$\sigma$ bands driven high-temperature superconductivity in hydrogenated hexagonal BC$_3$ monolayer

Material with metallic $\sigma$-bonding bands is expected to be a high-temperature superconductor, due to the sensitivity of $\sigma$ electrons to lattice vibration. Based on the first-principles calculations, electronic structures of hydrogenated BC$_3$ monolayers (H$_n$-B$_2$C$_6$ with $n$=1-8) are systematically investigated. At high coverage of hydrogen, the monolayer stabilizes in chair-like $sp^3$-hybridized configurations, leading to the metallization of $\sigma$ bands, especially in H$_7$-B$_2$C$_6$ and H$_8$-B$_2$C$_6$. This metallicity originates from the electron deficiency of boron, compared with insulating graphane. Utilizing Wannier interpolation, the electron-phonon coupling strengths for metallic phases of H$_n$-B$_2$C$_6$ are determined. As expected, strong couplings are identified between the conducting $\sigma$ electrons and low-frequency phonon modes. By solving the anisotropic Eliashberg equations, we confirm that H$_7$-B$_2$C$_6$ and H$_8$-B$_2$C$_6$ are single-gap superconductors with critical temperature being 87 K, exceeding the boiling point of liquid nitrogen. Considering that monolayer BC$_3$ has been synthesized in experiment, our results demonstrate that hydrogenation of two-dimensional BC$_3$ provides a viable pathway to achieve high-temperature superconductivity at ambient pressure.