Cubic BeB$_2$: A metastable $p$-type conductive material from first principles

Boron forms a wide variety of compounds with alkaline earth elements due to its unique bonding characteristics. Among these, binary compounds of Be and B display particularly rich structural diversity, attributed to the small atomic size of Be. Cubic BeB$_2$ is a particularly interesting phase, where Be donates electrons to stabilize a diamond-like boron network under high pressure. In this work, we employ \textit{ab initio} methods to conduct a detailed investigation of cubic BeB$_2$ and its functional properties. We show that this metastable phase is dynamically stable under ambient conditions, and its lattice match to existing substrate materials suggests possible epitaxial stabilization via thin-film growth routes. Through a comprehensive characterization of its electronic, transport, and superconductivity properties, we demonstrate that cubic BeB$_2$ exhibits high hole concentrations and high hole mobility, making it a potential candidate for efficient $p$-type transport. In addition, cubic BeB$_2$ is found to exhibit low-temperature superconductivity at degenerate doping levels, similar to several other doped covalent semiconductors such as diamond, Si, and SiC.