Conformally invariant charge fluctuations in a strange metal

Abstract

The strange metal is a peculiar phase of matter in which the electron scattering rate, ${\tau }^{-1}\sim k_{B}T/\hslash$, 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, ${\chi }^{\prime \prime }(q,\omega )$. 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 ${\chi }^{\prime \prime }(q,\omega )=T^{-\nu }f(\omega /T)$, with exponent $\nu =0.93$. 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 $\Delta =0.05$. Our study indicates that the strange metal is a universal phenomenon whose properties are not determined by microscopic properties of a particular material.

Comments: 14 pages, 4 figures + supplementary data