Anisotropic high- T c superconductivity above 90 K in hole-doped boron-nitrogen clathrates at ambient pressure

Breakthroughs in near-room-temperature superconductivity within clathrate hydrides underscore the effectiveness of theory-driven approaches to designing high-${T}_{c}$ superconductors. However, superconductivity in these clathrate hydrides has not been realized at low or ambient pressures. To explore phonon-mediated superconductors with ${T}_{c}$ exceeding the liquid-nitrogen temperature under ambient pressure, this study investigates the crystal structure, metallization, electron-phonon coupling, and anisotropic superconducting behavior in hole-doped ${(\mathrm{BN})}_{6}$ and ${(\mathrm{BN})}_{5}$ clathrates, with configurations akin to ${\mathrm{CaH}}_{6}$ and ${\mathrm{LaH}}_{10}$, utilizing first-principles calculations in junction with Wannier interpolation technique. By solving the fully anisotropic Migdal-Eliashberg equations, this work reveals a positive correlation between ${T}_{c}$ and hole-doping levels, with the highest ${T}_{c}$ approximately 32 K and 96 K in hole-doped ${(\mathrm{BN})}_{6}$ and ${(\mathrm{BN})}_{5}$, respectively, and both with single anisotropic energy gap nature. The high-${T}_{c}$ superconductivity in B-N clathrates arises from two primary factors: the enhanced density of states at the Fermi level and the presence of strong B-N $s{p}^{3}$-hybridized covalent $\ensuremath{\sigma}$-bonding bands. These insights provide a new perspective for revealing the superconductivity of B-N clathrates from an anisotropic perspective and offer valuable avenues for inducing high-${T}_{c}$ superconductors at ambient conditions.