Design principle for high-temperature superconductivity in ternary borides at ambient pressure

The discovery of metal borides with higher transition temperature (${T}_{\mathrm{c}}$) has been receiving continuous attention since the observation of superconductivity in ${\mathrm{MgB}}_{2}$ at 39 K. Here we propose a rational design strategy for high-${T}_{\mathrm{c}}$ ternary metal borides through the cosubstitution of Mg with two compensating metal elements that possess an effective isovalency of 2. Guided by this principle, we theoretically predict a collection of ternary boride superconductors, including a representative example of ${\mathrm{KAlB}}_{4}$ that has an isostructure to ${\mathrm{MgB}}_{2}$, with ${T}_{\mathrm{c}}$ up to 67 K at ambient pressure. Our detailed analysis reveals that, compared with ${\mathrm{MgB}}_{2}$, due to the Stark effect caused by the difference in valence of two metal ions, the $\ensuremath{\sigma}$ bands of B layers get significant splitting and exhibit more flat character, resulting in enhanced electronic occupation; furthermore, the softened in-plane ${E}_{2\mathrm{g}}$ modes produce larger deformation potential and electron-phonon coupling with B $\ensuremath{\sigma}$ states, which in turn results in larger superconducting gaps and much higher ${T}_{\mathrm{c}}$ value in ${\mathrm{KAlB}}_{4}$. We further propose a feasible synthesis route of ${\mathrm{KAlB}}_{4}$ to stimulate experimental progress. Our approach paves the way for finding more high-${T}_{\mathrm{c}}$ ternary boride superconductors at ambient pressure.