Chinese Physics Letters, 2023, Vol. 40, No. 11, Article code 117401 Physical Origin of Color Changes in Lutetium Hydride under Pressure Run Lv (吕润)1,2, Wenqian Tu (涂文倩)1,2, Dingfu Shao (邵定夫)1, Yuping Sun (孙玉平)1,3,4, and Wenjian Lu (鲁文建)1* Affiliations 1Key Laboratory of Materials Physics, Institute of Solid State Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China 2Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, China 3High Magnetic Field Laboratory, Institute of Solid State Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China 4Collaborative Innovation Center of Microstructures, Nanjing University, Nanjing 210093, China Received 19 July 2023; accepted manuscript online17 October 2023; published online 13 November 2023 *Corresponding author. Email: wjlu@issp.ac.cn Citation Text: Lv R, Tu W Q, Shao D F et al. 2023 Chin. Phys. Lett. 40 117401    Abstract Recently, near-ambient superconductivity was claimed in nitrogen-doped lutetium hydride (LuH$_{3-\delta}$N$_{\rm{\varepsilon}})$. 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 systematically investigated the optical properties of LuH$_{2}$ and LuH$_{3}$, and the effects of hydrogen vacancies and nitrogen doping using the first-principles calculations by considering both interband and intraband contributions. Our results demonstrate that the evolution of reflectivity peaks near blue and red light, which is driven by changes in the band gap and Fermi velocity of free electrons, resulting in the blue-to-red color change under pressure. In contrast, LuH$_{3}$ exhibits gray and no color change up to 50 GPa. Furthermore, we investigated the effects of hydrogen vacancies and nitrogen doping on its optical properties. Hydrogen vacancies can significantly decrease the pressure of blue-to-red color change in LuH$_{2}$ but do not have a noticeable effect on the color of LuH$_{3}$. The 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 a blue-to-red 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.
cpl-40-11-117401-fig1.png
cpl-40-11-117401-fig2.png
cpl-40-11-117401-fig3.png
cpl-40-11-117401-fig4.png
cpl-40-11-117401-fig5.png
DOI:10.1088/0256-307X/40/11/117401 © 2023 Chinese Physics Society Article Text The search for room-temperature superconductors has been a long-standing goal in condensed matter physics. According to the Bardeen–Cooper–Schrieffer theory, metallic hydrogen and hydrogen-rich compounds with light ionic mass can produce high-temperature superconductivity.[1,2] In recent years, materials such as H$_{3}$S (203 K at 155 GPa)[3,4] and LaH$_{10}$ (250 K at 190 GPa)[5,6] have been predicted by density-functional-theory calculations and confirmed by high-pressure experiments. Unfortunately, high pressure is always indispensable for the stability and superconductivity of these compounds.[7] Recently, near-ambient superconductivity was reported in N-doped lutetium hydride LuH$_{3-\delta}$N$_{\varepsilon}$.[8] The authors reported that superconductivity emerges at 0.3 GPa, reaches its maximum at 1 GPa, and vanishes above 3 GPa. Interestingly, the crystal color changes from blue to pink at 0.3 GPa and subsequently to red at 3 GPa. However, the following research on lutetium dihydride LuH$_{2}$[9,10] and LuH$_{2\pm x}$N$_{y}$[7,11-13] showed no near-ambient superconductivity but observed similar color changes under pressure. Moreover, the superconductivity transition temperature ($T_{\rm c})$ of LuH$_{3}$, considered N doping and an anharmonic effect in first-principles calculations, is much lower than room temperature.