Conformally invariant charge fluctuations in a strange metal

Abstract

The strange metal is a peculiar phase of matter in which the electron scattering rate, $\ddot{I}{„}^{-1}\sim k_{B}T/\hslash$, 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, $\ddot{I}{‡}^{\prime \prime }(q,\ddot{I}‰)$. 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 $\ddot{I}{‡}^{\prime \prime }(q,\ddot{I}‰)=T^{-\hat{I}½}f(\ddot{I}‰/T)$, with exponent $\hat{I}½=0.93$. 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 $\hat{I}”=0.05$. Our study indicates that the strange metal is a universal phenomenon whose properties are not determined by microscopic properties of a particular material.

14 pages, 4 figures + supplementary data