  Recently, near-ambient superconductivity was claimed in nitrogen-doped
lutetium hydride (LuH$_{3-\delta}$N$_{\epsilon}$) . Unfortunately, all
follow-up research still cannot find superconductivity signs in successfully
synthesized lutetium dihydride (LuH$_2$) and N-doped LuH$_{2\pm x}$N$_y$.
However, a similar intriguing observation was the pressure-induced color
changes (from blue to pink and subsequent red). The physical understanding of
its origin and the correlation between the color, crystal structure, and
chemical composition of Lu-H-N is still lacking. In this work, we theoretically
study the optical properties of LuH$_2$, LuH$_3$, and some potential N-doped
compounds using the first-principles calculations by considering both interband
and intraband contributions. Our results show that LuH$_2$ has an optical
reflectivity peak around blue light up to 10 GPa. Under higher pressure, the
reflectivity of red light gradually becomes dominant. This evolution is driven
by changes in the direct band gap and the Fermi velocity of free electrons
under pressure. In contrast, LuH$_3$ exhibits gray and no color change up to 50
GPa. Furthermore, we considered different types of N-doped LuH$_2$ and LuH$_3$.
We find that N-doped LuH$_2$ with the substitution of a hydrogen atom at the
tetrahedral position maintains the color change when the N-doping concentration
is low. As the doping level increases, this trend becomes less obvious. While
other N-doped structures do not show significant color change. Our results can
clarify the origin of the experimental observed blue-to-red color change in
lutetium hydride and also provide a further understanding of the potential
N-doped lutetium dihydride.
