Prediction of high-temperature superconductors with Tc up to 214.3 K in Mg-Zr-H ternary hydrides

Abstract

Ternary hydrides, with richer chemical compositions and structures compared to binary hydrides due to their high degrees of freedom, are expected to contain more candidates for high-$T_{\text{c}}$ superconductors with remarkable properties including higher $T_{\text{c}}$ and lower stabilizing pressures. In this work, the high-pressure structures, electronic properties, and superconductivity of MgZrH${}_{2n}$ ($n=1$-6) ternary system are investigated by combining the prediction method of particle swarm optimization algorithm and first-principles calculations. We find thermodynamically stable structures for MgZrH${}_2$, MgZrH${}_4$, and MgZrH${}_6$, respectively, while only metastable structures for $n⩾4$. During the predicted structures, our analysis mainly focuses on $P{6}_3/mmc$-MgZrH${}_2$, $R\bar{3}m$-MgZrH${}_4$, $Pm\bar{3}$-MgZrH${}_6$, and $Fd\bar{3}m$-MgZrH₁₂. $P{6}_3/mmc$-MgZrH${}_2$ and $R\bar{3}m$-MgZrH${}_4$ exhibit a low $T_{\text{c}}$ of 0.006 K at 40 GPa and 0.95 K at ambient pressure, respectively, due to low electronic contribution from hydrogen at the Fermi level. $Pm\bar{3}$-MgZrH${}_6$ shows a higher $T_{\text{c}}$ of 80.3 K at 36 GPa, primarily influenced by softened phonon modes and a high Hopfield ratio $I^2/M$. Furthermore, the superconducting figure of merit of $Pm\bar{3}$-MgZrH${}_6$ is $S=1.51$, significantly larger than that of MgB${}_2$. Remarkably, $Fd\bar{3}m$-MgZrH₁₂ is a high-$T_{\text{c}}$ superconductor with a $T_{\text{c}}$ up to 214.3 K at 300 GPa, due to its high hydrogen content and significant electronic contribution from hydrogen at the Fermi level. Our study provides valuable insights for future experiments and can serve as a useful reference for exploring potential high-temperature superconductors in ternary hydrides.