Thermodynamic stabilities of ternary metal borides : An ab initio guide for synthesizing layered superconductors

Density-functional theory calculations have been used to identify stable layered $\text{Li-}M\text{-B}$ crystal structure phases derived from a recently proposed binary metal-sandwich (MS) lithium monoboride superconductor. We show that the MS lithium monoboride gains in stability when alloyed with electron-rich metal diborides; the resulting ordered ${\text{Li}}_{2(1\ensuremath{-}x)}{M}_{x}{\text{B}}_{2}$ ternary phases may form under normal synthesis conditions in a wide concentration range of $x$ for a number of group-III-V metals $M$. In an effort to preselect compounds with the strongest electron-phonon coupling we examine the softening of the in-plane boron phonon mode at $\ensuremath{\Gamma}$ in a large class of metal borides. Our results reveal interesting general trends for the frequency of the in-plane boron phonon modes as a function of the boron-boron bond length and the valence of the metal. One of the candidates with a promise to be an ${\text{MgB}}_{2}$-type superconductor, ${\text{Li}}_{2}{\text{AlB}}_{4}$, has been examined in more detail: According to our ab initio calculations of the phonon dispersion and the electron-phonon coupling $\ensuremath{\lambda}$, the compound should have a critical temperature of $\ensuremath{\sim}4\text{ }\text{K}$.