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Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy

Nature Physics volume 17, pages 1154–1161 (2021)Cite this article

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Abstract

Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. Here we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe2. We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid.

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Fig. 1: Structure of SL TaSe2 and 1T/1H vertical heterostructures.
Fig. 2: Kondo resonance observed in a 1T/1H-TaSe2 vertical heterostructure.
Fig. 3: Super-modulations in SL 1T-TaSe2 visualized by spectroscopic imaging.
Fig. 4: Energy dependence of super-modulations in SL 1T-TaSe2.
Fig. 5: Super-modulation periodicities predicted from the spinon Fermi surface compared with experiment.

Data availability

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

Code availability

The codes used in this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank D.-H. Lee, J. E. Moore and M. Zaletel for helpful discussions. This research was supported by the vdW Heterostructure program (KCWF16) (STM/STS measurements) and the Advanced Light Source (sample growth and ARPES measurements) funded by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, US Department of Energy (DOE), under contract no. DE-AC02-05CH11231. Support was also provided by the National Science Foundation (NSF) via award no. DMR-1807233 (surface treatment and topographic characterization) and award no. DMR-1926004 (theoretical QPI analysis). Computational resources were provided by the NSF through the Extreme Science and Engineering Discovery Environment (XSEDE) resources. The work at the Stanford Institute for Materials and Energy Sciences and Stanford University (ARPES measurements) was supported by the Office of Basic Energy Sciences, Materials Sciences and Engineering Division, DOE. The work at Beamline 4-ID-D of the Advanced Photon Source, Argonne National Laboratory (X-ray absorption measurements), was supported by the Office of Science, Office of Basic Energy Sciences, DOE, under contract no. DE-AC02-06CH11357. P.A.L. acknowledges support by DOE Basic Energy Science award no. DE-FG02-03ER46076 (theoretical QSL analysis). S.T. acknowledges support by CPSF-CAS Joint Foundation for Excellent Postdoctoral Fellows. J.H. and C.H. acknowledge fellowship support from the NRF grant funded by the Korean government (MSIT) (no. 2021R1A2C1004266). H.-Z.T. acknowledges fellowship support from the Shenzhen Peacock Plan (grant nos. 827-000113, KQJSCX20170727100802505 and KQTD2016053112042971).

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Author notes

  1. These authors contributed equally: Wei Ruan, Yi Chen.

Authors and Affiliations

  1. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Wei Ruan, Yi Chen, Hsin-Zon Tsai, Meng Wu, Caihong Jia, Feng Wang, Steven G. Louie & Michael F. Crommie

  2. Department of Physics, University of California, Berkeley, CA, USA

    Wei Ruan, Yi Chen, Ryan L. Lee, Meng Wu, Salman Kahn, Franklin Liou, Caihong Jia, Andrew Aikawa, Feng Wang, Steven G. Louie & Michael F. Crommie

  3. Department of Physics, Fudan University, Shanghai, China

    Wei Ruan

  4. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA, USA

    Shujie Tang, Jinwoong Hwang & Zhi-Xun Shen

  5. Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA, USA

    Shujie Tang & Zhi-Xun Shen

  6. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Shujie Tang, Jinwoong Hwang, Hyejin Ryu & Sung-Kwan Mo

  7. CAS Center for Excellence in Superconducting Electronics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China

    Shujie Tang

  8. School of Physical Science and Technology, Shanghai Tech University, Shanghai, China

    Shujie Tang

  9. Department of Physics, Pusan National University, Busan, Korea

    Jinwoong Hwang & Choongyu Hwang

  10. International Collaborative Laboratory of 2D Materials for Optoelectronic Science and Technology of Ministry of Education, Engineering Technology Research Center for 2D Material Information Function Devices and Systems of Guangdong Province, Shenzhen University, Shenzhen, China

    Hsin-Zon Tsai

  11. Center for Spintronics, Korea Institute of Science and Technology, Seoul, Korea

    Hyejin Ryu

  12. Henan Key Laboratory of Photovoltaic Materials, Center for Topological Functional Materials, Henan University, Kaifeng, China

    Caihong Jia

  13. Kavli Energy NanoScience Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Feng Wang & Michael F. Crommie

  14. Advanced Photon Source, Argonne National Laboratory, Argonne, IL, USA

    Yongseong Choi

  15. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Patrick A. Lee

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Contributions

W.R., Y. Chen, P.A.L. and M.F.C. initiated and conceived this project. W.R., Y. Chen, R.L.L., H.-Z.T., S.K., F.L., C.J. and A.A. carried out the STM/STS measurements under the supervision of M.F.C. W.R., Y. Chen, F.W., P.A.L. and M.F.C. contributed to the microscopy data analysis. S.T., J.H. and H.R. performed the sample growth and ARPES measurements/analysis under the supervision of C.H., Z.-X.S. and S.-K.M. W.R., Y. Chen, R.L.L. and S.K. performed the XMCD measurements with support from Y. Choi. M.W. performed the DFT+U calculations under the supervision of S.G.L. P.A.L. provided theoretical support. W.R., Y. Chen and M.F.C. wrote the manuscript with the help from all the authors. All the authors contributed to the scientific discussion.

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Correspondence to Michael F. Crommie.

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Ruan, W., Chen, Y., Tang, S. et al. Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy. Nat. Phys. 17, 1154–1161 (2021). https://doi.org/10.1038/s41567-021-01321-0

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