Pressure-induced color change arising from transformation between intra- and inter-band transitions in LuH$_{2\pm x}$N$_{y}$

The pressure-induced color change in the nitrogen-doped lutetium hydride has triggered extensive discussions about the underlying physics. Here, we study the optical response of LuH$_{2 \pm x}$N$_{y}$ in a broad frequency range at ambient pressure and its evolution with pressure in the visible spectral range. The broad-band optical spectra at ambient pressure reveal a Drude component associated with intra-band electronic transitions and two Lorentz components (L1 and L2) arising from inter-band electronic transitions. The application of pressure causes a spectral weight transfer from L1 to the Drude component, leading to a blue shift of the plasma edge in the reflectivity spectrum alongside a reduction of the high-frequency reflectivity. Our results suggest that the pressure-induced color change in LuH$_{2 \pm x}$N$_{y}$ is closely related to the transformation between intra- and inter-band electronic transitions, providing new insights into the mechanism of the pressure-induced color change in LuH$_{2 \pm x}$N$_{y}$.