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First-principles study on the high-$T_\text{c}$ superconductivity of Mg-Ti-H ternary hydrides up to the liquid-nitrogen temperature range under high pressures

Pan Min, Wang Yujie, Hu Kaige, Deng Huiqiu

TL;DR

The paper addresses the challenge of achieving high-$T_\text{c}$ superconductivity in hydrogen-rich ternary hydrides by focusing on Mg-Ti-H under pressures up to $300$ GPa. It combines crystal-structure prediction (CALYPSO), first-principles electronic-structure calculations, phonon and electron-phonon coupling analyses, and Migdal-Eliashberg theory to evaluate $T_\text{c}$ via $T_\text{ADM}$, $T_\text{ML}$, and $T_\text{E}$ for $0.10\le\mu^*\le0.13$. The study identifies four thermodynamically stable Mg-Ti-H phases (notably $P4/nmm$-MgTiH$_6$ with a record $T_\text{c}$ of $81.9$ K at $170$ GPa) and two metastable ones, and shows that heavier-element substitution (Zr/Hf) lowers dynamical-stability pressures and can boost $T_\text{c}$ (e.g., $T_\text{c}=86$ K in $P4/nmm$-MgHfH$_6$). These results highlight a viable design strategy for achieving high-$T_\text{c}$ superconductivity in hydrogen-rich ternary hydrides at comparatively accessible pressures, guiding future experimental efforts.

Abstract

Ternary hydrides have emerged as the primary focus of the new wave of research into superconducting hydrides. In this work, Mg-Ti-H ternary hydrides are explored under high pressures up to 300 GPa using the prediction method of the particle swarm optimization algorithm combined with first-principles calculations. Two new structures, $P4/nmm$-MgTiH$_6$ and $Pmm2$-Mg$_3$TiH$_6$, are identified to be thermodynamically stable at both 200 GPa and 300 GPa. Thermodynamically stable structures of Mg$_3$TiH$_{12}$ are also identified, whose space groups are $R3/m$ at 200 GPa and $Pm\bar{3}m$ at 300 GPa, respectively. Among these Mg-Ti-H structures, $P4/nmm$-MgTiH$_6$ achieves a record-high $T_\text{c}$ of 81.9 K at 170 GPa, exceeding the boiling point of liquid nitrogen. Such a high $T_\text{c}$ is primarily attributed to strong electron-phonon coupling (EPC) driven by low-frequency acoustic phonon modes, with the EPC strength reaching a large value of 1.54. The $T_\text{c}$ of $Pm\bar{3}m$-Mg$_3$TiH$_{12}$ is predicted to be 40 K at 300 GPa. Furthermore, element substitution of Zr(Hf) for Ti achieves considerable enhancement of superconducting properties in our predicted hydrogen-rich and high-symmetric crystal structures, i.e., $P4/nmm$-MgTiH$_6$ and $Pm\bar{3}m$-Mg$_3$TiH$_{12}$. The high pressure required for dynamical stability is lowered to 100 GPa in both $Pm\bar{3}m$-Mg$_3$ZrH$_{12}$ and $Pm\bar{3}m$-Mg$_3$HfH$_{12}$, and to 90 GPa and 120 GPa for $P4/nmm$-MgZrH$_6$ and $P4/nmm$-MgHfH$_6$, respectively. Particularly, the electronic structure near the Fermi level is significantly modified in the $P4/nmm$-MgHfH$_6$ phase, and pronounced softening of low-frequency acoustic phonon modes occurs. As a result, the EPC strength is enhanced to 1.72, leading to a higher $T_\text{c}$ of 86 K.

First-principles study on the high-$T_\text{c}$ superconductivity of Mg-Ti-H ternary hydrides up to the liquid-nitrogen temperature range under high pressures

TL;DR

The paper addresses the challenge of achieving high- superconductivity in hydrogen-rich ternary hydrides by focusing on Mg-Ti-H under pressures up to GPa. It combines crystal-structure prediction (CALYPSO), first-principles electronic-structure calculations, phonon and electron-phonon coupling analyses, and Migdal-Eliashberg theory to evaluate via , , and for . The study identifies four thermodynamically stable Mg-Ti-H phases (notably -MgTiH with a record of K at GPa) and two metastable ones, and shows that heavier-element substitution (Zr/Hf) lowers dynamical-stability pressures and can boost (e.g., K in -MgHfH). These results highlight a viable design strategy for achieving high- superconductivity in hydrogen-rich ternary hydrides at comparatively accessible pressures, guiding future experimental efforts.

