Hardness and superconductivity in tetragonal LiB₄ and NaB₄

Boron-based compounds have triggered substantial attention due to their multifunctional properties, incorporating excellent hardness and superconductivity. While tetragonal metal borides LiB₄ and NaB₄ with BaAl₄-type structure and striking clathrate boron motif have been induced under compression, there is still a lack of deep understanding of their potential properties at ambient pressure. We herein conduct a comprehensive study on I4/mmm-structured LiB₄ and NaB₄ under ambient pressure via first-principles calculations. Remarkably, both LiB₄ and NaB₄ are found to possess high Vickers hardness of 39 GPa, which is ascribed to the robust boron framework with strong covalency. Furthermore, their high hardness values together with distinguished stability make them highly potential superhard materials. Meanwhile, electron-phonon coupling analysis reveals that both LiB₄ and NaB₄ are conventional phonon-mediated superconductors, with critical temperatures of 6 and 8 K at 1 atmosphere pressure (atm), respectively, mainly arising from the coupling of B 2p electronic states and the low-frequency phonon modes associated with Li-, Na-, and B-derived vibrations. This work provides valuable insights into the mechanical and superconducting behaviors of metal borides and will boost further studies of emergent borides with multiple functionalities.