Ambient-Pressure Anisotropic Single-Gap Superconductivity in La-Trapped B₂₆ Cages with Superior Hardness

Recently, a breakthrough in the high-pressure synthesis of sp^3-bonded clathrate-like R-3m-LaB_8 featuring La-trapped B_26 cages was achieved. Although the superconducting critical temperature (T_\rm c) and Vickers hardness (H_\rm v) of LaB_8 were estimated, the anisotropic superconductivity and superconducting gap nature remain unclear. The stability of pure B_26 cages under ambient conditions is of interest for exploring the B_26 hardness and the role of La atoms in the LaB_8 hardness. By resolving the Allen-Dynes modified McMillan equation and the anisotropic Eliashberg equations, it was found that LaB_8 exhibits anisotropic single-gap superconductivity with T_\rm c=19.0\sim26.5 K, and the superconducting gap anisotropic ratio reaches 48.50% at 5 K. Most significantly, our work fundamentally validated the coupling of B-2p orbitals with the optical double-degenerate E_\rm g phonon modes and A_\rm g phonon mode from a novel perspective. The H_\rm v of B_26 cages was determined to be 18.6 GPa, which is lower than that of La-trapped B_26 cages (i.e., LaB_8), indicating that La acts as a hardness enhancer for LaB_8.