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# Interplay between superconductivity and the strange-metal state in FeSe

## Abstract

In contrast to conventional Fermi liquids where resistivity scales quadratically with temperature, unconventional superconductors usually exhibit a normal-state resistivity that varies as a linear function of temperature (T-linear) in the low-temperature limit. This phenomenon, termed as the strange metal, has been extensively studied in cuprates and is thought to be intimately linked to superconductivity. A quantitative description of its relationship with superconductivity is, therefore, of great importance for developing further theoretical understanding; however, so far, comprehensive studies are scarce due to the difficulties in realizing a systematic control of the superconducting state. Here we report the observation of a typical strange-metal behaviour in FeSe, namely, T-linear resistivity, linear-in-field magnetoresistance and universal scaling of magnetoresistance. More importantly, when we tune the superconductivity by ionic-liquid gating, the superconducting transition temperature increases from approximately 10 to 45 K, and the T-linear resistivity coefficient exhibits a quadratic dependence on the critical temperature. This is a ubiquitous feature that describes the relation between these parameters in various systems including overdoped cuprates and Bechgaard salts. This suggests that there may be a universal mechanism underlying the T-linear resistivity and unconventional superconductivity.

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## Data availability

Source data are provided with this paper. All other data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank R. Yu, H. Xie, D. Zhang, G. Xu, Z. Zhang, G. Zhang, K. Liu, X. Wu, G. He, L. Liang and B. Leridon for stimulating discussions. This work was supported by the National Key Basic Research Program of China (2022YFA1403900 (J.H., Q.C., K. Jiang), 2022YFA1403000 (Q.C.), 2021YFA0718700 (K. Jin), 2017YFA0302900 (T.X., K. Jin)), the National Natural Science Foundation of China (12225412 (K. Jin), 11834016 (K. Jin, J.Y.), 11888101 (T.X.), U1832214 (M.Y., J.W.), 11874359 (Z.W.), 11927808 (K. Jin, J.Y.), 11961141008 (B.Z.) and 12274439 (Y.L.)), the Beijing Nova Program of Science and Technology (Grant No. 20220484014 (Q.C.)), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB25000000 (K. Jin), XDB33000000 (Q.C.)), Beijing Natural Science Foundation (Z190008 (K. Jin, J.Y., Q.C.)), CAS Project for Young Scientists in Basic Research (2022YSBR-048 (K. Jin, J.Y., Y.L.)). The Key Area Research and Development Program of Guangdong Province (grant no. 2020B0101340002 (K. Jin)). A portion of this work was performed on the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, Chinese Academy of Sciences, and supported by the High Magnetic Field Laboratory of Anhui Province. The pulsed field measurements were performed at Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology.

## Author information

Authors

### Contributions

Q.C., K. Jin. and Zhongxian Zhao conceived and supervised the project. Q.C., X.J., M.Q. and X.W. performed the electrical transport and TCMI measurements. M.Q. and R.Z. designed the TCMI measurement device. M.Q., L.X. and Q.C. performed the high-magnetic-field measurements, with help from J.K., H.Z., R.Z., Q.L., Z. Wei, P.X., C.X., Z. Wang, M.Y. and J.W. Zhanyi Zhao, Z.L., Z.F. and F.C. synthesized the FeSe films. X.J. and Q.C. analysed the experimental data, with assistance from J.Y., B.Z. and Y.L. T.X., J.H. and K. Jiang contributed to the theoretical discussions. X.J., Q.C. and K. Jin wrote the manuscript with input from all authors.

### Corresponding authors

Correspondence to Qihong Chen or Kui Jin.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Physics thanks Ivan Bozovic, Luca de’ Medici and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 The imaginary part of the pick-up signal.

ImVp as a function of temperature in successive gating sequences, with one-to-one correspondence (same colour coding) to the data in Fig. 2b of the main text.

### Extended Data Fig. 2 Linear- to quadratic-in-H crossover of MR.

Normalized resistivity [$$\tilde \rho = \rho (T,H)/\rho \left( {250{{{\mathrm{K}}}},0{{{\mathrm{T}}}}} \right)$$] as a function of field at different temperatures for a gated FeSe film with a, Tc ≈ 35 K and b, Tc ≈ 43 K. From the bottom to the top curve in each panel, the temperatures are a, 30, 33, 36, 39, 42, 46 and 50 K, and b, 36, 39, 42, 45, 48, 51, 55, 60, 65 and 70 K. The black dashed and blue dashed lines are fits using linear- and H2-dependence, respectively.

### Extended Data Fig. 3 Normal-state transport of an ion-gated FeSe film.

Temperature dependence of resistivity for an ion-gated state with Tc ≈ 43 K, at 0T (solid line) and 50 T (red dots). The dashed line is a linear guide.

### Extended Data Fig. 4 Tc versus $$A_{1^\square }$$ plots for different unconventional superconductors.

Symbols are data extracted from literature and solid curves are fits with the formula ($$\tilde A_{1^\square }$$)n = αTc+β, where n is a fitting parameter. Data for La2–xSrxCuO4, are extracted from ref. 34; data for (TMTSF)2PF6 and Tl2Ba2CuO6+δ (Tl2201) are from ref. 16 and references therein; data for (Pb/La)-doped Bi2Sr2CuO6+δ (Bi2201) are extracted from ref. 44. The error bars are reproduced from published data and reflect the uncertainty in determining Tc and the T-linear coefficient.

## Supplementary information

### Supplementary Information

Supplementary Sections 1–7.

## Source data

### Source Data Fig. 1

Source data for Fig. 1.

### Source Data Fig. 2

Source data for Fig. 2.

### Source Data Fig. 3

Source data for Fig. 3.

### Source Data Extended Data Fig. 1

Source data for Extended Data Fig. 1.

### Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2.

### Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3.

### Source Data Extended Data Fig. 4

Source data for Extended Data Fig. 4.

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Jiang, X., Qin, M., Wei, X. et al. Interplay between superconductivity and the strange-metal state in FeSe. Nat. Phys. 19, 365–371 (2023). https://doi.org/10.1038/s41567-022-01894-4

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• DOI: https://doi.org/10.1038/s41567-022-01894-4