Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T-TaSe2

Abstract

Quantum spin liquids are highly entangled, disordered magnetic states that are expected to arise in frustrated Mott insulators and to exhibit exotic fractional excitations such as spinons and chargons. Despite being electrical insulators, some quantum spin liquids are predicted to exhibit gapless itinerant spinons that yield metallic behaviour in the charge-neutral spin channel. We deposited isolated magnetic atoms onto single-layer 1T-TaSe2, a candidate gapless spin liquid, to probe how itinerant spinons couple to impurity spin centres. Using scanning tunnelling spectroscopy, we observe the emergence of new, impurity-induced resonance peaks at the 1T-TaSe2 Hubbard band edges when cobalt adatoms are positioned to have maximal spatial overlap with the local charge distribution. These resonance peaks disappear when the spatial overlap is reduced or when the magnetic impurities are replaced with nonmagnetic impurities. Theoretical simulations of a modified Anderson impurity model show that the observed peaks are consistent with a Kondo resonance induced by spinons combined with spin-charge binding effects that arise due to fluctuations of an emergent gauge field.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Co adatoms at the on-centre position on single-layer (SL) 1T-TaSe2 show new resonance peaks at Hubbard band edges.
Fig. 2: Electronic behaviour of Co adatoms at different locations on SL 1T-TaSe2.
Fig. 3: STM spectrum of a single nonmagnetic impurity (Au) on SL 1T-TaSe2.
Fig. 4: Calculated spinon Kondo effect.
Fig. 5: Gauge-field fluctuations induce electronic band-edge resonances and bound states.

Data availability

The data represented in Figs. 1d, 2e, 3, 4 and 5 are available as Source Data files. All other data that support the plots within this paper and other findings of this study are available upon request. Source data are provided with this paper.

Code availability

The codes used in the calculations shown in Figs. 4, 5c, 5d, S6a–c, S6d, S7, S8 and S9 are available as Supplementary Data Files 18.

References

  1. Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).

    Article  MathSciNet  ADS  Google Scholar 

  2. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    Article  ADS  Google Scholar 

  3. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

    Article  ADS  Google Scholar 

  4. Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2016).

    Article  ADS  Google Scholar 

  5. Motrunich, O. I. Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)2Cu2(CN)3. Phys. Rev. B 72, 045105 (2005).

    Article  ADS  Google Scholar 

  6. Block, M. S., Sheng, D. N., Motrunich, O. I. & Fisher, M. P. A. Spin Bose-metal and valence bond solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder. Phys. Rev. Lett. 106, 157202 (2011).

    Article  ADS  Google Scholar 

  7. He, W.-Y., Xu, X. Y., Chen, G., Law, K. T. & Lee, P. A. Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS2. Phys. Rev. Lett. 121, 046401 (2018).

    Article  ADS  Google Scholar 

  8. Lee, S.-S. & Lee, P. A. U(1) gauge theory of the Hubbard model: spin liquid states and possible application to κ-(BEDT−TTF)2Cu2(CN)3. Phys. Rev. Lett. 95, 036403 (2005).

    Article  ADS  Google Scholar 

  9. Mross, D. F. & Senthil, T. Charge Friedel oscillations in a Mott insulator. Phys. Rev. B 84, 041102 (2011).

    Article  ADS  Google Scholar 

  10. Yamashita, M. et al. Highly mobile gapless excitations in a two-dimensional candidate quantum spin liquid. Science 328, 1246–1248 (2010).

    Article  ADS  Google Scholar 

  11. Shen, Y. et al. Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540, 559–562 (2016).

    Article  ADS  Google Scholar 

  12. Paddison, J. A. M. et al. Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Nat. Phys. 13, 117–122 (2017).

    Article  Google Scholar 

  13. Klanjšek, M. et al. A high-temperature quantum spin liquid with polaron spins. Nat. Phys. 13, 1130–1134 (2017).

    Article  Google Scholar 

  14. Yamashita, M. Boundary-limited and glassy-like phonon thermal conduction in EtMe3Sb[Pd(dmit)2]2. J. Phys. Soc. Jpn. 88, 083702 (2019).

    Article  ADS  Google Scholar 

  15. Bourgeois-Hope, P. et al. Thermal conductivity of the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2: no evidence of mobile gapless excitations. Phys. Rev. X 9, 041051 (2019).

    Google Scholar 

  16. Ni, J. M. et al. Absence of magnetic thermal conductivity in the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2. Phys. Rev. Lett. 123, 247204 (2019).

    Article  ADS  Google Scholar 

  17. Zhu, Z., Maksimov, P. A., White, S. R. & Chernyshev, A. L. Disorder-induced mimicry of a spin liquid in YbMgGaO4. Phys. Rev. Lett. 119, 157201 (2017).

    Article  ADS  Google Scholar 

  18. Madhavan, V., Chen, W., Jamneala, T., Crommie, M. F. & Wingreen, N. S. Tunneling into a single magnetic atom: spectroscopic evidence of the Kondo resonance. Science 280, 567–569 (1998).

