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Chin. Phys. B, 2021, Vol. 30(6): 067401    DOI: 10.1088/1674-1056/abdea5

Temperature and doping dependent flat-band superconductivity on the Lieb-lattice

Feng Xu(徐峰)1,2,†, Lei Zhang(张磊)1,2, and Li-Yun Jiang(姜立运)1,2
1 School of Physics and Telecommunication Engineering, Shaanxi University of Technology, Hanzhong 723001, China;
2 Institute of Graphene at Shaanxi Key Laboratory of Catalysis, Shaanxi University of technology, Hanzhong 723001, China
Abstract  We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron-electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron-electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-Tc superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-Tc superconductors. However, unlike the exponential dependence of Tc on the electron-electron interaction strength in the conventional high-Tc superconductors, the BKT transition temperature for a flat band system depends linearly on the electron-electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-Tc superconductors.
Keywords:  flat-band superconductivity      strong electron-electron interaction      superfluid weight      Berezinskii-Kosterlitz-Thouless (BKT) transition temperature  
Received:  10 September 2020      Revised:  10 December 2020      Accepted manuscript online:  22 January 2021
PACS:  74.20.-z (Theories and models of superconducting state)  
  74.20.Mn (Nonconventional mechanisms)  
  74.25.Bt (Thermodynamic properties)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11804213), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No. 20JK0573), the Scientific Research Foundation of Shaanxi University of Technology (Grant No. SLGRCQD2006), and the Natural Science Basic Research Program of Shaanxi (Grant No. 2021JQ-748).
Corresponding Authors:  Feng Xu     E-mail:

Cite this article: 

Feng Xu(徐峰), Lei Zhang(张磊), and Li-Yun Jiang(姜立运) Temperature and doping dependent flat-band superconductivity on the Lieb-lattice 2021 Chin. Phys. B 30 067401

[1] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi E, Kaxiras E and Jarillo-Herrero P 2018 Nature 556 43
[2] Chebrolu N R, Chittari B L and Jung J 2019 Phys. Rev. B 99 235417
[3] Hu X, Hyart T, Pikulin D I and Rossi E 2019 Phys. Rev. Lett. 123 237002
[4] Roy B and Juricic V 2019 Phys. Rev. B 99 121407(R)
[5] Julku A, Peltonen T J, Liang L, Heikkila T T and Torma P 2020 Phys. Rev. B 101 060505(R)
[6] Kopnin N B, Heikkila T T and Volovik G E 2011 Phys. Rev. B 83 220503(R)
[7] Iglovikov V I, Hebert F, Batrouni G G and Scalettar R T 2014 Phys. Rev. B 90 094506
[8] Lieb E H 1989 Phys. Rev. Lett. 62 1201
[9] Mielke A 1991 J. Phys. A 24 L73,1991 J. Phys. A 24 3311
[10] Tasaki H 1992 Phys. Rev. Lett. 69 1608
[11] Tasaki H 1998 Prog. Theor. Phys. 99 489
[12] Kopnin N B, Heikkila T T and Volovik G E 2011 Phys. Rev. B 83 220503(R)
[13] Wang H, Yu S L and Li J X 2014 Phys. Lett. A 378 3360
[14] Julku A, Peotta S, Vanhala T I, Kim D H and Torma P 2016 Phys. Rev. Lett. 117 045303
[15] Huhtinen K F,Tylutki M, Kumar P, Vanhala T I, Peorra S and Torma P 2018 Phys. Rev. B 97 214503
[16] Tylutki M and Torma P 2018 Phys. Rev. B 98 094513
[17] Sun K, Gu Z, Katsura H and Sarma S D 2011 Phys. Rev. Lett. 106 236803
[18] Tang E, Mei J W and Wen X G 2011 Phys. Rev. Lett. 106 236802
[19] Neupert T, Santos L, Chamon C and Mudry C 2011 Phys. Rev. Lett. 106 236804
[20] Roy R 2014 Phys. Rev. B 90 165139
[21] Slot M R, Gardenier T S, Jacobse P H, van Miert G C P, Kempkes S N, Zevenhuizen S J M, Smith C M, Vanmaekelbergh D and Swart I 2017 Nature Physics 13 672
[22] Lin Z, Choi J H, Zhang Q, Qin W, Yi S, Wang P, Li L, Wang Y, Zhang H, Sun Z, Wei L, Zhang S, Guo T, Lu Q, Cho J H, Zeng C and Zhang Z 2018 Phys. Rev. Lett. 121 096401
[23] Xia S, Ramachandran A, Xia S, Li D, Liu X, Tang L, Hu Y, Song D, Xu J, Leykam D, Flach S and Chen Z 2018 Phys. Rev. Lett. 121 263902
[24] Saito Y, Ge J, Watanabe K, Taniguchi T and Young A F 2018 Nature Physics 14 3681
[25] Kauooila V J, Aikebaier F and Heikkila T T 2016 Phys. Rev. B 93 214505
[26] Xu F, Chou P, Chung C H, Lee T K and Mou C Y 2018 Phys. Rev. B 98 205103
[27] Xu F and Zhang L 2019 Chin. Phys. B 28 117403
[28] Berezinskii V L 1972 Sov. Phys. JETP 34 610
[29] Kosterlitz J M and Thouless D J 1973 J. Phys. C 6 1181
[30] Nelson D R and Kosterlitz J M 1977 Phys. Rev. Lett. 39 1201
[31] Lee P A, Nagaosa N and Wen X G 2006 Rev. Mod. Phys. 78 17
[32] Edegger B, Muthukumar V N and Gros C 2007 Adances in Physics 56 927
[33] Scalapino D J, White S R and Zhang S C 1992 Phys. Rev. Lett. 68 2830
[34] Scalapino D J, White S R and Zhang S C 1993 Phys. Rev. B 47 7996
[35] Zhong Y, Lu H and Luo H 2016 Eur. Phys. J. B 89 28
[36] Shao S, Zhou K and Zhang Z 2019 Chin. Phys. B 28 070501
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