First-principles study of regulation of electron and hole doping in superconducting ternary hydride CaYH<sub>12</sub>

In the past few decades, achieving room-temperature superconductivity has become an unremitting pursuit of scientists. Guided by the “chemical precompression” theory, hydrogen-rich compounds have emerged as the main candidates for high-temperature superconductors, positioning them at the forefront of superconducting materials research. Extensive computational studies have identified numerous binary hydrides with predicted superconducting transition temperatures (<i>T</i><sub>c</sub>) exceeding 200 K, such as CaH<sub>6</sub>, H<sub>3</sub>S, MgH<sub>6</sub>, YH<sub>6</sub>, YH<sub>9</sub>, YH<sub>10</sub>, and LaH<sub>10</sub>. Significantly, the high-<i>T</i><sub>c</sub> super-conductivities of H<sub>3</sub>S, LaH<sub>10</sub>, CaH<sub>6</sub>, YH<sub>6</sub>, YH<sub>9</sub> have been experimentally confirmed. Compared with binary hydrides, ternary hydrides offer more diverse chemical compositions and structures, potentially leading to enhanced properties. Zhang et al. [Zhang Z, Cui T, Hutcheon M J, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevLett.128.047001">2022 <i>Phys. Rev. Lett.</i> <b>128</b> 047001</ext-link>] theoretically designed a series of <i>AX</i>H<sub>8</sub>-type (<i>A</i> = Sc, Ca, Y, Sr, La, Ba; <i>X</i> = Be, B, Al) ternary hydrides with “fluorite-type” backbone, which were predicted to have high-<i>T</i><sub>c</sub> values under moderate pressure. Among those ternary hydrides, LaBeH<sub>8</sub> has been experimentally confirmed to achieve a <i>T</i><sub>c</sub> value of 110 K at 80 GPa. The <i>T</i><sub>c</sub> values of ternary clathrate hydrides of Li<sub>2</sub>MgH<sub>16</sub> and Li<sub>2</sub>NaH<sub>17</sub> have been predicted to greatly exceed the room temperature, while the required stabilization pressures all exceeded 200 GPa. Xie et al. [Xie H, Duan D F, Shao Z J, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1088/1361-648X/ab09b4">2019 <i>J. Phys. Condens. Matter.</i> <b>31</b> 245404</ext-link>] and Liang et al. [Liang X W, Bergara A, Wang L Y, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.100505">2019<i>Phys. Rev. B</i> <b>99</b> 100505(R)</ext-link> ] independently predicted CaYH<sub>12</sub> compounds with <inline-formula><tex-math id="M4">\begin{document}$ Pm\bar 3m $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ Fd\bar 3m $\end{document}</tex-math></inline-formula> space groups, both of which exhibited high-<i>T</i><sub>c</sub> above 200 K at about 200 GPa. Other ternary hydrides, such as La-B-H, K-B-H, La-Ce-H, and Y-Ce-H, have also been extensively investigated. At current stage, a major focus of superconducting hydrides is to achieve high-temperature superconductivity at lower pressures. In this study, taking <inline-formula><tex-math id="M6">\begin{document}$ Pm\bar 3m $\end{document}</tex-math></inline-formula> (CaYH<sub>12</sub>) as a representative, we systematically investigate the effects of electron and hole doping on the dynamical stability and superconductivity in ternary hydride by first-principal calculations. The <inline-formula><tex-math id="M7">\begin{document}$ Pm\bar 3m $\end{document}</tex-math></inline-formula> (CaYH<sub>12</sub>) exhibits a <i>T</i><sub>c</sub> value of 218 K at 200 GPa, which is consistent with that reported previously. When decompressing to below 180 GPa, imaginary phonons emerge. The analysis of doping simulations demonstrates that the electron doping exacerbates the softening of the imaginary phonons, whereas hole doping eliminates the imaginary frequencies. At the pressures of 130, 100 and 70 GPa, the <inline-formula><tex-math id="M8">\begin{document}$ Pm\bar 3m $\end{document}</tex-math></inline-formula> (CaYH<sub>12</sub>) phase can be stabilized by hole doping at the concentrations of 0.9, 0.8, and 1.1 e/cell, respectively. Further electron-phonon coupling calculations show that the <i>T</i><sub>c</sub> values of <inline-formula><tex-math id="M9">\begin{document}$ Pm\bar 3m $\end{document}</tex-math></inline-formula> (CaYH<sub>12</sub>) at 130, 100 and 70 GPa are 194, 209, and 194 K at the corresponding doping level, which are only 10–20 K less than the <i>T</i><sub>c</sub> at 200 GPa. At the pressure of 70 GPa, <i>T</i><sub>c</sub> slightly decreases to 189 K at a doping level of 1.2 e/cell, primarily due to the reduced <i>ω</i><sub>log</sub> compared with that in the case of 1.1 e/cell. And the enhanced <i>λ</i> at 1.2 e/cell is mainly contributed by the average electron-phonon coupling matrix element <inline-formula><tex-math id="M10">\begin{document}$ \langle {I^2}\rangle $\end{document}</tex-math></inline-formula> and average phonon frequency <inline-formula><tex-math id="M11">\begin{document}$ {\langle {\omega ^2}\rangle ^{1/2}} $\end{document}</tex-math></inline-formula>, rather than the electronic density of states at the Fermi level <i>N</i>(<i>ε</i><sub>F</sub>). These results indicate that hole doping represents a promising and effective strategy for optimizing the superconductivity of <inline-formula><tex-math id="M12">\begin{document}$ Pm\bar 3m $\end{document}</tex-math></inline-formula> (CaYH<sub>12</sub>) by maintaining high-<i>T</i><sub>c</sub> at low pressures. Our study paves an avenue for realizing high-temperature superconductors at low pressure.