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Electronic origin of high superconducting critical temperature in trilayer cuprates

Abstract

In high-temperature cuprate superconductors, the superconducting transition temperature (Tc) depends on the number of CuO2 planes in the structural unit and the maximum Tc is realized in the trilayer system. Trilayer superconductors also exhibit an unusual phase diagram where Tc is roughly constant in the overdoped region, which is in contrast to the decrease usually found in other cuprate superconductors. The mechanism for these two effects remains unclear. Here we report features in the electronic structure of Bi2Sr2Ca2Cu3O10+δ superconductor that helps to explain this issue. Our angle-resolved photoemission spectroscopy measurements show the splitting of bands from the three layers, and this allows us to parameterize a three-layer interaction model that effectively describes the data. This, in turn, demonstrates the electronic origin of the maximum Tc and its persistence in the overdoped region. These results are qualitatively consistent with a composite picture where a high Tc is realized in an array of coupled planes with different doping levels such that a high pairing strength is derived from the underdoped planes, whereas a large phase stiffness comes from the optimally or overdoped ones.

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Fig. 1: Observation of three Fermi surface sheets in Bi2223.
Fig. 2: Momentum-dependent band structures of Bi2223 measured at 18 K in the superconducting state and their global simulations.
Fig. 3: Photoemission spectra and the superconducting gap of Bi2223 along the three Fermi surface sheets measured at 18 K.
Fig. 4: Determination of interlayer hopping, interlayer pairing and band hybridization parameters in Bi2223.

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Data availability

All raw data generated during the study are available from the corresponding author upon request.

Code availability

The codes used for the fitting and simulation process in this study are available from the corresponding author upon request.

References

  1. Lee, P. A., Nagaosa, N. & Wen, X. G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17 (2006).

    Article  ADS  Google Scholar 

  2. Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

    Article  ADS  Google Scholar 

  3. Scott, B. A. et al. Layer dependence of the superconducting transition temperature of HgBa2Can−1CunO2n+2+δ. Phys. C 230, 239–245 (1994).

    Article  ADS  Google Scholar 

  4. Chakravarty, S., Kee, H.-Y. & Volker, K. An explanation for a universality of transition temperatures in families of copper oxide superconductors. Nature 428, 53–55 (2004).

    Article  ADS  Google Scholar 

  5. Iyo, A. et al. Tc vs n relationship for multilayered high-Tcsuperconductors.J. Phys. Soc. Jpn 76, 094711 (2007).

    Article  ADS  Google Scholar 

  6. Eisaki, H. et al. Effect of chemical inhomogeneity in bismuth-based copper oxide superconductors. Phys. Rev. B 69, 064512 (2004).

    Article  ADS  Google Scholar 

  7. Chu, C. W., Deng, L. Z. & Lv, B. Hole-doped cuprate high temperature superconductors. Phys. C 514, 290–313 (2015).

    Article  ADS  Google Scholar 

  8. Fujii, T., Terasaki, I., Watanabe, T. & Matsuda, A. Doping dependence of anisotropic resistivities in the trilayered superconductor Bi2Sr2Ca2Cu3O10+δ. Phys. Rev. B 66, 024507 (2002).

    Article  ADS  Google Scholar 

  9. Piriou, A., Fasano, Y., Giannini, E. & Fischer, Ø. Effect of oxygen-doping on Bi2Sr2Ca2Cu3O10+δ vortex matter: crossover from electromagnetic to Josephson interlayer coupling. Phys. Rev. B 77, 184508 (2008).

    Article  ADS  Google Scholar 

  10. Muller, R. et al. Fermi surface and superconducting gap of triple-layered Bi2Sr2Ca2Cu3O10+δ. J. Supercond. 15, 147–152 (2002).

    Article  ADS  Google Scholar 

  11. Feng, D. L. et al. Electronic structure of the trilayer cuprate superconductor Bi2Sr2Ca2Cu3O10+δ. Phys. Rev. Lett. 88, 107001 (2002).

    Article  ADS  Google Scholar 

  12. Sato, T. et al. Low energy excitation and scaling in Bi2Sr2Can−1CunO2n+4(n = 1−3): angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 89, 067005 (2002).

