Abstract We study the coexistence of antiferromagnetism and unconventional superconductivity on the Creutz lattice which shows strictly flat bands in the noninteracting regime. The famous renormalized mean-field theory is used to deal with strong electron-electron repulsive Hubbard interaction in the effective low-energy t-J model, the superfluid weight of the unconventional superconducting state has been calculated via the linear response theory. An unconventional superconducting state with both spin-singlet and staggered spin-triplet pairs emerges beyond a critical antiferromagnetic coupling interaction, while antiferromagnetism accompanies this state. The superconducting state with only spin-singlet pairs is dominant with paramagnetic phase. The A phase is analogous to the pseudogap phase, which shows that electrons go to form pairs but do not cause a supercurrent. We also show the superfluid behavior of the unconventional superconducting state and its critical temperature. It is proven directly that the flat band can effectively raise the critical temperature of superconductivity. It is implementable to simulate and control strongly-correlated electrons' behavior on the Creutz lattice in the ultracold atoms experiment or other artificial structures. Our results may help the understanding of the interplay between unconventional superconductivity and magnetism.
Fund: Project supported by the Natural Science Basic Research Program of Shaanxi (Program Nos. 2023KJXX-064 and 2021JQ-748), the National Natural Science Foundation of China (Grant Nos. 11804213 and 12174238), and Scientific Research Foundation of Shaanxi University of Technology (Grant No. SLGRCQD2006).
Feng Xu(徐峰) and Lei Zhang(张磊) Coexistence of antiferromagnetism and unconventional superconductivity in a quasi-one-dimensional flat-band system: Creutz lattice 2024 Chin. Phys. B 33 037402
[1] Foley A, Verret S, Tremblay A M S and Senechal D 2019 Phys. Rev. B99 184510 [2] Qi Y,Liang L, Sun K and Gu Z C 2020 Phys. Rev. B102 245140 [3] Gu X Y, Chen C,Leaw J L, et al., 2020 Phys. Rev. B101 180506(R) [4] Psaltakis G C and Penton E W 1983 J. Phys. C: Solid State Phys. 16 3913 [5] Zhang Y, Demler E and Sachdev S 2002 Phys. Rev. B66 094501 [6] Vorontsov A B, Vavilov M G and Chubukov A V 2010 Phys. Rev. B81 174538 [7] Kaczmarczyk J and Spalek J 2011 Phys. Rev. B84 125140 [8] Lu Y M, Xiang T and Lee D H 2014 Nat. Phys. 10 634 [9] Romer A T, Eremin I, Hirschfeld P J and Andersen B M 2016 Phys. Rev. B93 174519 [10] Almeida D E, Frenaandes R M and Miranda E 2017 Phys. Rev. B96 014514 [11] Cao Y, Park J M, Watanabe K and Taniguchi T 2021 Natrure595 526 [12] Yu W, Higgins J S,Bach P and Greene R L 2007 Phys. Rev. B76 020503(R) [13] Li Z, Zhou R, Liu Y, et al., 2012 Phys. Rev. B86 180501(R) [14] Kawasaka S, Mabuchi T, Maeda S, et al., 2015 Phys. Rev. B92 180508(R) [15] Rosa P F S, Kang J, Luo Y, et al., 2017 Proc. Natl. Acad. Sci. USA114 5384 [16] Peotta R and Törmä P 2015 Nat. Commun. 6 8944 [17] Julku A, Peotta S, Vanhala T I, Kim D and Törmä P 2016 Phys. Rev. Lett. 117 045303 [18] Tovmasyan M, Peotta S, Törmä P and Huber S D 2016 Phys. Rev. B94 245149 [19] Tovmasyan M, Peotta S, Liang L, Törmä P and Huber S D 2018 Phys. Rev. B98 134513 [20] Xu F, Chou P, Chung C H, Lee T K and Mou C Y 2018 Phys. Rev. B98 205103 [21] Xu F and Zhang L 2019 Chin. Phys. B28 117403 [22] Xu F, Zhang L and Jiang L Y 2021 Chin. Phys. B30 067401 [23] Tovmasyan M, Nieuwenburg E P and Huber S D 2013 Phys. Rev. B88 220510 [24] Takayoshi S,Katsura H, Watanabe N and Aoki H 2013 Phys. Rev. A88 063613 [25] Mondaini R, Batrouni G G and Gremaud B 2018 Phys. Rev. B98 155142 [26] Jiang Y F, Jiang H C, Yao H and Kivelson S A 2017 Phys. Rev. B95 245105 [27] Hou J, Lee T K and Chen Y 2019 Phys. Rev. B99 094510 [28] Yang K Y, Chen W Q, Rice T M, Sigrist M and Zhang F C 2009 New J. Phys. 11 055053 [29] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi E, Kaxiras E and Jarillo-Herrero P 2018 Nature556 43 [30] Chebrolu N R, Chittari B L and Jung J 2019 Phys. Rev. B99 235417 [31] Hu X, Hyart T, Pikulin D I and Rossi E 2019 Phys. Rev. Lett. 123 237002 [32] Roy B and Juricic V 2019 Phys. Rev. B99 121407(R) [33] Julku A, Peltonen T J, Liang L, Heikkila T T and Torma P 2020 Phys. Rev. B101 060505(R) [34] Kopnin N B, Heikkila T T and Volovik G E 2011 Phys. Rev. B83 220503 [35] Heikkila T T, Kopnin N B and Volovik G E 2011 JETP Lett. 94 233 [36] Huber S D and Altman E 2010 Phys. Rev. B82 184502 [37] Creutz M 1999 Phys. Rev. Lett. 83 2636 [38] Misumi T and Aoki H 2017 Phys. Rev. B96 155137 [39] Rizzi M, Cataudella V and Fazio R 2006 Phys. Rev. B73 100502(R) [40] Scalapino D J, White S R and Zhang S C 1992 Phys. Rev. Lett. 68 2830 [41] Scalapino D J, White S R and Zhang S C 1993 Phys. Rev. B47 7996 [42] Zhong Y, Lu H and Luo H 2016 Eur. Phys. J. B89 28 [43] Ogata M and Himeda A 2003 J. Phys. Soc. Jpn. 72 374 [44] Tylutki M and Torma P 2018 Phys. Rev. B98 094513 [45] Mulkerin B C, He L, Dyke P, Vale C, Liu X and Hu H 2017 Phys. Rev. A96 053608 [46] Matsuda Y and Shimahara H 2007 J. Phys. Soc. Jpn. 76 051005 [47] Chen L H, Wang D, Zhou Y and Wang Q H 2020 Chin. Phys. Lett. 37 017403 [48] Zhang F C, Gros C, Rice T M and Shiba H 1988 Supercond. Sci. Technol. 1 36 [49] Edegger B, Muthukumar V N and Gros C 2007 Advances in Physics56 927
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