The localization of charge carriers by electronic repulsion was suggested by Mott in the 1930s to explain the insulating state observed in supposedly metallic NiO. The Mott metal–insulator transition has been subject of intense investigations ever since1,2,3—not least for its relation to high-temperature superconductivity4. A detailed comparison to real materials, however, is lacking because the pristine Mott state is commonly obscured by antiferromagnetism and a complicated band structure. Here we study organic quantum spin liquids, prototype realizations of the single-band Hubbard model in the absence of magnetic order. Mapping the Hubbard bands by optical spectroscopy provides an absolute measure of the interaction strength and bandwidth—the crucial parameters that enter calculations. In this way, we advance beyond conventional temperature–pressure plots and quantitatively compose a generic phase diagram for all genuine Mott insulators based on the absolute strength of the electronic correlations. We also identify metallic quantum fluctuations as a precursor of the Mott insulator–metal transition, previously predicted but never observed. Our results suggest that all relevant phenomena in the phase diagram scale with the Coulomb repulsion U, which provides a direct link to unconventional superconductivity in cuprates and other strongly correlated materials.

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We thank K. Kanoda and R. Valentí for fruitful discussions. Part of the work is supported by the Deutsche Forschungsgemeinschaft via DR228/41-1 and DR228/48-1. We also thank the Deutscher Akademischer Austauschdienst for support. This work was partially supported by JSPS KAKENHI grant no. JP16H06346. We acknowledge the Russian Ministry of Education and Science (Program ‘5 top 100’). We also acknowledge support from the Croatian Science Foundation project IP-2013-11-1011. J.A.S. acknowledges support from the Independent Research and Development program from the NSF while working at the Foundation and from the National High Magnetic Field Laboratory User Collaboration Grants Program. Work in Florida was supported by the NSF grant no. DMR-1410132, and the National High Magnetic Field Laboratory through the NSF cooperative agreement no. DMR-1157490 and the State of Florida. Parts of the text and results reported in this work are reproduced from the thesis of A.P.33 at the University of Stuttgart, and accessible at https://doi.org/10.18419/opus-9487.

Author information


  1. Physikalisches Institut, Universität Stuttgart, Stuttgart, Germany

    • A. Pustogow
    • , M. Bories
    • , A. Löhle
    • , R. Rösslhuber
    • , R. Hübner
    •  & M. Dressel
  2. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

    • E. Zhukova
    •  & B. Gorshunov
  3. Institut za fiziku, Zagreb, Croatia

    • S. Tomić
  4. Division of Materials Research, National Science Foundation, Arlington, VA, USA

    • J. A. Schlueter
  5. Materials Science Division, Argonne National Laboratory, Argonne, IL, USA

    • J. A. Schlueter
  6. Biomedizinische Chemie, Institut für Klinische Radiologie und Nuklearmedizin, Universität Heidelberg, Mannheim, Germany

    • R. Hübner
  7. Faculty of Agriculture, Meijo University, Nagoya, Japan

    • T. Hiramatsu
    • , Y. Yoshida
    •  & G. Saito
  8. Division of Chemistry, Graduate School of Science, Kyoto University, Kyoto, Japan

    • Y. Yoshida
  9. Toyota Physical and Chemical Research Institute, Nagakute, Japan

    • G. Saito
  10. Condensed Molecular Materials Laboratory, RIKEN, Wako-shi, Saitama, Japan

    • R. Kato
  11. Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA

    • T.-H. Lee
    •  & V. Dobrosavljević
  12. Institut Néel – CNRS and Université Grenoble Alpes, Grenoble, France

    • S. Fratini


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Most of the optical experiments and their analysis were conducted by A.P. with the help of M.B. The terahertz measurements were performed by E.Z. and B.G. Crystal growth and d.c. transport measurements on EtMe crystals were performed by R.K., and d.c. transport on AgCN and CuCN was measured by R.R. and A.L., respectively. The AgCN salts were grown by A.L., R.H., T.H., Y.Y. and G.S., and the CuCN crystals by A.L., R.H. and J.S. Theoretical calculations were carried out by T.-H.L. and V.D. in communication with S.F. The interpretation and draft of the manuscript were made by A.P. and M.D. who also conceived the project. All the authors contributed to the discussion and the final manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to A. Pustogow.

Supplementary information

  1. Supplementary Information

    Supplementary Notes 1–8, Supplementary Table 1, Supplementary Figures 1–16, Supplementary References 1–31

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