  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.
