Topologically protected conduction state at carbon foam surfaces:An ab-initio study

We report results of \textit{ab initio} electronic structure and quantum conductance calculations indicating the emergence of conduction at the surface of semiconducting carbon foams. Occurrence of new conduction states is intimately linked to the topology of the surface and not limited to foams of elemental carbon. Our interpretation based on rehybridization theory indicates that conduction in the foam derives from first- and second-neighbor interactions between $p_\|$ orbitals lying in the surface plane, which are related to $p_\perp$ orbitals of graphene. The topologically protected conducting state occurs on bare and hydrogen-terminated foam surfaces and is thus unrelated to dangling bonds. Our results for carbon foam indicate that the conductance behavior may be further significantly modified by surface patterning.