Universality of Strange Metals

The strange metal is a peculiar phase of matter in which the electron scattering rate, $\tau^{-1} \sim k_B T/\hbar$, 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, $\chi''(q,\omega)$. In this talk I will 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 $\chi''(q,\omega) = T^{-\nu} f(\omega/T)$, with exponent $\nu = 0.93$. The universal function, $f(\omega/T)$ has a relaxational form and is {\it nearly} momentum-independent, indicating some kind of emergent, local physics is at work. Finally, I will show find the overall 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 $\Delta = 0.05$. Our study suggests that the strange metal is a universal phenomenon whose behavior is not determined by microscopic properties of a particular material.