Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La _{2– <i>x</i>} Ba <i> _x </i> CuO ₄

Abstract

Charge order is universal among high-<i>T</i> _c cuprates, but its relation to superconductivity is unclear. While static order competes with superconductivity, dynamic order may be favorable and even contribute to Cooper pairing. Using time-resolved resonant soft x-ray scattering at a free-electron laser, we show that the charge order in prototypical La_2-<i>x</i> Ba <i>_x</i> CuO₄ exhibits transverse fluctuations at picosecond time scales. These sub-millielectron volt excitations propagate by Brownian-like diffusion and have an energy scale remarkably close to the superconducting <i>T</i> _c. At sub-millielectron volt energy scales, the dynamics are governed by universal scaling laws defined by the propagation of topological defects. Our results show that charge order in La_2-<i>x</i> Ba <i>_x</i> CuO₄ exhibits dynamics favorable to the in-plane superconducting tunneling and establish time-resolved x-rays as a means to study excitations at energy scales inaccessible to conventional scattering techniques.