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Crossed Luttinger liquid hidden in a quasi-two-dimensional material

Abstract

Although the concept of the Luttinger liquid (LL) describing a one-dimensional (1D) interacting fermion system1,2 collapses at higher dimensions, it has been proposed to be relevant to enigmatic problems in condensed matter physics including the normal state of cuprate superconductors3,4,5, unconventional metals6,7 and quantum criticality8,9. Here we investigate the electronic structure of quasi-2D η-Mo4O11, a charge-density wave material, using high-resolution angle-resolved photoemission spectroscopy and ab initio calculations. We show a prototypical LL behaviour originating from the crossed quasi-1D chain arrays hidden in the quasi-2D crystal structure. Our results suggest that η-Mo4O11 materializes the crossed LL phase10,11,12 in its normal state, where the orthogonal orbital components substantially reduce the coupling between intersecting quasi-1D chains and therefore maintain the essential properties of the LL. Our finding not only presents a realization of a 2D LL, but also provides a new angle to understand non-Fermi liquid behaviour in other 2D and 3D quantum materials.

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Fig. 1: Physics in arrays of 1D chains and basic properties of η-Mo4O11.
Fig. 2: Comparison between the experimental and calculated electronic structure of η-Mo4O11.
Fig. 3: LL behaviour in η-Mo4O11.
Fig. 4: Ab initio calculations of the electronic structure and Wannier orbitals of η-Mo4O11.

Data availability

The datasets that support the findings of this study are available from the corresponding authors on reasonable request.

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Acknowledgements

We thank C. Chen, D.H. Lu, T. Kim, C. Cacho, Z. Sun, J. Fujii and I. Vobornik for helping with ARPES experiments. This work is funded by the National Natural Science Foundation of China (Grants No. 12274251 and No. 11774190), the National Key R&D Program of China (Grant No. 2017YFA0304600) and the EPSRC Platform Grant (Grant No. EP/M020517/1). L.X.Y. acknowledges support from the Tsinghua University Initiative Scientific Research Program. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-76SF00515. We thank Diamond Light Source for access to beamline I05 (Proposal No. SI22375-1). We acknowledge Elettra Sincrotrone Trieste for providing access to beamline APE.

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Contributions

L.X.Y. conceived the experiments. X.D. and L.K. carried out ARPES measurements with the assistance of J.S.Z., X.G., R.Z.X., Q.Q.Z., Z.X.Y., W.X.Z., Y.D.L., S.M.H., D.P., M.X.W. and Z.K.L. Data analyses on the ARPES results and the ab initio calculations were performed by X.D. Single crystals were synthesized and characterized by Y.Y.L. and Y.B.C. The first draft of the paper was written by X.D.; L.X.Y. and Y.L.C. contributed to the revision of the manuscript. All authors contributed to the scientific planning and discussion.

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Correspondence to Y. L. Chen or L. X. Yang.

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Supplementary Figs. 1–14, Tables 1 and 2 and Notes 1–15.

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Du, X., Kang, L., Lv, Y.Y. et al. Crossed Luttinger liquid hidden in a quasi-two-dimensional material. Nat. Phys. 19, 40–45 (2023). https://doi.org/10.1038/s41567-022-01829-z

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