    Article  ADS  Google Scholar 

  19. Hudson, E. W. et al. Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+δ. Nature 411, 920–924 (2001).

    Article  ADS  Google Scholar 

  20. Ribeiro, P. & Lee, P. A. Magnetic impurity in a U(1) spin liquid with a spinon Fermi surface. Phys. Rev. B 83, 235119 (2011).

    Article  ADS  Google Scholar 

  21. Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, 1993).

  22. Gomilšek, M. et al. Kondo screening in a charge-insulating spinon metal. Nat. Phys. 15, 754–758 (2019).

    Article  Google Scholar 

  23. Chen, Y. et al. Strong correlations and orbital texture in single-layer 1T-TaSe2. Nat. Phys. 16, 218–224 (2020).

    Article  Google Scholar 

  24. Ruan, W. et al. Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy. Nat. Phys. 17, 1154–1161 (2021).

    Article  Google Scholar 

  25. Ge, Y. & Liu, A. Y. First-principles investigation of the charge-density-wave instability in 1T-TaSe2. Phys. Rev. B 82, 155133 (2010).

    Article  ADS  Google Scholar 

  26. Heinrich, A. J., Gupta, J. A., Lutz, C. P. & Eigler, D. M. Single-atom spin-flip spectroscopy. Science 306, 466–469 (2004).

    Article  ADS  Google Scholar 

  27. Hirjibehedin, C. F., Lutz, C. P. & Heinrich, A. J. Spin coupling in engineered atomic structures. Science 312, 1021–1024 (2006).

    Article  ADS  Google Scholar 

  28. Garnier, L. et al. The Kondo effect of a molecular tip as a magnetic sensor. Nano Lett. 20, 8193–8199 (2020).

    Article  ADS  Google Scholar 

  29. Franchini, C., Reticcioli, M., Setvin, M. & Diebold, U. Polarons in materials. Nat. Rev. Mater. 6, 560–586 (2021).

    Article  ADS  Google Scholar 

  30. Setvin, M. et al. Direct view at excess electrons in TiO2 rutile and anatase. Phys. Rev. Lett. 113, 086402 (2014).

    Article  ADS  Google Scholar 

  31. Tütto, I. & Zawadowski, A. Quantum theory of local perturbation of the charge-density wave by an impurity: Friedel oscillations. Phys. Rev. B 32, 2449–2470 (1985).

    Article  ADS  Google Scholar 

  32. Cai, P. et al. Visualizing the evolution from the Mott insulator to a charge-ordered insulator in lightly doped cuprates. Nat. Phys. 12, 1047–1051 (2016).

    Article  Google Scholar 

  33. Ye, C. et al. Visualizing the atomic-scale electronic structure of the Ca2CuO2Cl2 Mott insulator. Nat. Commun. 4, 1365 (2013).

    Article  ADS  Google Scholar 

  34. Okada, Y. et al. Imaging the evolution of metallic states in a correlated iridate. Nat. Mater. 12, 707–713 (2013).

    Article  ADS  Google Scholar 

  35. Battisti, I. et al. Universality of pseudogap and emergent order in lightly doped Mott insulators. Nat. Phys. 13, 21–25 (2017).

    Article  Google Scholar 

  36. Zhao, H. et al. Atomic-scale fragmentation and collapse of antiferromagnetic order in a doped Mott insulator. Nat. Phys. 15, 1267–1272 (2019).

    Article  Google Scholar 

  37. Yan, Y. J. et al. Electron-doped Sr2IrO4: an analogue of hole-doped cuprate superconductors demonstrated by scanning tunneling microscopy. Phys. Rev. X 5, 041018 (2015).

    Google Scholar 

  38. Sun, Z. et al. Evidence for a percolative Mott insulator–metal transition in doped Sr2IrO4. Phys. Rev. Res. 3, 023075 (2021).

    Article  Google Scholar 

  39. Cho, D., Cho, Y.-H., Cheong, S.-W., Kim, K.-S. & Yeom, H. W. Interplay of electron–electron and electron–phonon interactions in the low-temperature phase of 1T−TaS2. Phys. Rev. B 92, 293602 (2015).

    Article  Google Scholar 

  40. Zhu, X.-Y. et al. Realization of a metallic state in 1T-TaS2 with persisting long-range order of a charge density wave. Phys. Rev. Lett. 123, 206405 (2019).

    Article  ADS  Google Scholar 

  41. Qiao, S. et al. Mottness collapse in 1T−TaS2−xSex transition-metal dichalcogenide: an interplay between localized and itinerant orbitals. Phys. Rev. X 7, 041054 (2017).

    Google Scholar 

  42. Madhavan, V., Chen, W., Jamneala, T., Crommie, M. F. & Wingreen, N. S. Local spectroscopy of a Kondo impurity: Co on Au(111). Phys. Rev. B 64, 165412 (2001).