[14,15] Other lutetium hydrides, such as LuH$_{3}$[16] and Lu$_{4}$H$_{23}$[17] show superconductivity below 12 K (122 GPa) and 71 K (218 GPa), respectively. Undoubtedly, the microscopic crystal structure and chemical composition of lutetium hydride and its N-doped compounds are still controversial. However, the color change observed in several experiments is generally consistent. Color is a basic property of materials and is determined by their optical reflectivity to light with different wavelengths. Different structures and chemical compositions have different electronic properties, which determine their optical properties, such as reflection and absorption. Therefore, the color and its changes under pressure can provide basic information about the electronic structure of the material, which can be used as important evidence to study its structure and chemical composition. Several theoretical studies[18-21] have shown that LuH$_{2}$ exhibits the blue-to-red color change consistent with experimental reports, and the concentration of H vacancies can influence the pressure of color changes.[18] However, the physical origin of the blue-to-red color change is not fully clear. Furthermore, the possible occupation position and the effect of the doped nitrogen atom are still unknown. In this work, we systematically investigated the optical properties of nitrogen-doped lutetium hydrides under pressure through first-principles calculations. Firstly, we investigated the optical properties of LuH$_{2}$ and LuH$_{3}$. Our results indicate that under pressure, LuH$_{2}$ undergoes a color change from blue to red, while LuH$_{3}$ maintains its gray color. Based on the dielectric function and electronic properties, we elucidate that both interband and intraband transitions are important for forming peaks of reflectivity spectra in the blue and red regions. Changes in its band gaps and Fermi velocity of free electrons drive the evolution of these peaks, resulting in the blue-to-red color change. Furthermore, we studied the influence of hydrogen vacancies and nitrogen doping on the optical properties. Hydrogen vacancies can significantly decrease the pressure of the blue-to-red color change in LuH$_{2}$. When these vacancies are abundant, the structure could exhibit a yellow color under high pressure. However, hydrogen vacancies do not have a significant impact on the color of LuH$_{3}$ under pressure. N-doped lutetium dihydride, Lu$_{18}$H$_{35}$N (LuH$_{1.944}$N$_{0.056})$, with N replacing H at the tetrahedral site, exhibits a similar trend in reflectivity and blue-to-red color change. When the doping concentration of the N atom is higher, the color change becomes less obvious. However, the other five N-doped compounds considered in this work show no similar color change. The present results suggest that lutetium dihydride with N at the tetrahedral site is a potential structure of nitrogen-doped lutetium hydride. Additionally, we calculated the phonon dispersion under different pressures and also considered anharmonic effects. The phonon dispersions indicate that LuH$_{2}$ is dynamically stable, while LuH$_{3}$ is unstable under near-ambient conditions. Calculation Details. The first-principles calculations based on the density functional theory were performed by the Vienna ab initio Simulation Package (VASP).[22,23] The pseudopotential was described by using projector augmented wave methods, and exchange-correlation interaction was treated by generalized gradient approximation, which is parameterized by Perdew–Burke–Ernzerhof version.[24] The plane-wave kinetic cut-off energy was set to 500 eV. Both lattice parameters and atom positions were fully optimized. The Brillouin zone was sampled with an $18\times 18\times 18$ $k$-points mesh for structural optimization. The electronic properties calculation used a $40\times 40\times 40$ $k$-points mesh for LuH$_{2}$ and LuH$_{3}$ and at least a $10\times 10\times 10$ $k$-points mesh for N-doped superstructures. Convergence criteria for energy and force were set to 10$^{-8}$ eV and 10$^{-3}$ eV/Å, respectively. The dielectric function (only for interband contribution) was calculated by the independent particle approximation using the same $k$-points mesh with electron properties. For metals, the dielectric function has contributions from both interband and intraband transitions. The interband contribution describes all allowed direct transitions, defined as \begin{align*} \varepsilon^{\rm{inter}}(\omega)=\varepsilon_{1}^{\rm{inter}}(\omega) +i\varepsilon_{2}^{\rm{inter}}(\omega). \end{align*} It was post-processed with a VASPKIT code.