T-C₅₆: a low-density transparent superhard carbon allotrope assembled from C₁₆ cage-like cluster

Owing to the various ways of chemical bonding, carbon can form abundant allotropes with different frameworks, which harbor rich mechanical and electronic properties. Taking the cage-like isomer of C₁₆ cluster as a building block, we design a new low-density carbon allotrope, which has tetragonal symmetry (I4/mmm) and a 56-atom unit cell, hence termed as T-C₅₆. Our first-principles calculations reveal that T-C₅₆ is not only energetically, dynamically, thermally (above 1800 K) and mechanically stable, but even more stable than the experimentally synthesized C20-sc and T-carbon. Remarkably, although the framework of T-C₅₆ is low density (2.72 g cm^-3), it exhibits novel superhard properties with a Vickers hardness of 48.71 GPa. The obtained Yang's modulus and ideal strength show that T-C₅₆ is mechanically anisotropic. In particular, our analysis of electronic and optical properties suggest that T-C₅₆ is a transparent indirect semiconductor with a wide bandgap of 3.18 eV (HSE06). These findings highlight a distinct carbon allotrope, having promising applications for optical and aerospace devices due to its light, transparent, superhard features.