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# Spin–orbit–parity coupled superconductivity in atomically thin 2M-WS2

## Abstract

The investigation of two-dimensional atomically thin superconductors—especially those hosting topological states—attracts growing interest in condensed-matter physics. Here we report the observation of spin–orbit–parity coupled superconducting state in centrosymmetric atomically thin 2M-WS2, a material that has been predicted to exhibit topological band inversions. Our magnetotransport measurements show that the in-plane upper critical field not only exceeds the Pauli paramagnetic limit but also exhibits a strongly anisotropic two-fold symmetry in response to the in-plane magnetic field direction. Furthermore, tunnelling spectroscopy measurements conducted under high in-plane magnetic fields reveal that the superconducting gap possesses an anisotropic magnetic response along different in-plane magnetic field directions, and it persists much above the Pauli limit. Self-consistent mean-field calculations show that this unusual behaviour originates from the strong spin–orbit–parity coupling arising from the topological band inversion in 2M-WS2, which effectively pins the spin of states near the topological band crossing and gives rise to an anisotropic renormalization of the effect of external Zeeman fields. Our results identify the unconventional superconductivity in atomically thin 2M-WS2, which serves as a promising platform for exploring the interplay between superconductivity, topology and strong spin–orbit–parity coupling.

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## Data availability

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

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## Acknowledgements

This work was supported by the National Key Research and Development Program of China (grant nos. 2017YFA0303302 and 2018YFA0305601), the National Natural Science Foundation of China (grant nos. 52225207, 52150103, 11934005 and 11874116), the Science and Technology Commission of Shanghai (grant no. 19511120500), the Shanghai Municipal Science and Technology Major Project (grant no. 2019SHZDZX01), the Program of Shanghai Academic/Technology Research Leader (grant no. 20XD1400200), the Shanghai Pilot Program for Basic Research—Fudan University 21TQ1400100(21TQ006) and the Henry Royce Institute for Advanced Materials, funded through EPSRC grants EP/R00661X/1, EP/S019367/1, EP/P025021/1 and EP/P025498/1. E.Z. acknowledges support from China Postdoctoral Innovative Talents Support Program (grant no. BX20190085) and China Postdoctoral Science Foundation (grant no. 2019M661331). Y.F. acknowledges support from China Postdoctoral Innovative Talents Support Program (grant no. BX2021329) and National Natural Science Foundation of China (52103353). J.Z. was supported by the National Natural Science Foundation of China (grant nos. 12122411 and U1932154). Y.-C.Z. thanks the financial support from the Guangzhou Basic and Applied Basic Research Foundation (202201011074), the National Natural Science Foundation of China (grant no. 12104517) and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (22qntd0101). S.J.H. acknowledges the funding from the European Research Council under the Horizon 2020 research and innovation programme (EvoluTEM grant no. [715502]). K.T.L. acknowledges the support of the Ministry of Science and Technology of China and the HKRGC through MOST20SC04, RFS2021-6S03, C6025-19G, AoE/P-701/20, 16310219, 16309718 and 16310520. Part of the sample fabrication was performed at Fudan Nano-fabrication Laboratory.

## Author information

Authors

### Contributions

F.X. conceived the idea and supervised the experiments. E.Z., Yuda Zhang, Z.J., L.A., S.L. and J. Yan carried out the device fabrication. Y.F., W.Z. and F.H. synthesized the 2M-WS2 bulk crystals. Y.-C.Z. and S.J.H. performed structural characterization and analysis. Y.-M.X., X.-J.G. and K.T.L. performed the theoretical work. E.Z., J.Z., P.L., Yong Zhang, and X.K. performed low-temperature measurements. E.Z., Y.-M.X., X.X., K.T.L., J. Yang, S.D. and F.X. analysed the data and co-wrote the paper with help from all the other authors.