[25] The imaginary part of the $3\times 3$ dielectric tensor is defined as[26] \begin{align*} \varepsilon_{2,\alpha \beta }^{{\rm inter}}(\omega)=\,&\frac{4\pi^{2}e^{2}}{\varOmega}\lim\limits_{q\rightarrow0}\frac{1}{q^{2}}\sum\nolimits_{c,v,{\boldsymbol k}}{2w_{k}} \delta(\epsilon_{c{\boldsymbol k}}-\epsilon_{v{\boldsymbol k}}-\omega)\\ &\times\langle u_{c{\boldsymbol k}+{\boldsymbol e}_{\alpha {\boldsymbol q}}}|u_{v{\boldsymbol k}}\rangle\langle u_{c{\boldsymbol{k}+{\boldsymbol e}_{\beta {\boldsymbol q}}}|u_{v{\boldsymbol{k}}}}\rangle^{*}, \end{align*} where the indices $c$ and $v$ denote the conduction and the valence band states that $w_{k}$ donates the weight of the $k$ points, and ${\boldsymbol {e}}_{\alpha}$ and ${\boldsymbol{e}}_{\beta}$ are three Cartesian directions. The real part of the interband part is related to the imaginary part by the Kramers–Kronig relation[26] \begin{align*} \varepsilon_{1,\alpha \beta }^{\rm{inter}}(\omega)=1+\frac{2}{\pi}\,{\rm P}\!\int_0^\infty \frac{\varepsilon_{2,\alpha \beta}^{\rm{inter}}(\omega')\omega'}{\omega'^{2}-\omega^{2}} d\omega ', \end{align*} where P represents the principal value. The intraband part was calculated by using the Drude model,[27,28] \begin{align*} &\varepsilon^{\rm intra}(\omega)=\varepsilon_{1}^{\rm intra}(\omega)+i\varepsilon_{2}^{\rm intra}(\omega),\\ &\varepsilon_{1}^{\rm intra}(\omega)=1-\frac{\omega_{\rm p}^{2}}{\omega^{2}+{\varGamma}^{2}},\\ &\varepsilon_{2}^{\rm intra}(\omega)=\frac{\omega_{\rm p}^{2}{\varGamma}}{\omega^{3}+\omega {\varGamma}^{2}}, \end{align*} where $\omega_{\rm{p}}$ and $\varGamma$ represent plasma frequency and relaxation rate, respectively. Here we select a typical value $\varGamma =0.2$, and obtain $\omega_{\rm{p}}$ as follows: \begin{align*} \omega_{\rm{p},\alpha \beta }^{2}=\frac{4\pi e^{2}}{V\hbar^{2}}\sum\nolimits_{n,k} {2g_{k}\frac{\partial f(E_{n,k})}{\partial E}\Big({\boldsymbol e}_{\alpha}\frac{\partial E_{n,k}}{\partial k}\Big)\Big({\boldsymbol e}_{\beta }\frac{\partial E_{n,k}}{\partial k}\Big)}, \end{align*} where $V$ denotes the volume of the unit cell, $g_{k}$ is the weight of the $k$ points, $f$ is the occupancy, $E$ is the band energy, ${\boldsymbol e}_{\alpha}$ and ${\boldsymbol e}_{\beta}$ denote three directions. Finally, we can reach the total dielectric function \begin{align*} \varepsilon (\omega)=\varepsilon^{\rm{inter}}(\omega)+\varepsilon^{\rm{intra}}(\omega). \end{align*} Then, the optical reflectivity is calculated by[29] \begin{align*} R(\omega)=\Bigg|\frac{\sqrt {\varepsilon (\omega)}-1}{\sqrt{\varepsilon (\omega)}+1}\Bigg|^{2}. \end{align*} The colorimetry theory[30] is used to calculate the color of materials. Based on the reflectivity $R(\omega)$, the power distribution of reflected light under the D$_{65}$ standard illumination (simulates daylight) can be expressed as \begin{align*} P(\omega)=P_{\rm{D}_{\rm{65}}}(\omega)\times R(\omega). \end{align*} Then, the tristimulus values $(R,G,B)$, i.e., the color coordinates, are calculated by \begin{align*} &R=\int_{380}^{780} {P(\lambda)\bar{r}(\lambda){d}\lambda} ,\\ &G=\int_{380}^{780} {P(\lambda)\bar{g}(\lambda){d}\lambda} ,\\ &B=\int_{380}^{780} {P(\lambda)\bar{b}(\lambda){d}\lambda} . \end{align*} Here, $\lambda$ represents the wavelength; $\bar{r}(\omega)$, $\bar{g}(\omega)$ and $\bar{b}(\omega)$ are color-matching functions corresponding to the $({R,\,G,\,B})$ tristimulus space. Results and Discussions. We first calculated the dielectric function of LuH$_{2}$ and LuH$_{3}$. The dielectric function reveals fundamental electronic structure information and determines optical properties, such as reflection and absorption. The color of the material can then be derived from the reflectivity. The dielectric function of interband transitions consists of a real part and an imaginary part. The imaginary part represents all allowed direct transitions from occupied to unoccupied states. The real and imaginary parts are related by the Kramers–Kronig relation.