Four new tetragonal superhard sp3 carbon allotropes with wide direct band gaps

• Four new tetragonal superhard carbon allotropes were uncovered. • The four carbon allotropes are wide direct band semiconductors. • The hardness values of the four structures were 81, 72, 71, and 58 GPa, respectively. In this study, four new tetragonal sp 3 carbon allotropes with high dynamic and mechanical stabilities ( I 4 1 / acd -C112, I 4/ mcm -C128, I 4/ mcm -C112, and I 4 1 / amd -C64) were predicted using first-principles calculations. The I 4 1 / acd -C112, I 4/ mcm -C128, I 4/ mcm -C112, and I 4 1 / amd -C64 allotropes exhibited semiconductor behavior, as confirmed by their wide band gaps (calculated to be 3.80, 3.22, 3.56, and 3.51 eV, respectively) and superhardness, as evidenced through hardness and ideal strength calculations.