    Article  ADS  Google Scholar 

  43. Kim, B. J. et al. Distinct spinon and holon dispersions in photoemission spectral functions from one-dimensional SrCuO2. Nat. Phys. 2, 397–401 (2006).

    Article  Google Scholar 

  44. Florens, S. & Georges, A. Quantum impurity solvers using a slave rotor representation. Phys. Rev. B 66, 165111 (2002).

    Article  ADS  Google Scholar 

  45. He, W.-Y. & Lee, P. A. Magnetic impurity as a local probe of the U(1) quantum spin liquid with spinon Fermi surface. Phys. Rev. B 105, 195156 (2022).

    Article  ADS  Google Scholar 

  46. Florens, S. & Georges, A. Slave-rotor mean-field theories of strongly correlated systems and the Mott transition in finite dimensions. Phys. Rev. B 70, 035114 (2004).

    Article  ADS  Google Scholar 

  47. Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866–1878 (1961).

    Article  MATH  ADS  Google Scholar 

  48. Wen, X.-G. & Lee, P. A. Theory of underdoped cuprates. Phys. Rev. Lett. 76, 503–506 (1996).

    Article  ADS  Google Scholar 

  49. Lee, P. A., Nagaosa, N., Ng, T.-K. & Wen, X.-G. SU(2) formulation of the tJ model: application to underdoped cuprates. Phys. Rev. B 57, 6003–6021 (1998).

    Article  ADS  Google Scholar 

  50. Nagaosa, N. Quantum Field Theory in Strongly Correlated Electronic Systems (Springer, 1999).

  51. Dhochak, K., Shankar, R. & Tripathi, V. Magnetic impurities in the honeycomb Kitaev model. Phys. Rev. Lett. 105, 117201 (2010).

    Article  ADS  Google Scholar 

  52. Vojta, M., Mitchell, A. K. & Zschocke, F. Kondo impurities in the Kitaev spin liquid: numerical renormalization group solution and gauge-flux-driven screening. Phys. Rev. Lett. 117, 037202 (2016).

    Article  ADS  Google Scholar 

  53. Banerjee, A. et al. Neutron scattering in the proximate quantum spin liquid α-RuCl3. Science 356, 1055–1059 (2017).

    Article  ADS  Google Scholar 

  54. Janša, N. et al. Observation of two types of fractional excitation in the Kitaev honeycomb magnet. Nat. Phys. 14, 786–790 (2018).

    Article  Google Scholar 

  55. Wang, L., Maxisch, T. & Ceder, G. Oxidation energies of transition metal oxides within the GGA + U framework. Phys. Rev. B 73, 195107 (2006).

    Article  ADS  Google Scholar 

  56. de la Peña O’Shea, V. A., Moreira, I. D. P. R., Roldán, A. & Illas, F. Electronic and magnetic structure of bulk cobalt: the α, β, and ε-phases from density functional theory calculations. J. Chem. Phys. 133, 024701 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research was supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator (STM/STS measurements) and the Advanced Light Source (sample growth) funded by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under contract no. DE-AC02-05CH11231. Support was also provided by National Science Foundation awards DMR-2221750 (topographic characterization) and DMR-1926004 (DFT calculations). The work at the Stanford Institute for Materials and Energy Sciences and Stanford University (surface treatment) was supported by the DOE Office of Basic Energy Sciences, Division of Material Science. P.A.L. acknowledges support from DOE Basic Energy Science award number DE-FG02-03ER46076 (theoretical QSL analysis). H.R. acknowledges support from a National Research Foundation of Korea grant funded by the government of Korea (MSIT) (no. 2021R1A2C2014179) (growth characterization). W.R. acknowledges fellowship support from Shanghai Science and Technology Development Funds (no. 22QA1400600).

Author information

Authors and Affiliations

Authors

Contributions

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

Corresponding author

Correspondence to Michael F. Crommie.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Elio Koenig and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Notes 1–3 and Figs. 1–9.

Supplementary Data 1

Code for simulations of Fig. 4.

Supplementary Data 2

Code for simulations of Fig. 5c.

Supplementary Data 3

Code for simulations of Fig. 5d.

Supplementary Data 4

Code for simulations of Fig. S6a–c.

Supplementary Data 5

Code for simulations of Fig. S6d.

Supplementary Data 6

Code for simulations of Fig. S7.

Supplementary Data 7

Code for simulations of Fig. S8.

Supplementary Data 8

Code for simulations of Fig. S9.

Source data

Source Data Fig. 1

Raw data for Fig. 1d.

Source Data Fig. 2

Raw data for Fig. 2e.

Source Data Fig. 3

Raw data for Fig. 3.

Source Data Fig. 4

Raw data for Fig. 4.

Source Data Fig. 5

Raw data for Fig. 5.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, Y., He, WY., Ruan, W. et al. Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T-TaSe2. Nat. Phys. 18, 1335–1340 (2022). https://doi.org/10.1038/s41567-022-01751-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01751-4

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing