Abstract
In conventional metallic superconductors such as aluminium, the large number of weakly bounded Cooper pairs become phase-coherent as soon as they start to form. The cuprate high-temperature superconductors belong to a different category because, being doped Mott insulators, they are known to have low superfluid density and are therefore susceptible to phase fluctuations. It has been proposed that pairing and phase coherence may occur separately in cuprates, and that the measured critical temperature corresponds to the phase-coherence temperature controlled by the superfluid density. Here we examine the evolution of pairing and phase-ordering in underdoped cuprates, and find that a chequerboard plaquette pattern of charge order plays a crucial role, such that the global phase coherence is established once its spatial occupation exceeds a threshold. We make these observations via scanning tunnelling microscopy on underdoped Bi2LaxSr2 − xCuO6 + δ. We observe a smooth crossover from the Mott insulator to superconductor on small islands that have chequerboard order. Each chequerboard plaquette contains approximately two holes and exhibits a stripy internal structure that has a strong influence on the superconducting spectroscopic features. The local spectra remain qualitatively the same across the insulator-to-superconductor transition, and the quasiparticle interference becomes long-ranged.
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Data are available from the corresponding author upon reasonable request. Source data are provided with this paper.
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Acknowledgements
We thank Z.Y. Weng, G.M. Zhang and C.L. Song for helpful discussions and technical support. This work is supported by the Basic Science Center Project of NSFC (grant no. 52388201), the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302502), NSFC grant no. 11888101 and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB25000000). Yayu Wang is supported by the New Cornerstone Science Foundation through the New Cornerstone Investigator Program and the XPLORER PRIZE.
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Y.W. and X.Z. supervised the project. H.Y. and Y.C. prepared the single crystal. S.Y., C.Z. and M.X. carried out the STM experiments under the supervision of Y.W. Z.D., Y.J. and S.Y. performed the transport experiments. S.Y. and Y.W. prepared the manuscript, with comments from all authors.
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Supplementary sections 1–12 and Figs. 1–15.
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Source Data Fig. 1
Temperature dependent resistance curve and spatially averaged spectra of three samples.
Source Data Fig. 2
Linecut spectra, alpha cluster analysis and corresponding 2nd derivative curves of three samples.
Source Data Fig. 3
Linecut spectra of p = 0.08 and p = 0.11 samples.
Source Data Fig. 5
Extracted QPI wavevectors of the three samples in Fig. 5a,b.
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Ye, S., Zou, C., Yan, H. et al. The emergence of global phase coherence from local pairing in underdoped cuprates. Nat. Phys. 19, 1301–1307 (2023). https://doi.org/10.1038/s41567-023-02100-9
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DOI: https://doi.org/10.1038/s41567-023-02100-9
