Quantum critical behavior of cuprate superconductors observed by inelastic X-ray scattering

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 La_2-xSr_xCuO₄ and uncover the quantum critical scaling, a key feature required for a QCP. Specifically, \djh{we observed that the inverse correlation lengths for various dopings and temperatures collapsed onto a universal scaling curve, yielding a critical exponent ν of 0.75. 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 be in the universality class characterized by the O(4) symmetry, in reminiscence of the microscopic SO(4) symmetry in the Hubbard model at half filling. Further analysis indicates that the QCP is associated with a large quasi-particle lifetime, revealing the intertwined nature of quantum fluctuations.