Conformally invariant charge fluctuations in a strange metal

TL;DR

This study provides experimental evidence that the charge fluctuations in a strange metal exhibit conformal invariance and scale-invariant behavior, supporting theories that describe strange metals as universal quantum critical states.

Contribution

First direct measurement of conformally invariant charge fluctuations in a strange metal, confirming theoretical predictions of scale invariance and conformal symmetry in these materials.

Findings

Charge susceptibility follows a scale-invariant form with exponent ~0.93.

Response consistent with conformal invariance and characterized by a conformal dimension ~0.05.

Properties are universal and not dependent on microscopic details.

Abstract

The strange metal is a peculiar phase of matter in which the electron scattering rate, $\tau^{-1} \sim k_B T/\hbar$, 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, $\chi''(q,\omega)$. 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 $\chi''(q,\omega) = T^{-\nu} f(\omega/T)$, 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.