[26] Black lines in Figs. 1(b) and 1(d) show the interband dielectric function of LuH$_{2}$ at 0 GPa. Considering that LuH$_{2}$ is a metal, intraband transitions also contribute to the dielectric function. The Drude free electron model[27,28] is used to describe the intraband part. The blue dashed lines in Figs. 1(b) and 1(d) represent the contribution of intraband transitions to the dielectric function. Compared to the dielectric function without intraband transitions, the inclusion of the intraband part significantly affects the imaginary dielectric function below 3 eV. Its effect on the real dielectric function is below 5 eV, due to the plasma frequency of 5.82 eV. The calculated total dielectric function is also in good agreement with the experimental[31] and theoretical reports.[18-21] Figure 1(c) shows the reflectivity of LuH$_{2}$ at 0 GPa. If only interband transitions are considered, the reflectivity exhibits little variation within the visible light range, as shown by the black line. However, when intraband transitions are taken into account, a peak appears in the blue light region, and only a narrow energy range with high reflectivity near red light. Therefore, blue light is predominantly reflected, and the material has a blue appearance, which is also consistent with previous theoretical reports.[18,19]
cpl-40-11-117401-fig1.png
Fig. 1. (a) Crystal structure of lutetium hydride with the fluorite structure ($Fm\bar{3}m$). The pink and green H atoms occupy tetrahedral and octahedral sites, respectively. The structure of LuH$_{3}$ contains pink and green H atoms, while that of LuH$_{2}$ only contains pink H atoms. The calculated imaginary part $\varepsilon_{\rm{2}}$ (b) and real part $\varepsilon_{1}$ (d) of the dielectric function of LuH$_{2}$. (c) Reflectivity $R(\omega)$ spectra of LuH$_{2}$.
To explore the pressure-induced color changes, we calculated the dielectric function and reflectivity under different pressures. Figure 2(a) shows the imaginary and real parts of the total dielectric function. The plasma frequencies under different pressures are listed in Table S1 in the Supplemental Material. For the imaginary part $\varepsilon_{2}$ of the total dielectric function, its peak moves to higher energy when pressure increases, resulting in a decrease around 3 eV. This is mainly contributed by interband transitions. Below 2 eV, there is a slight increase, contributed by both interband and intraband transitions, as shown in Fig. 3(a). The real part $\varepsilon_{1}$ also shifts its peak to higher energy and decreases below 3 eV. These changes result in a variation of the reflectivity, as shown in Fig. 2(b). Under higher pressure, the reflectivity of blue light gradually decreases, while the reflectivity of red light increases. Consequently, the color of LuH$_{2}$ shifts to violet at $\sim$ 20 GPa and to red at $\sim$ 30 GPa. The reflectivity in 1.8 eV (red light) and 2.8 eV (blue light) under different pressures are listed in Table S1. The calculated color displayed in Fig. 2(c) is well consistent with the experimental observation[7] in Fig. 2(d). We also noted a difference in the pressure of color transition between calculations and observations in Refs. [9,10,13]. This discrepancy will be discussed in the section related to hydrogen vacancies.
cpl-40-11-117401-fig2.png
Fig. 2. (a) Imaginary part $\varepsilon_{2}$ (dashed line) and real part $\varepsilon_{1}$ (solid line) of the dielectric function of LuH$_{2}$ under different pressures. (b) Reflectivity spectra $R(\omega)$ of LuH$_{2}$. (c) Calculated color and (d) experimentally observed optical microscope images of LuH$_{2}$ under different pressures (from Ref. [7]). (e) Imaginary part of the dielectric function of LuH$_{3}$. (f) Reflectivity spectra $R(\omega)$ of LuH$_{3}$ under different pressures. Insets show the corresponding color.
