A novel three-dimensional superhard carbon allotrope with a direct band gap

Carbon is one of the earliest widely used light elements, which forms a variety of allotropes that show abundant physical properties. To further determine their exciting physical characteristics, in this manuscript, we carry out structure predictions combined with density functional theory (DFT) and design a new three-dimensional (3D) sp(3) hybridized carbon phase, named t-C-32, with tetragonal symmetry and the P42/mmc space group. In addition to mechanical and dynamic stability at ambient pressure, t-C-32 exhibits thermal stability at a high temperature of 500 K, as verified by ab initio molecular dynamics simulations. t-C-32 has a low relative enthalpy of 0.364 eV/atom and greater hardness (similar to 75 GPa) than cubic boron nitride (similar to 65 GPa) based on Chen's model. The elastic properties and anisotropy under high pressure were also investigated, and the results show that the Young modulus and bulk modulus can reach 1314 GPa and 718 GPa at 100 GPa, respectively. The electronic band structure based on the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional indicates that t-C-32 carbon is a direct band gap semiconductor with a wide band gap of 3.861 eV. This work extends the family of superhard semiconductor carbon and may provide a novel field for the construction of new electronic devices.