Singular Density Fluctuations in the Strange Metal Phase of a Copper-Oxide Superconductor*

The “strange metal” is a poorly understood phase of matter characterized by a lack of well-defined quasi-particles, violating a core tenet of Fermi Liquid theory. In ordinary metals, the interactions between quasi-particles give rise to propagating collective charge excitations; however, the analogous excitations of the strange metal are unknown. Here, we show measurements of the charge susceptibility χ(q,ω) across the phase diagram of the strange metal, Bi_2.1Sr_1.9CaCu₂O_8+x (Bi-2212) using momentum-resolved inelastic electron scattering (M-EELS). Surprisingly, we find an energy- and momentum-independent continuum of scale-invariant charge fluctuations extending to 1eV, instead of dispersing plasmons. This continuum is temperature-independent at optimal doping, but undergoes a significant redistribution of spectral weight at low temperatures away from optimal doping. Our results indicate that the strange metal phase arises from an anomalous type of charge dynamics, especially sensitive to doping, that is not described by any known theory of quantum matter.