Origin of the density wave instability in trilayer nickelate La$_{4}$Ni$_{3}$O$_{10}$ revealed by optical and ultrafast spectroscopy

In the intricate phase diagram of unconventional superconductors characterized by intertwined electronic orders and superconductivity, a key step in understanding the superconducting mechanism is to investigate the parent compounds from which superconductivity emerges through doping or pressure. In this study, we employed optical spectroscopy and ultrafast reflectivity measurements to examine the density wave instability in the trilayer nickelate La$_{4}$Ni$_{3}$O$_{10}$, which displays pressure-induced superconductivity up to 30 K. Our optical spectroscopy measurements reveal that La$_{4}$Ni$_{3}$O$_{10}$ behaves as a metal with a high plasma frequency. Upon cooling, we observed a distinct formation of a density wave energy gap in both optical conductivity and pump-probe measurements. The gap feature is more pronounced compared to the bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$. Through a comparison of the experimentally determined plasma frequency with first-principles calculations, we classify La$_{4}$Ni$_{3}$O$_{10}$ as a moderately electron-correlated material, resembling the parent compound of iron-based superconductors but exhibiting weaker correlation than the bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$. The enhanced gap feature and weaker electronic correlation in La$_{4}$Ni$_{3}$O$_{10}$ may explain its lower superconductivity transition temperature under high pressure. These findings significantly advance our comprehension of the density wave and superconductivity mechanisms in the trilayer nickelate La$_{4}$Ni$_{3}$O$_{10}$.