# Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor

## Abstract

In cuprate superconductors, the existence of various intertwined orders associated with spin, charge and Cooper pairs1,2 is an obstacle in understanding the mechanism of Cooper pairing. The ubiquitous charge order is particularly important2,3,4,5,6,7. Various theories have been proposed to explain the origin of the charge order and its implications for the superconducting phase, including charge stripes8, electronic nematicity8,9 and Fermi surface instability5,10. A highly appealing physical picture is the ‘pair density wave’, a spatially periodic modulation of Cooper pairing, which may also induce a charge order2,11,12,13,14,15,16,17,18,19,20,21. To elucidate the existence and nature of the pair density wave, we use scanning tunnelling microscopy to investigate a severely underdoped cuprate, in which superconductivity just emerges on top of a pronounced chequerboard charge order. We observe a periodic modulation of both the superconducting coherence peak and gap depth, indicating the existence of a density wave order of Cooper pairing based on the empirical relationship between superconducting coherence and superfluid density22,23,24,25,26,27. The pair density wave has the same spatial periodicity as the charge order, and the amplitudes of the two orders exhibit clear positive correlation. These results shed new light on the origin of and interplay between the charge order and Cooper pairing modulation in the cuprates.

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## Data availability

All raw and derived data used to support the findings of this work are available from the authors on request.

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## Acknowledgements

This work was supported by the Basic Science Center Project of NSFC under grant no. 51788104, NSFC grants 11190022, 11334010 and 11374335, MOST of China grants 2015CB921000 and 2017YFA0302900, and the Chinese Academy of Sciences grant XDB07020300. D.-H.L. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, grant DE-AC02-05CH11231. This work is supported in part by the Beijing Advanced Innovation Center for Future Chip (ICFC).

## Author information

W.R. and Y.W. proposed and designed the research. W.R., X.L., Z.H., H.L. and P.C. carried out the STM experiments. W.R. analysed the data with the help from Z.H. and H.L. C.H. and X.Z. provided the Bi-2212 single crystals. D.-H.L. provided theoretical analysis. Y.W. supervised STM experiments and coordinated the collaborations. Y.W. prepared the manuscript with comments from all authors.

Correspondence to Yayu Wang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary materials

Supplementary Figures 1–5, Supplementary Reference 1

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Reprints and Permissions

Ruan, W., Li, X., Hu, C. et al. Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor. Nature Phys 14, 1178–1182 (2018). https://doi.org/10.1038/s41567-018-0276-8

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