Visualization of the Zhang–Rice singlet, electronic molecules and Cooper pair formation in a cuprate superconductor

Nature Physics (2026) Cite this article High-temperature superconductivity in cuprates can be realized by doping holes into an antiferromagnetic insulator. To understand the mechanism by which this happens, one must elucidate the electronic state of a single doped hole and the coupling between them that gradually leads to pairing. Experimental progress has been hindered by the technical challenges in probing the electronic properties of a small number of holes dispersed into an insulating oxide. Here we show that in Ca2CuO2Cl2 with dilute hole doping, an isolated dopant exhibits an in-gap electronic state with a spatial pattern consistent with a localized Zhang–Rice singlet. The dopant forms a bound state with a hole in a copper orbital. With increasing hole density, the overlap of Zhang–Rice singlets generates rod-shaped patterns. These electronic molecules spontaneously segregate into plaquettes with a lateral size of approximately four lattice constants. Our spectroscopic-imaging scanning tunnelling microscopy shows that the first indication of pairing is a U-shaped energy gap that emerges in the electronic molecules. It evolves smoothly into a sharp V-shaped gap characteristic of d-wave superconductivity in extended islands of electronic molecules. These results provide insights into the emergence of Cooper pairing in cuprates.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutSource data are provided with this paper. Further data supporting the findings of this study are available from the corresponding author upon reasonable request.Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).Article ADS Google Scholar Anderson, P. W. et al. The physics behind high-temperature superconducting cuprates: the plain vanilla version of RVB. J. Phys. Condens. Matter 16, R755–R769 (2004).Article Google Scholar Weng, Z.-Y. Superconducting ground state of a doped Mott insulator. New J. Phys. 13, 103039 (2011).Article ADS Google Scholar Zhang, F. C. & Rice, T. M. Effective Hamiltonian for the superconducting Cu oxides. Phys. Rev. B 37, 3759–3761 (1988).Article ADS Google Scholar Corboz, P., Rice, T. M. & Troyer, M. Competing states in the t–J model: uniform d-wave state versus stripe state. Phys. Rev. Lett. 113, 046402 (2014).Article ADS Google Scholar Huang, E. W. et al. Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors. Science 358, 1161–1164 (2017).Article ADS MathSciNet Google Scholar Jiang, H.-C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t′. Science 365, 1424–1428 (2019).Article ADS MathSciNet Google Scholar Zheng, B.-X. et al. Stripe order in the underdoped region of the two-dimensional Hubbard model. Science 358, 1155–1160 (2017).Article ADS MathSciNet Google Scholar Qin, M. et al. Absence of superconductivity in the pure two-dimensional Hubbard model. Phys. Rev. X 10, 031016 (2020).

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Zou for helpful discussions.Y.W. is supported by the Basic Science Center Project of the NSFC (Grant No. 52388201), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302502) and the New Cornerstone Science Foundation through the New Cornerstone Investigator Program and the XPLORER PRIZE. The work at IOPCAS was supported by National Natural Science Foundation of China (Grant No. 12204515), the National Key Research and Development Program of China (Grant Nos. 2022YFA1403804 and 2023YFA1406001) and the Young Elite Scientists Sponsorship Program of CAST (Grant No. 2022QNRC001).These authors contributed equally: Shusen Ye, Jianfa Zhao, Zhiheng Yao, Sixuan Chen.State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, ChinaShusen Ye, Zhiheng Yao, Sixuan Chen, Zehao Dong, Zhenqi Hao & Yayu WangBeijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, ChinaJianfa Zhao, Xintong Li, Luchuan Shi, Qingqing Liu & Changqing JinCenter for High-Pressure Science and Technology Advanced Research, Beijing, ChinaRunze YuNew Cornerstone Science Laboratory, Frontier Science Center for Quantum Information, Beijing, ChinaYayu WangHefei National Laboratory, Hefei, ChinaYayu WangSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarY.W. supervised this project. J.Z., R.Y., L.S., Q.L. and C.J. prepared the CCOC single crystals. S.Y., Z.Y., S.C., Z.D., Z.H. and X.L. carried out the STM experiments and data analysis. S.Y. and Y.W. prepared the paper with comments from all authors.Correspondence to Yayu Wang.The authors declare no competing interests.Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a, Topographic image of the p = 0.015 sample, showing isolated and coupled hole dopants. The magenta box highlights the dopant position. b-j, The dI/dV maps in the same area as in a, at Vb = −200, 0, 100, 200, 300, 400, 600, 800 and 1000 mV, respectively. The dashed magenta square in f marks the case where the ZRS shows intensity variations on the four lobes. The data are taken at T = 77 K.a, Topography of the single dopant with the electronic state centered around the dopant. b-f, The dI/dV maps of the area in a at Vb = 0, 200, 400, 600 and 800 mV, respectively. g-l, Similar dataset to panels a-f, but for a single-hole state where the dI/dV map is centered around the Cu site, exhibiting a four-lobe clover pattern. This experiment is conducted on the p = 0.015 sample at T = 35 K. The magenta boxes indicate the dopant position.a, Topography of two coupled dopants with a distance of (3, 0). b-h, dI/dV maps of the region in a at Vb = −200, −100, 100, 150, 200, 300 and 400 mV, respectively. i, The spectra taken along the arrow in a. j-r, Similar dataset as a-i of the two coupled dopants with a distance of (3, 1). This experiment is carried out on the p = 0.015 sample at T = 35 K. The magenta box indicates the positions of the dopants.a, Topographic image of the p = 0.03 sample in the same FOV as main text Fig. 2a taken at T = 23 K. The magenta dots represent the hole dopant positions. b-d, dI/dV maps at −50, 50 and 400 mV in the same area of a with the same box and dot markers, respectively. e-h, Similar dataset as a-d, but for a different FOV with larger area and using a different tip to eliminate possible artifact. The dashed magenta squares in d and h mark the cases where the ZRS shows intensity variations on the four lobes.a-c, The FT maps of the dI/dV maps at −50, 50 and 400 mV, respectively, from the FOV in Fig. 2a. Yellow circles indicate the Bragg peaks corresponding to the Cu lattice. d, Line profiles along the arrows in a-c, respectively. e-h, Same data analysis for dI/dV maps on the SC p = 0.10 sample.a, dI/dV map of the p = 0.07 sample at 30 mV taken at T = 5 K. The spatial occupation of rod-shaped electronic molecule with plaquette and internal stripy orbitals increases proportionally compared to the p = 0.05 sample. b-c, The zoom-in dI/dV map at 30 mV and 300 mV in the area enclosed by the cyan dashed box in a. d-e, The spectra taken along the arrows in b, displaying the U-shaped and V-shaped low-energy gaps, respectively.a-d, Zoomed-in views of dI/dV maps of the electronic molecules in the p = 0.03, 0.05, 0.07, 0.10 samples, respectively. The left panels show the low-energy stripe-shaped patterns, while right panels display the high-energy ladder-shaped patterns.a-d, Topography and dI/dV maps at −30, 30 and 200 mV of the p = 0.10 sample. e-h, Zoom-in of a-d exhibiting the stripe-ladder structure at different energies. The zoom-in area is enclosed by the yellow boxes in a-d.a, dI/dV map at 30 mV in the p = 0.10 sample, displaying the checkerboard order consisting of packed electronic molecules with 4a0 plaquettes. b, Current map of the p = 0.10 sample at 30 mV. The red dots indicate the positions of plaquette centers. c, Short red and blue bars mark the stripe orientation of each plaquette. d, Schematic diagram of parallel and perpendicular directions of plaquettes. e, Bars mark the stripe orientation with the dI/dV map background. f, Histograms of inter-plaquette distances for parallel and perpendicular orientations in the p = 0.10 sample. Both peak around 4a0, but the parallel one is much more pronounced. g-h, Similar data analysis as c-d for the p = 0.07 sample. i-j, Similar data analysis as c-d for the p = 0.05 sample, k-l, Similar data analysis as c-d for the p = 0.03 sample. The tendency of parallel alignment is more dominant in samples with lower doping level.a, dI/dV map of the p = 0.05 sample at 50 mV, displaying a crisscross of stripy patterns. b, Extracted gap-shape parameter β for a dense grid in the FOV of a. c, Spectra sorted by the gap-shape parameter β. d-f, Similar dataset as a-c for the p = 0.07 sample. g-i, Similar dataset as a-c for the p = 0.10 sample.Supplementary Sections I–V, Figs. 1–10 and Table 1.Line-cut spectra across two distinct types of single-hole state in the p = 0.015 sample.Line-cut spectra at various locations of the molecular orbital in the p = 0.03 sample.Line-cut spectra exhibiting large U-shaped, small U-shaped and V-shaped gaps in the p = 0.05 sample.Statistics of stripy orientation, representative line-cut spectra and clustered spectra for the p = 0.10, 0.05 sample.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsYe, S., Zhao, J., Yao, Z. et al. Visualization of the Zhang–Rice singlet, electronic molecules and Cooper pair formation in a cuprate superconductor. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03375-4Download citationReceived: 13 March 2025Accepted: 12 June 2026Published: 07 July 2026Version of record: 07 July 2026DOI: https://doi.org/10.1038/s41567-026-03375-4Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative