  A new kind of three-dimensional carbon allotropes, termed carbon honeycomb
(CHC), has recently been synthesized [PRL 116, 055501 (2016)]. Based on the
experimental results, a family of graphene networks are constructed, and their
electronic and phonon properties are calculated by using first principles
methods. All networks are porous metal with two types of electron transport
channels along the honeycomb axis and they are isolated from each other: one
type of channels is originated from the orbital interactions of the carbon
zigzag chains and is topologically protected, while the other type of channels
is from the straight lines of the carbon atoms that link the zigzag chains and
is topologically trivial. The velocity of the electrons can reach ~10^6 m/s.
Phonon transport in these allotropes is strongly anisotropic, and the thermal
conductivities can be very low when compared with graphite by at least a factor
of 15. Our calculations further indicate that these porous carbon networks
possess high storage capacity for gaseous atoms and molecules in agreement with
experiment.
