Superconducting $T_\mathrm{c}$ up to 20.6 K in bulk YSi$_2$ and YSi$_2$/Si superlattices due to chemical flattening

Abstract: Currently, the fundamental building blocks of leading quantum computers are Josephson junctions, whose core is usually the superconducting Al on Si wafers. However, the transition temperature $T_\mathrm{c}$ of bulk Al ($\sim1.1$ K) is below the boiling point of liquid helium ($\sim4.2$ K), which is one of the challenges to its widespread application. Here, we propose a Si-matched AlB$<em>2$-type superconductor YSi$_2$ as a promising alternative to Al. The solution of anisotropic (isotropic) Migdal-Eliashberg equation without (with) anharmonicity gives $T</em>\mathrm{c}\sim20.6$ K ($17.2$ K), which is at the highest level in silicides. Its excellent superconductivity can be attributed mainly to the Si honeycombs, which become plane here due to the 'chemical flattening' effects of the Y atoms instead of being buckled in most silicides. We tested its thermodynamical, kinetic, dynamical, and mechanical stability by first-principles calculations. Particularly, the negative elastic stiffness constant $C_{66}$ calculated by usual methods turns positive even without the zero-point energy once the Si honeycombs are compressed below a threshold. This strain can also make its calculated lattice constants agree with the experimental ones. We propose structures to realize this strain, i.e., YSi$<em>2$(0001)/Si(111) superlattices, which can also strengthen the overall stability of YSi$_2$ while maintaining its $T</em>\mathrm{c}$ above $7.0$ K.