To investigate whether LuH$_{3}$ could exhibit a similar color change, we calculated its dielectric function, reflectivity, and color under different pressures. Figure 2(e) shows the imaginary part of the dielectric function of LuH$_{3}$ at 0 GPa. The plasma frequency of LuH$_{3}$ is 1.62 eV (the plasma frequencies at other pressures are also listed in Table S1 in the Supplemental Material). As a result, intraband transitions contribute to the dielectric function of LuH$_{3}$ mainly below 1 eV, which is lower than the energy range of visible light. Therefore, the total dielectric function in the visible light energy range is mainly determined by interband transitions. Moreover, the dielectric function within the energy range of visible light shows slight variation and does not have a prominent peak, resulting in a small variation of reflectivity in this range. Using its reflectivity, we calculated the color of LuH$_{3}$ under different pressures and found that it remains gray, as displayed in the inset of Fig. 2(d). This is consistent with a previous report.[18]
cpl-40-11-117401-fig3.png
Fig. 3. (a) Imaginary part of the dielectric function contributed by interband (solid line) and intraband (dashed line) transitions, (b) band structure, and (c) Fermi surface of LuH$_{2}$ under 0 and 50 GPa.
To gain a deeper understanding of the physical origin of the change in optical properties, we analyze the electronic structure of LuH$_{2}$. In Fig. 2(a), the imaginary part of the total dielectric function increases around 1.8 eV and decreases around 2.8 eV, resulting in color changes. These changes can be attributed to interband and intraband transitions, as shown in Fig. 3(a). Compared to the blue solid line (0 GPa), the peak of the red solid line (50 GPa) moves to 4.3 eV, resulting in a decrease of reflectivity in 2.8 eV. Around 1.8 eV, the red solid line shows a slight increase. In its band structure, the bandgap at the $W$ point increased from 2.8 eV to 4.3 eV, while the bandgap at the $\varGamma$ point decreased from 2.0 eV to 1.8 eV. These changes correspond to the variations in interband transitions. The imaginary part of the intraband transitions, represented by the red dashed line, shows a slight increase at 1.8 eV. However, its contribution to the real part is significant, as shown in Fig. S1 of the Supplemental Material. This is attributed to an increase in the Fermi velocity of electrons on the Fermi surface, leading to a higher plasma frequency ($\omega_{\rm p})$ (listed in Table S1). Figure 3(c) shows the Fermi surface of LuH$_{2}$ at 0 GPa and 50 GPa, with red indicating regions for high Fermi velocity. The increase in Fermi velocity is accompanied by a decrease in effective mass, which results in higher electron mobility. This causes LuH$_{2}$ to exhibit better metallic behavior at higher pressures.[7] In some experimental reports,[7,8,11-13] the hydrogen is non-stoichiometric, and the pressure of color changes is lower than our calculated results. Therefore, we calculate the optical properties of LuH$_{2}$ and LuH$_{3}$ with different ratios of hydrogen vacancies. Figure 4 shows the calculated results. Figures 4(a), 4(c), and 4(e) are the reflectivity of LuH$_{2}$ with different ratios of H vacancies under different pressures. Compared with LuH$_{2}$, LuH$_{1.875}$ has a higher reflectivity for red light under the same pressure, so its blue-to-red color change can occur at a lower pressure. As the ratio of H vacancies in LuH$_{2}$ continues to increase, such as LuH$_{1.750}$ and LuH$_{1.625}$, the calculated results show that its reflectivity near yellow light increases under high pressure, causing the color changing to yellow. This different color change has been observed in Ref. [10]. Similar results have also been reported in previous calculations on LuH$_{2}$ with H vacancies.[18,19] Next, we calculated LuH$_{3}$ with different ratios of H vacancies, as shown in Figs. 4(b), 4(d), and 4(f). In these results, H vacancies moderate change its reflectivity. However, there is still not a dominant peak within the visible light energy range, resulting in a gray appearance with no significant changes under pressure.
cpl-40-11-117401-fig4.png
Fig. 4. Reflectivity of LuH$_{2}$ with different ratios of H vacancy: (a) LuH$_{1.875}$, (c) LuH$_{1.750}$, and (e) LuH$_{1.625}$. Reflectivity of LuH$_{3}$ with different ratios of H vacancy: (b) LuH$_{2.875}$, (d) LuH$_{2.750}$, and (f) LuH$_{2.625}$. Insets show the color at the corresponding pressure.
Furthermore, we considered the effect of different N doping on the color of Lu–H–N compounds. As shown in Fig. 1(a), there are two types of H atom positions in the $Fm\bar{3}m$ structure of lutetium hydride: tetrahedral and octahedral sites. For LuH$_{2}$, nitrogen can replace an H atom at the tetrahedral site or occupy the octahedral site. Firstly, we simply considered doping one N atom into a $2\times 2\times 2$ supercell of LuH$_{2}$, which can form Lu$_{8}$H$_{15}$N (LuH$_{1.875}$N$_{0.125})$ and Lu$_{8}$H$_{16}$N (LuH$_{2}$N$_{0.125})$. We calculated their dielectric function, reflectivity, and color. The reflectivity and color of these materials under different pressures are shown in Figs. 5(a) and 5(b). Compared to LuH$_{2}$, there was no significant color change from blue to red. However, the reflectivity of Lu$_{8}$H$_{15}$N in the visible light range exhibits a similar distribution and evolution to that of LuH$_{2}$. Our results align with those reported in Ref. [18]. Under high pressure, the reflectivity of the blue light decreases while that of the red light increases. In contrast, the reflectivity of Lu$_{8}$H$_{16}$N does not exhibit the above characteristics. This similar trend in reflectivity of Lu$_{8}$H$_{15}$N under high pressure inspired us to consider that, at lower N doping concentrations, it may be possible to exhibit a significant color change similar to LuH$_{2}$. Therefore, we considered replacing one H atom with an N atom in a $3\times 3\times 2$ supercell of LuH$_{2}$, forming Lu$_{18}$H$_{35}$N (LuH$_{1.944}$N$_{0.056})$. Figure 5(c) shows that Lu$_{18}$H$_{35}$N could exhibit a very similar trend of reflectivity and color change under different pressures. These results suggest that the doped N atoms are more likely to be located at the tetrahedral positions.
cpl-40-11-117401-fig5.png
Fig. 5. Reflectivity of (a) Lu$_{8}$H$_{15}$N (LuH$_{1.875}$N$_{0.125}$, nitrogen atom at the tetrahedral site), (b) Lu$_{8}$H$_{16}$N (LuH$_{2}$N$_{0.125}$, nitrogen atom at the octahedral site), (c) Lu$_{18}$H$_{35}$N (LuH$_{1.944}$N$_{0.056}$, nitrogen atom at the tetrahedral site), (d) Lu$_{8}$H$_{23}$N (LuH$_{2.875}$N$_{0.125}$, nitrogen atom at the tetrahedral site). Insets show the color at the corresponding pressure.
