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# Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides

## Abstract

The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many-body physics. Conventional superconductors are insensitive to dilute non-magnetic impurities, known as Anderson’s theorem1. Destruction of superconductivity and even superconductor–insulator transitions2,3,4,5,6,7,8,9,10 occur in the regime of strong disorder. Hence, disorder-enhanced superconductivity is rare and has been observed only in some alloys or granular states11,12,13,14,15,16,17. Owing to the entanglement of various effects, the mechanism of enhancement is still under debate. Here, we report a well-controlled disorder effect in the recently discovered monolayer NbSe2 superconductor. The superconducting transition temperatures of NbSe2 monolayers are substantially increased by disorder. Realistic theoretical modelling shows that the unusual enhancement possibly arises from the multifractality18,19 of electron wavefunctions. This work provides experimental evidence of the multifractal superconducting state.

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## Data availability

All relevant data are available from the corresponding authors on reasonable request.

## Code availability

All relevant codes or algorithms are available from the corresponding authors on reasonable request.

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## Acknowledgements

We thank A. M. García-García for stimulating discussions. This work is supported by the Ministry of Science and Technology of China (grant nos. 2018YFA0305600, 2016YFA0301002, 2017YFA0303302, 2013CB934600), the National Natural Science Foundation of China (grant nos. 51561145005, 11622433, 11574175, 51522212, 11774008, 11704414). K.T.L. would like to acknowledge the support of HKRGC (grants 16324216, 16309718, 6307117 and C6026-16W), Croucher Foundation and Dr. Tai-Chin Lo Foundation. L.G. is partially supported by Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB07030200). M.S.B. and N.N. gratefully acknowledge support from the CREST, JST (no. JPMJCR16F1). N.N. is also supported by JSPS KAKENHI grant numbers 18H03676 and 26103006. M.S.B. is also supported by the Japan Society for Promotion of Science (Grant-in-Aid for Scientific Research (S) no. 24224009).

## Author information

Authors

### Contributions

S.-H.J. and X.C. coordinated the project and designed the experiments. K.Z., H.L. and W.H. performed the molecular beam epitaxy growth and STM experiments. X.X. and K.T.L. provided the multifractal interpretation and the model calculations. W.Y., M.Y. and S.Z. contributed the ARPES measurement. Q.Z. and L.G. contributed the STEM characterization. M.S.B. calculated the electronic band by density functional theory. Z.-X.L., S.H., H.Y. and N.N. contributed part of the theoretical analysis. K.Z., H.L., X.X., K.T.L., S.-H.J. and X.C. co-wrote the paper. All authors discussed the results and commented on the manuscript.

### Corresponding authors

Correspondence to Xi Chen or Shuai-Hua Ji.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary text, Figs. 1–23 and refs.

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Reprints and Permissions

Zhao, K., Lin, H., Xiao, X. et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nat. Phys. 15, 904–910 (2019). https://doi.org/10.1038/s41567-019-0570-0

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