Abstract

Ternary hydrides have emerged as the primary focus of the new wave of research into superconducting hydrides. In this work, Mg-Ti-H ternary hydrides are explored under high pressures up to 300 GPa using the prediction method of the particle swarm optimization algorithm combined with first-principles calculations. Two new structures, -MgTiH and -MgTiH, are identified to be thermodynamically stable at both 200 GPa and 300 GPa. Thermodynamically stable structures of MgTiH are also identified, whose space groups are at 200 GPa and at 300 GPa, respectively. Among these Mg-Ti-H structures, -MgTiH achieves a record-high of 81.9 K at 170 GPa, exceeding the boiling point of liquid nitrogen. Such a high is primarily attributed to strong electron-phonon coupling (EPC) driven by low-frequency acoustic phonon modes, with the EPC strength reaching a large value of 1.54. The of -MgTiH is predicted to be 40 K at 300 GPa. Furthermore, element substitution of Zr(Hf) for Ti achieves considerable enhancement of superconducting properties in our predicted hydrogen-rich and high-symmetric crystal structures, i.e., -MgTiH and -MgTiH. The high pressure required for dynamical stability is lowered to 100 GPa in both -MgZrH and -MgHfH, and to 90 GPa and 120 GPa for -MgZrH and -MgHfH, respectively. Particularly, the electronic structure near the Fermi level is significantly modified in the -MgHfH phase, and pronounced softening of low-frequency acoustic phonon modes occurs. As a result, the EPC strength is enhanced to 1.72, leading to a higher of 86 K.
Paper Structure (8 sections, 13 equations, 13 figures, 2 tables)

This paper contains 8 sections, 13 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Computational methods
  3. Results
  4. Predicted stable and metastable structures of the Mg-Ti-H system
  5. Electronic properties and superconductivity of the Mg-Ti-H phases
  6. Element substitution in the hydrogen-rich phases Pm-3m-Mg3TiH12 and P4/nmm-MgTiH6
  7. Conclusions
  8. Supplementary Material

Figures (13)

  • Figure 1: Ternary phase diagrams (convex hull) of the Mg$_x$TiH$_{2y}$ ($x=1$-3, $y=3$-8) system at (a) 200 and (b) 300 GPa, respectively. The color of each structure represents its energy difference from the convex hull.
  • Figure 2: Crystal structures of (a) $P4/nmm$-MgTiH$_6$ at 200 GPa, (b) $Pmm2$-Mg$_3$TiH$_6$ at 200 GPa, (c) $I4_1amd$-MgTiH$_8$ at 300 GPa, (d) $P4/nmm$-MgTiH$_{10}$ at 300 GPa, (e) $R3m$-Mg$_3$TiH$_{12}$ at 200 GPa, and (f) $Pm\bar{3}m$-Mg$_3$TiH$_{12}$ at 300 GPa.
  • Figure 3: Electron localization function (ELF) of (a) the (100) plane of $P4nmm$-MgTiH$_6$ at 200 GPa, (b) the (100) plane of $Pmm2$-Mg$_3$TiH$_6$ at 200 GPa, (c) the (001) plane of $I4_1amd$-MgTiH$_8$ at 300 GPa, (d) the (100) plane of $P4nmm$-MgTiH$_{10}$ at 300 GPa, (e) the (010) plane of $R3m$-Mg$_3$TiH$_{12}$ at 200 GPa, and (f) the (001) plane of $Pm\bar{3}m$-Mg$_3$TiH$_{12}$ at 300 GPa.
  • Figure 4: Electronic band structure and PDOS of (a) $Pmm2$-Mg$_3$TiH$_6$ at 200 GPa, (b) $R3m$-Mg$_3$TiH$_{12}$ at 200 GPa, (c) $P4/nmm$-MgTiH$_6$ at 200 GPa, (d) $I4_1amd$-MgTiH$_8$ at 300 GPa, (e) $P4/nmm$-MgTiH$_{10}$ at 300 GPa, and (f) $Pm\bar{3}m$-Mg$_3$TiH$_{12}$ at 300 GPa. The Fermi level is set to zero.
  • Figure 5: Calculated phonon dispersion curves, projected phonon density of states, $\alpha^2F(\omega)$ and electron-phonon integrals $\lambda$ for (a) $Pmm2$-Mg$_3$TiH$_6$ at 200 GPa, (b) $R3m$-Mg$_3$TiH$_{12}$ at 200 GPa, (c) $P4/nmm$-MgTiH$_6$ at 200 GPa, (d) $I4_1amd$-MgTiH$_8$ at 300 GPa, (e) $P4/nmm$-MgTiH$_{10}$ at 300 GPa, and (f) $Pm\bar{3}m$-Mg$_3$TiH$_{12}$. The isotropic superconducting gaps at various temperatures for (g) $P4/nmm$-MgTiH$_6$ at 200 GPa, (h) $I4_1amd$-MgTiH$_8$ at 300 GPa, (i) $P4/nmm$-MgTiH$_{10}$ at 300 GPa, and (j) $Pm\bar{3}m$-Mg$_3$TiH$_{12}$ at 300 GPa. The colors mapped in the phonon dispersion curves indicate the magnitude of $\lambda_{\bm{q}\nu}$.
  • ...and 8 more figures