Unusual conduction mechanism at graphitic carbon foam surfaces: An \textit{ab initio} study*

Using {\em ab initio} electronic structure and quantum conductance calculations, we identify an unusual conduction mechanism at the surface of a previously described graphitic carbon foam structure. The emergence of a new, topologically protected conduction band in this semiconducting system is intimately linked to the topology of the foam. In contrast to conduction bands of graphitic structures, which are related to nearest-neighbor interactions between $p_\perp$ orbitals normal to the surface, the new band responsible for metallic behavior derives from interactions between $p_\|$ orbitals lying in the surface plane. The conducting surface state occurs on bare and hydrogen-terminated surfaces and is thus unrelated to dangling bonds. We find that the conductance behavior can be further significantly modified by surface patterning.