Stability, electronic disruption, and anisotropic superconductivity of hydrogenated trilayer metal tetraborides (MB${}_4$H; M=Be, Mg, Ca, Al)

The discovery of superconductivity in MgB${}_2$ ($T_c=39$ K) \cite{nagamatsu2001superconductivity} established metal diborides (MB${}_2$) as a promising class of conventional superconductors. Recent advances in fabrication techniques have enabled the synthesis of 2D MgB${}_2$ with a $T_c$ of 36 K \cite{cheng2018fabrication}, reigniting interest in layered metal borides. This has led to predictions of superconductivity in various 2D metal borides, including MB${}_4$ (M = Be, Mg, Ca, Al), with CaB${}_4$ exhibiting the highest estimated $T_c$ of 36.1 K. To explore the impact of hydrogenation on superconductivity, we systematically investigate two-dimensional hydrogenated trilayer metal borides (MB${}_4$H; M = Be, Mg, Ca, Al). Our results reveal that these materials retain a metallic nature dominated by boron $p$-orbitals, while hydrogenation significantly alters their band dispersion and Fermi surface topology. Phonon calculations confirm their dynamical stability and reveal strong electron-phonon interactions, leading to multi-gap superconductivity. Among the studied compounds, MgB${}_4$H, AlB${}_4$H, and CaB${}_4$H exhibit possible two superconducting gaps, with CaB${}_4$H showing the strongest electron-phonon coupling, resulting in an intrinsic superconducting transition temperature of 64 K. In contrast, AlB${}_4$H shows the weakest coupling, with $T_c=22$ K. The calculated electron-phonon coupling constants ($\lambda$) range from 0.62 to 0.99, demonstrating the tunability of superconducting properties through elemental substitution. These findings provide valuable insights into superconductivity in hydrogenated metal borides and highlight their potential for high-$T_c$ applications.