### Corresponding authors

Correspondence to Jinshan Yang, Fuqiang Huang, K. T. Law or Faxian Xiu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 Normalized angular-dependent magnetoresistance of 2D 2M-WS2 at temperatures below and beyond TC.

a, b, Normalized angular dependent magnetoresistance of a 2D 2M-WS2 device (Device 11, thickness approximately 5 nm, TC = 7.7 K) at various temperatures under in-plane magnetic field B = 8 T (a) and 9 T (b), respectively. In both (a) and (b), the angular dependent R/RN exhibits two-fold oscillation behavior. The oscillation behavior diminishes at elevated temperatures especially when T > TC.

### Extended Data Fig. 2 Theoretical calculated in-plane spin susceptibility of bilayer 2M-WS2.

a, Calculated normalized in-plane spin susceptibility χS/χ0 as a function of temperature along the direction of γ = 0° (red solid line) and γ = 90° (black solid line). At T > TC, the spin susceptibility of normal states χN is reduced to values that are smaller than χ0 by the SOPC. b, Calculated angular dependence of χN/χ0 for the case with (green solid line) and without SOPC (red solid line).

### Extended Data Fig. 3 Temperature-dependent tunneling spectra of Device 06.

a, Contour plot of normalized tunneling conductance of Device 06 as a function of bias voltage and temperature (magnetic field B = 0 T). b, Normalized tunneling conductance as a function of bias voltage at various temperatures. The two symmetric peaks become less prominent at elevated temperatures. c, Shifted normalized tunneling conductance as a function of bias voltage at elevated temperatures. The red dashed lines are the fit to the BTK model for the NIS junction. d, Extracted temperature-dependent superconducting gap Δ from (c). The red solid line is the fit to standard BCS theory $${{{\mathrm{{\Delta}}}}}\left( 0 \right) = {{{\mathrm{tanh}}}}\left( {\sqrt {{{{\mathrm{Ta}}}}/{{{\mathrm{T}}}}_{{{\mathrm{C}}}} - 1} } \right)$$. The extracted zero-temperature gap value is Δ(0) = 1.33 meV. 2Δ(0) ≈ 3.67kBTC which is nearly in line with the BCS value of 3.52kBTC. The error bars of Δ correspond to the BTK fitting errors.

### Extended Data Fig. 4 Calculated superconducting phase diagram of atomically thin 2M-WS2.

a, b, Theoretically calculated $$B_{C2}^{||}/B_p - T/T_C$$ phase found from minimizing the free energy of bilayer 2M-WS2 without (a) and with (b) adding the orbital effect, respectively. The color represents the magnitude of the superconducting gap Δ/Δ0 (The zero-field BCS gap Δ0 = 1.764 kBTC) at different magnetic fields and temperatures. c. The calculated Δ/Δ0 as a function of B||/BP without (red solid line) and with (violet solid line) considering an orbital effect, corresponding to the line cut of (a) and (b) at T = 0.2 TC. Note that the $$B_{C2}^{||}/B_P$$ value at which the superconducting gap reaches zero changes very little with and without the orbital effect ($$\lesssim 7{{{\mathrm{\% }}}}$$), which indicates that the reduction of the $$B_{C2}^{||}$$ by the weak orbital effect is roughly less than 7%.

## Supplementary information

### Supplementary Information

Supplementary Text 1–11, Figs. 1–18, Tables 1 and 2 and Refs. 1–38.

## Source data

### Source Data Fig. 2

Statistical source data for Fig. 2.

### Source Data Fig. 3

Statistical source data for Fig. 3.

### Source Data Fig. 4

Statistical source data for Fig. 4a,c,d,f.

### Source Data Extended Data Fig. 1

Statistical source data for Extended Data Fig. 1.

### Source Data Extended Data Fig. 2

Statistical source data for Extended Data Fig. 2.

### Source Data Extended Data Fig. 3

Statistical source data for Extended Data Fig. 3.

### Source Data Extended Data Fig. 4

Statistical source data for Extended Data Fig. 4.

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Zhang, E., Xie, YM., Fang, Y. et al. Spin–orbit–parity coupled superconductivity in atomically thin 2M-WS2. Nat. Phys. 19, 106–113 (2023). https://doi.org/10.1038/s41567-022-01812-8

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• DOI: https://doi.org/10.1038/s41567-022-01812-8

• ### A highly anisotropic polymorph

• Joseph Falson

Nature Physics (2023)