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

Recently, a breakthrough in the high-pressure synthesis of sp³-bonded clathrate-like R-3m-LaB₈ featuring Latrapped B₂₆ cages was achieved. Although the superconducting critical temperature (T_c) and Vickers hardness (H_v) of LaB₈ were estimated, the anisotropic superconductivity and superconducting gap nature remain unclear. The stability of pure B₂₆ cages under ambient conditions is of interest for exploring the B₂₆ hardness and the role of La atoms in the LaB₈ hardness. By resolving the Allen–Dynes modified McMillan equation and the anisotropic Eliashberg equations, it was found that LaB₈ exhibits anisotropic single-gap superconductivity with T_c = 19.0 ~ 26.5 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_g phonon modes and A_g phonon mode from a novel perspective. The H_v of B₂₆ cages was determined to be 18.6 GPa, which is lower than that of La-trapped B₂₆ cages (i.e., LaB₈), indicating that La acts as a hardness enhancer for LaB₈.