Conformally invariant charge fluctuations in a strange metal

The strange metal is a peculiar phase of matter in which the electron scattering rate, $τ^{-1} \sim k_B T/\hbar$, which determines the electrical resistance, is universal across a wide family of materials and determined only by fundamental constants. In 1989, theorists hypothesized that this universality would manifest as scale-invariant behavior in the dynamic charge susceptibility, $χ''(q,ω)$. Here, we present momentum-resolved inelastic electron scattering measurements of the strange metal Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ showing that the susceptibility has the scale-invariant form $χ''(q,ω) = T^{-ν} f(ω/T)$, with exponent $ν= 0.93$. We find the response is consistent with conformal invariance, meaning the dynamics may be thought of as occurring on a circle of radius $1/T$ in imaginary time, characterized by conformal dimension $Δ= 0.05$. Our study indicates that the strange metal is a universal phenomenon whose properties are not determined by microscopic properties of a particular material.