Refined phase diagram and kagome-lattice superconductivity in Mg-Si system

In this work, by employing a variable-composition evolutionary algorithm combined with first-principles calculations, we have performed a comprehensive structural search for the magnesium silicide (Mg-Si) system and determined a hyperfine pressure-composition phase diagram. Three new pressure-stabilized structures, namely, $P6/mmm\text{\ensuremath{-}}{\mathrm{MgSi}}_{3}, Cmmm$-MgSi, and $Pm\overline{3}m\text{\ensuremath{-}}{\mathrm{Mg}}_{3}\mathrm{Si}$, are found. Of particular interest is that $P6/mmm\text{\ensuremath{-}}{\mathrm{MgSi}}_{3}$ with silicon kagome-lattice characteristic is a single-gap superconductor with a superconducting transition temperature (${T}_{\mathrm{c}}$) about 13.7 K (higher than those of the experimental reported kagome superconductors), which is closely associated with strong electron-phonon coupling mainly determined by silicon kagome lattice. Moreover, $Pm\overline{3}m\text{\ensuremath{-}}{\mathrm{Mg}}_{3}\mathrm{Si}$ exhibits a zero-dimensional (0D) electride characteristic with the excess electrons trapped in the Mg-based octahedral cavity. Our findings not only refine the phase diagram of the Mg-Si system, but also expend an in-depth comprehension of the structural diversity and unique electronic states in the alkaline-earth metal silicides under high pressure, which also provide insights into exploring the formation and evolution of the structure of the rocky planets.