Next, we adopted four structures for N-doped LuH$_{3}$ that were previously suggested in Ref. [32]. These compounds have a high density of states near the Fermi energy, which can benefit the occurrence of superconductivity.[32] However, the calculated colors of these four compounds do not exhibit the blue-to-red color change. Figure 5(d) shows the reflectivity of Lu$_{8}$H$_{23}$N (LuH$_{2.875}$N$_{0.125})$, where one H atom is replaced by an N atom at the tetrahedral site in a $2\times 2\times 2$ supercell of LuH$_{3}$. Under pressure, it shows a similar distribution to that of LuH$_{2}$, but it does not have a similar evolution. Figures S5(b) and S5(c) in the Supplemental Material show its dielectric function at 25 GPa. Intraband transitions mainly contribute below 1.5 eV, similar to LuH$_{3}$. Thus, Lu$_{8}$H$_{23}$N with N at the tetrahedral site retains its blue color under high pressures. The other three compounds exhibit gray color under different pressures (see Figs. S6–S8 in the Supplemental Material). All considered structures and related dielectric functions of the N-doped lutetium hydrides are displayed in the Supplemental Material. Additionally, we calculated the phonon dispersion of LuH$_{2}$ and LuH$_{3}$ to investigate their structural stability. Figures S15(a) and S15(b) show that LuH$_{2}$ is dynamically stable from 0 GPa to 50 GPa, while LuH$_{3}$ is unstable at low pressures ($ < $ 25 GPa). For LuH$_{3}$, as pressure is higher than 25 GPa, the imaginary frequency vanishes. Using the mode decomposition technique developed in the DynaPhoPy code,[33] we also calculated the anharmonic phonon dispersion at 300 K. The comparison with harmonic and anharmonic phonon dispersion is shown in Figs. S15(c) and S15(d). When anharmonic effects are included, the phonon dispersion of LuH$_{2}$ shows only minor corrections. For LuH$_{3}$, most of the imaginary frequencies have vanished, but large imaginary frequencies remain near the $W$ point, indicating its instability. The above results are consistent with the previous report on the thermodynamic stability of lutetium hydride.[34] In summary, we have investigated the optical properties of LuH$_{2}$ and LuH$_{3}$, as well as the effects of hydrogen vacancies and nitrogen doping lutetium hydrides under different pressures. By calculating the dielectric function and reflectivity, we find that LuH$_{2}$ can reproduce the pressure-induced color changes observed in experiments. Both interband and intraband transitions contribute to the formation of reflectivity peaks in the blue-light and red-light regions. Under high pressure, the increase in the direct energy gap at the $W$ point, the decrease in the gap at the $\varGamma$ point, and the increase in the Fermi velocity of free electrons cause the reflectivity of blue light to decrease and that of the red light to increase, resulting in the blue-to-red color change. Furthermore, we study the influence of hydrogen vacancies and nitrogen doping. Hydrogen vacancies can significantly decrease the pressure of blue-to-red color change in LuH$_{2}$, and abundant vacancies lead to a yellow appearance under pressure. However, hydrogen vacancies do not have an obvious impact on the color of LuH$_{3}$ under different pressures. The results of different N-doped compounds show only lutetium dihydride, with N replacing H at the tetrahedral site, which could exhibit a similar trend of color changes of LuH$_{2}$ when the doping concentration of the N atom is low. Other N-doped compounds show no similar color change. Additionally, our calculated phonon dispersions show that LuH$_{3}$ is dynamically unstable under near-ambient conditions. Our results clarify the physical origin of the pressure-induced blue-to-red color change of lutetium hydride observed in experiments and provide further understanding of the potential N-doped lutetium dihydride. Acknowledgment. This work was supported by the National Key Research and Development Program of China (Grant Nos. 2022YFA1403203 and 2021YFA1600200), and the National Natural Science Foundation of China (Grant Nos. U2032215 and 12241405).
