Ambient-pressure anisotropic single-gap superconductivity in La-trapped B_26 cages with superior hardness

Recently, the breakthrough high-pressure synthesis of the sp^3-bonded clathrate-like R-3m-LaB_8 featuring La-trapped B_26 cages was achieved. Although the superconducting critical temperature (T_c) and Vickers hardness (H_v) for LaB_8 were estimated, the anisotropic superconductivity and the superconducting gaps nature remain unclear. Meanwhile, the stability of pure B_26 cages under ambient conditions also piqued our interest in exploring the hardness of B_26 and the role of La atoms in hardness of LaB_8. By resolving the Allen-Dynes modified McMillan equation and the anisotropic Eliashberg equations, it is revealed that LaB_8 exhibits anisotropic single-gap superconductivity with T_c of 19.0 \sim 26.5 K, and the anisotropic ratio of the superconducting gap reaches up to 48.50% at 5 K. Most significantly, our work fundamentally validated the coupling of B-2p orbitals with the optical double-degenerate E_g phonon modes and A_g phonon mode from a novel perspective. The H_v of B_26 cages was determined to be 18.6 GPa, which is lower than that of La-trapped B_26 ones (i.e., LaB_8), indicating that the element La act as an enhancer of hardness for LaB_8.