    Article  ADS  Google Scholar 

  13. Matsui, H. et al. BCS-like Bogoliubov quasiparticles in high-Tc superconductors observed by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 90, 217002 (2003).

    Article  ADS  Google Scholar 

  14. Ideta, S. et al. Enhanced superconducting gaps in the trilayer high-temperature Bi2Sr2Ca2Cu3O10+δ cuprate superconductor. Phys. Rev. Lett. 104, 227001 (2010).

    Article  ADS  Google Scholar 

  15. Ideta, S. et al. Angle-resolved photoemission study of the tri-layer high-Tc superconductor Bi2Sr2Ca2Cu3O10+δ: effects of inter-layer hopping. Phys. C 470, S14 (2010).

    Article  ADS  Google Scholar 

  16. Ideta, S. et al. Energy scale directly related to superconductivity in high-Tc cuprates: universality from the temperature-dependent angle-resolved photoemission of Bi2Sr2Ca2Cu3O10+δ. Phys. Rev. B 85, 104515 (2012).

    Article  ADS  Google Scholar 

  17. Kunisada, S. et al. Observation of Bogoliubov band hybridization in the optimally doped trilayer Bi2Sr2Ca2Cu3O10+δ. Phys. Rev. Lett. 119, 217001 (2017).

    Article  ADS  Google Scholar 

  18. Ideta, S. et al. Hybridization of Bogoliubov quasiparticles between adjacent CuO2 layers in the triple-layer cuprate Bi2Sr2Ca2Cu3O10+δ studied by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 127, 217004 (2021).

    Article  ADS  Google Scholar 

  19. Camargo-Martínez, J. A., Espitia, D. & Baquero, R. First-principles study of electronic structure of Bi2Sr2Ca2Cu3O10. Rev. Mex. Fis. 60, 39–45 (2014).

    Google Scholar 

  20. Feng, D. L. et al. Bilayer splitting in the electronic structure of heavily overdoped Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 86, 5550 (2001).

    Article  ADS  Google Scholar 

  21. Chuang, Y.-D. et al. Doubling of the bands in overdoped Bi2Sr2CaCu2O8+δ: evidence for c-axis bilayer coupling. Phys. Rev. Lett. 87, 117002 (2001).

    Article  ADS  Google Scholar 

  22. Bogdanov, P. V. et al. Photoemission study of Pb doped Bi2Sr2CaCu2O8+δ: a Fermi surface picture. Phys. Rev. B 64, 180505(R) (2001).

    Article  ADS  Google Scholar 

  23. Ai, P. et al. Distinct superconducting gap on two bilayer-split Fermi surface sheets in Bi2Sr2CaCu2O8+δ superconductor. Chinese Phys. Lett. 36, 067402 (2019).

    Article  ADS  Google Scholar 

  24. Markiewicz, R. S., Sahrakorpi, S., Lindroos, M., Lin, H. & Bansil, A. One-band tight-binding model parametrization of the high-Tc cuprates including the effect of kz dispersion. Phys. Rev. B 72, 054519 (2005).

    Article  ADS  Google Scholar 

  25. Yu, Y. J. et al. High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ. Nature 575, 156 (2019).

    Article  ADS  Google Scholar 

  26. Pavarini, E., Dasgupta, I., Dasgupta, T. S., Jepsen, O. & Andersen, O. K. Band-structure trend in hole-doped cuprates and correlation with Tcmax. Phys. Rev. Lett. 87, 047003 (2001).

    Article  ADS  Google Scholar 

  27. Zhong, Y. G. et al. Extraction of tight binding parameters from in-situ ARPES on the continuously doped surface of cuprates. Sci. China Phys. Mech. Astron. 61, 127403 (2018).

    Article  ADS  Google Scholar 

  28. Mori, M., Tohyama, T. & Maekawa, S. Fermi surface splittings in multilayered high-Tc cuprates.Phys. C 445, 23–25 (2006).

    Article  ADS  Google Scholar 

  29. Nishiguchi, K., Kuroki, K., Arita, R., Oka, T. & Aoki, H. Superconductivity assisted by interlayer pair hopping in multilayered cuprates. Phys. Rev. B 88, 014509 (2013).

