSb monolayer, Phys. Rev. Lett. 124(2), 027002 (2020)
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)
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)
X. G. Xu and W. Li, Electronic and magnetic structures of ternary iron telluride KFe2Te2, Front. Phys. 10(4), 107403 (2015)
D. J. Singh, Electronic structure and doping in BaFe2As2 and LiFeAs: Density functional calculations, Phys. Rev. B 78(9), 094511 (2008)
W. C. Huang, W. Li, and X. Liu, Exotic ferromagnetism in the two-dimensional quantum materials C3N, Front. Phys. 13(2), 137104 (2018)
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(Fe0.75Ruo.25)2As2, Phys. Rev. B 100, 060406(R) (2019)
J. B. Goodenough, Theory of the role of covalence in the perovskite-type manganites [La,M(II)]MnO3, Phys. Rev. 100(2), 564 (1955)
S. Maekawa, T. Tohyama, S. E. Barnes, S. Ishihara, W. Koshibae, and G. Khaliullin, Physics of Transition Metal Oxides, Berlin Heidelberg: Springer-Verlag, 2004
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)
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)
K. Hattori and H. Tsunetsugu, p-wave superconductivity near a transverse saturation field, Phys. Rev. B 87(6), 064501 (2013)
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)
C. Kallin and J. Berlinsky, Chiral superconductors, Rep. Prog. Phys. 79(5), 054502 (2016)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 11927807) and the Natural Science Foundation of Shanghai of China (Grant Nos. 19ZR1402600 and 20DZ1100604). W. L. also acknowledges the startup funding from Fudan University.
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arXiv: 2004.10200. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-020-1040-y.
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Yuan, TZ., Zou, MY., Jin, WT. et al. Pairing symmetry in monolayer of orthorhombic CoSb. Front. Phys. 16, 43500 (2021). https://doi.org/10.1007/s11467-020-1040-y
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DOI: https://doi.org/10.1007/s11467-020-1040-y