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

Abstract Recently, a breakthrough in the high-pressure synthesis of sp 3 -bonded clathrate-like R -3 m -LaB 8 featuring La-trapped B 26 cages was achieved. Although the superconducting critical temperature ( T c ) and Vickers hardness ( H 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 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-2 p 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 cages (i.e., LaB 8 ), indicating that La acts as a hardness enhancer for LaB 8 .