Abstract
Progress toward a complete understanding of cuprate superconductors has been hindered by their intricate phase diagram, potentially linked to a quantum critical point (QCP). However, conclusive evidence for the QCP is lacking, as the presumed QCP is buried under the superconducting dome, disguising its presence. Here, we use high-resolution resonant inelastic X-ray scattering to examine the dynamical charge-charge correlation in La2−xSrxCuO4 and uncover the quantum critical scaling, a key feature required for a QCP. Specifically, we observed that the inverse correlation lengths for various dopings and temperatures collapsed onto a universal scaling curve, yielding a critical exponent ν of 0.74 ± 0.08. The non-negativity of this exponent confirms the presence of a QCP. Remarkably, the value of ν suggests that while the QCP is manifested through the charge-density wave, other orders also participate, such that the QCP appears to belong to the universality class characterized by the O(4) symmetry, reminiscent of the microscopic SO(4) symmetry in the Hubbard model at half-filling. Further analysis indicates that the QCP is highly dissipative with a short quasi-particle lifetime, reflecting the intertwined quantum fluctuations due to its being buried inside the superconducting state.
Acknowledgements
The authors acknowledge Chung-Hou Chung, Yu-Te Hsu, Riccardo Arpaia, and Gregory S. Boebinger for their insightful discussions. DJH acknowledges support from the National Science and Technology Council of Taiwan [NSTC112-2112-M-213-026]. HYH acknowledges support from the National Science and Technology Council of Taiwan [NSTC113-2112-M-213-016 and NSTC114-2112-M-213-010]. CYM acknowledges support from the National Science and Technology Council of Taiwan [NSTC112-2112-M-007-031] and the Center for Quantum Science and Technology within the framework of the Higher Education Sprout Project of the Ministry of Education (MOE) of Taiwan. AF acknowledges support from the National Science and Technology Council of Taiwan [NSTC113-2112-M-007-033] and the Yushan Fellow Program under the MOE of Taiwan.
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Huang, H.Y., Mou, C.Y., Singh, A. et al. Quantum critical behavior of cuprate superconductors observed by inelastic X-ray scattering. Nat Commun (2026). https://doi.org/10.1038/s41467-026-72812-y
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DOI: https://doi.org/10.1038/s41467-026-72812-y
