Researchers from Kyoto University and Kurume Institute of Technology have discovered a scaling law that determines high-order harmonic generation in the solid-layered perovskite material, Ca2RuO4. The work could enable scientists to control material properties with light. High-order harmonic generation is a nonlinear optical phenomenon where extreme ultraviolet photons are emitted by a material as a result of interaction with high-intensity light. “The phenomenon, which was first observed in atomic gas systems, has since paved the way to attosecond science,” said study author Kento Uchida, a researcher at Kyoto University. “But it is slightly more unpredictable in some strongly correlated solids, like Ca2RuO4.” Graphical representation of the newly discovered scaling law in Mott-insulating Ca2RuO4. Courtesy of Kento Uchida/Kyoto University. Due to the strong interaction between electrons in these solids, the characteristics of high-order harmonic generation can only be established by understanding how these electrons move in the presence of light. To solve this problem, the research team set out to observe the relationship between temperature and photon emission in Ca2RuO4. They used a mid-infrared pulse to measure and map out high harmonic generation intensity at temperatures from an extremely low 50 to a moderate 290 Kelvin. At the low end, the team recorded high-order harmonic generation several hundred times more intense than at room temperature. Photon emissions continued to intensify with increasing gap energy — the energy required for electrons to conduct electricity — along with the drop in temperature. The team found that such emissions occurred in the Mott-insulating phase of the material, where the strong repulsion between electrons and high gap energy transforms the metal from an electrical conductor to an insulator. “We discovered that high-order harmonics in strongly correlated materials highly depend on the gap energy of the materials,” Uchida said. The scaling law not only depends on the gap energy of the materials, but also the photon emission energy. Such a scaling law can’t be explained by the electronic structure change in the single-particle model and, to the researchers’ knowledge, has not been predicted by previous theoretical studies on high harmonic generation in the simple Mott-Hubbard model. The results suggest that the highly nonlinear optical response of strongly correlated materials is influenced by competition among the multiple degrees of freedom and electron-electron correlations. The researchers predict that the scaling law can direct theoretical studies toward more refined descriptions of nonequilibrium electron dynamics in strongly correlated materials, a central issue in condensed matter physics. “Our findings also provide a foundation for materials design to achieve more efficient nonlinear optical devices,” Uchida said. The research was published in Physical Review Letters (www.doi.org/10.1103/PhysRevLett.128.127401).