    Article  ADS  Google Scholar 

  30. Kivelson, S. A. Making high Tc higher: a theoretical proposal. Phys. B 318, 61–67 (2002).

    Article  ADS  Google Scholar 

  31. Berg, E., Orgad, D. & A. Kivelson, S. Route to high-temperature superconductivity in composite systems. Phys. Rev. B 78, 094509 (2008).

    Article  ADS  Google Scholar 

  32. Okamoto, S. & Maier, T. A. Enhanced superconductivity in superlattices of high-Tc cuprates. Phys. Rev. Lett. 101, 156401 (2008).

    Article  ADS  Google Scholar 

  33. Emery, V. J. & Kivelson, S. A. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).

    Article  ADS  Google Scholar 

  34. Uemura, Y. J. et al. Universal correlations between Tc and ns/m* (carrier density over effective mass) in high-Tc cuprate superconductors. Phys. Rev. Lett. 62, 2317 (1989).

    Article  ADS  Google Scholar 

  35. Božović, I., He, X., Wu, J. & Bollinger, A. T. Dependence of the critical temperature in overdoped copper oxides on superfluid density. Nature 536, 309–311 (2016).

  36. Feng, D. L. et al. Signature of superfluid density in the single-particle excitation spectrum of Bi2Sr2CaCu2O8+δ. Science 289, 277–281 (2000).

    Article  ADS  Google Scholar 

  37. Ding, H. et al. Coherent quasiparticle weight and its connection to high-Tc superconductivity from angle-resolved photoemission. Phys. Rev. Lett. 87, 227001 (2001).

    Article  ADS  Google Scholar 

  38. Liang, B., Lin, C. T., Shang, P. & Yang, G. Single crystals of triple-layered cuprates Bi2Sr2Ca2Cu3O10+δ: growth, annealing and characterization. Phys. C 383, 75–88 (2002).

    Article  ADS  Google Scholar 

  39. Liu, G. D. et al. Development of a vacuum ultraviolet laser-based angle-resolved photoemission system with a superhigh energy resolution better than 1meV. Rev. Sci. Instrum. 79, 023105 (2008).

    Article  ADS  Google Scholar 

  40. Zhou, X. J. et al. New developments in laser-based photoemission spectroscopy and its scientific applications: a key issues review. Rep. Prog. Phys. 81, 062101 (2018).

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (grant nos. 11888101 (to X.J.Z.), 11922414 (to L.Z.) and 11974404 (to G.L.)), the National Key Research and Development Program of China (grant nos. 2021YFA1401800 (to X.J.Z.), 2017YFA0302900 (to T.X.) and 2018YFA0305600 (to G.L.)), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (grant no. XDB25000000 (to X.J.Z.)), Innovation Program for Quantum Science and Technology (grant no. 2021ZD0301800 (to X.J.Z.)), the Youth Innovation Promotion Association of CAS (grant no. Y2021006 (to L.Z.)) and the Synergetic Extreme Condition User Facility (SECUF).

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Authors

Contributions

X.J.Z. and X.L. proposed and designed the research. X.L., H.C., C.Y., Q.G. and H.Y. carried out the ARPES experiments. C.L. grew the single crystals. H.C., C.Y., T.M., H.L., Y.S., Y.C., S.Z., Z.W., F.Z., F.Y., Q.P., G.L., L.Z., Z.X. and X.J.Z. contributed to the development and maintenance of the laser ARPES and ARTOF systems. X.L., Y.L., Q.G. and T.X. contributed to the theoretical analysis. X.L. and X.J.Z. analysed the data and wrote the paper. All authors participated in the discussions and commented on the paper.

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Correspondence to X. J. Zhou.

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Nature Physics thanks Robert Markiewicz and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections 1–9, Figs. 1–10 and Equations (1)–(12).

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Luo, X., Chen, H., Li, Y. et al. Electronic origin of high superconducting critical temperature in trilayer cuprates. Nat. Phys. 19, 1841–1847 (2023). https://doi.org/10.1038/s41567-023-02206-0

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