Monoclinic mC28 carbon: A sp2-sp3 hybridized carbon allotrope with superhard and metallic properties

New carbon allotropes with mixed sp, sp(2) and sp(3) bonds are now the focus of theoretical and experimental researches due to their abnormal properties. We here theoretically proposed a novel three-dimensional carbon structure with mixed sp(2) and sp(3) bonds (named as mC28 carbon) via particle swarm optimization method. mC28 carbon is built by the 'diamond-like' sp(3) networks connected by sp(2) bonded carbon atoms. It has a lower enthalpy than graphite after similar to 29 GPa and is dynamically stable at zero pressure. More interesting, mC28 carbon is metallic, which can be attributed to the connected sp(2) bonding carbon atoms. They provide a channel for their extra delocalized valence electron that siting at pz orbital. mC28 carbon is also a superhard material with theoretical Vickers hardness of 85 GPa.