References Metallic Hydrogen: A High-Temperature Superconductor?Hydrogen Dominant Metallic Alloys: High Temperature Superconductors?Pressure-induced metallization of dense (H2S)2H2 with high-Tc superconductivityConventional superconductivity at 203 kelvin at high pressures in the sulfur hydride systemSuperconductivity at 250 K in lanthanum hydride under high pressuresMultiband nature of room-temperature superconductivity in LaH 10 at high pressureAbsence of near-ambient superconductivity in LuH2±xNyEvidence of near-ambient superconductivity in a N-doped lutetium hydridePressure-Induced Color Change in the Lutetium Dihydride LuH2Pressure tuning of optical reflectivity in LuH2Pressure induced color change and evolution of metallic behavior in nitrogen-doped lutetium hydrideNo evidence of superconductivity in a compressed sample prepared from lutetium foil and H2/N2 gas mixtureFirst-principles study on the conventional superconductivity of N-doped fcc -LuH3Superconducting ScH3 and LuH3 at Megabar PressuresSuperconductivity above 70 K observed in lutetium polyhydridesMicroscopic theory of colour in lutetium hydrideLeading components and pressure-induced color changes in N-doped lutetium hydridePressure-induced color change arising from transformation between intra- and inter-band transitions in LuH$_{2\pm x}$N$_{y}$Ab initio study of the structural, vibrational and optical properties of potential parent structures of nitrogen-doped lutetium hydrideAb initio molecular dynamics for liquid metalsEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleVASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP codeLinear optical properties in the projector-augmented wave methodologyCorrelated metals as transparent conductorsElectronic structure, chemical bonding, and optical properties of paraelectric BaTiO 3 Electronic structure of metal hydrides. I. Optical studies of Sc H 2 , Y H 2 , and Lu H 2 Novel Electronic Structure of Nitrogen-Doped Lutetium HydridesDynaPhoPy: A code for extracting phonon quasiparticles from molecular dynamics simulationsLu–H–N Phase Diagram from First-Principles Calculations
[1] Ashcroft N W 1968 Phys. Rev. Lett. 21 1748
[2] Ashcroft N W 2004 Phys. Rev. Lett. 92 187002
[3] Duan D F et al. 2014 Sci. Rep. 4 6968
[4] Drozdov A P et al. 2015 Nature 525 73
[5] Drozdov A P et al. 2019 Nature 569 528
[6] Wang C Z, Yi S, and Cho J H 2020 Phys. Rev. B 101 104506
[7] Ming X et al. 2023 Nature 620 72
[8] Dasenbrock-Gammon N et al. 2023 Nature 615 244
[9] Shan P F et al. 2023 Chin. Phys. Lett. 40 046101
[10] Zhao X et al. 2023 Sci. Bull. 68 883
[11] Zhang Y J et al. 2023 Sci. Chin. Phys. Mech. & Astron. 66 287411
[12] Cai S et al. 2023 Matter Radiat. Extremes 8 048001
[13]Xing X et al. 2023 arxiv:2303.17587 [cond-mat.supr-con]
[14]Lucrezi R et al. 2023 arxiv:2304.06685 [cond-mat.supr-con]
[15] Huo Z et al. 2023 Matter Radiat. Extremes 8 038402
[16] Shao M et al. 2021 Inorg. Chem. 60 15330
[17] Li Z W et al. 2023 Sci. Chin. Phys. Mech. & Astron. 66 267411
[18] Kim S W et al. 2023 arXiv:2304.07326v1 [cond-mat.supr-con]
[19] Tao X R et al. 2023 Sci. Bull. 68 1372
[20] Liu Z et al. 2023 arXiv:2305.06103v1 [cond-mat.supr-con]
[21] Dangić Đ et al. 2023 arXiv:2305.06751v1 [cond-mat.supr-con]
[22] Kresse G and Hafner J 1993 Phys. Rev. B 47 558
[23] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[24] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[25] Wang V et al. 2021 Comput. Phys. Commun. 267 108033
[26] Gajdoš M et al. 2006 Phys. Rev. B 73 045112
[27]Millis A J (Baeriswyl D, Degiorgi ed) L 2004 Strong Interactions in Low Dimensions (Dordrecht: Springer Netherlands) p 195
[28] Zhang L et al. 2016 Nat. Mater. 15 204
[29] Saha S, Sinha T P, and Mookerjee A 2000 Phys. Rev. B 62 8828
[30]Wyszecki G and Stiles W S 1982 Color Science: Concepts Methods, Quantitative Data and Formulae (New York: Wiley)
[31] Weaver J H, Rosei R and Peterson D T 1979 Phys. Rev. B 19 4855
[32] Denchfield A, Park H and Hemley R J 2023 arXiv:2305.18196 [cond-mat.supr-con]
[33] Carreras A, Togo A and Tanaka I 2017 Comput. Phys. Commun. 221 221
[34] Xie F K et al. 2023 Chin. Phys. Lett. 40 057401