Evolution of Weyl-like semi-metallicity in an all-sp² carbon allotrope

Based on first-principles calculations, we design a stable 3D all-sp² carbon allotrope by assembling the dehydrogenized helical polyethylenes and dehydrogenized ethylenes. It possesses 32 carbon atoms in its unit cell with orthorhombic symmetry, thus termed oC32. In the absence of spin-orbit-coupling (SOC), oC32 possesses a Weyl-like loop protected by the coexistence of time-reversal, spatial inversion, and mirror reflection symmetries. By displacing the carbon atoms of dehydrogenized ethylenes, the spatial symmetries of oC32 are broken and topological phase transitions occur from the Weyl-like loop state to Weyl-like point states. To probe the origin of the Weyl-like points, we further examine the electronic properties of a 2D sheet composed of the dehydrogenized helical polyethylenes embedded in oC32 since the charge near the Fermi level is regularly distributed around these 2D sheets. We find that the Weyl-like points also appear in these 2D sheets, indicating that the Weyl-like points in the symmetry-broken oC32 come from the 2D sheets embedded in oC32. Our work demonstrates that carbon materials can exhibit rich topological states and topological phase transitions due to the flexible bonding and negligible spin-orbital interaction of carbon atom.