Systematic search for low-enthalpy sp3 carbon using evolutionary metadynamics

We present a systematic search for low-energy metastable superhard carbon allotropes by using the recently developed evolutionary metadynamics technique. It is known that cold compression of graphite produces an allotrope at 15-20 GPa. Here we look for all low-enthalpy structures accessible from graphite. Starting from 2H- or 3R-graphite and applying the pressure of 20 GPa, a large variety of intermediate $sp^3$ carbon allotropes were observed in evolutionary metadynamics simulation. Our calculation not only found all the previous proposed candidates for `superhard graphite', but also predicted two allotropes (\emph{X}-carbon and \emph{Y}-carbon) showing novel 5+7 and 4+8 topologies. These superhard carbon allotropes can be classified into five families based on 6 (diamond/lonsdaleite), 5+7 (\emph{M/W}-carbon), 5+7 (\emph{X}-carbon), 4+8 (bct C$_4$), and 4+8 (\emph{Y}-carbon) topologies. This study shows evolutionary metadynamics is a powerful approach both to find the global minima and systematically search for low-energy metastable phases reachable from given starting materials.