  Recent experimental observations have reported that, rather than randomly
distributed, nitrogen atoms may prefer to be located on one of the two
sub-lattices of graphene. It has been suggested that such a preference may
present a possible avenue to tailor the band gap of graphene whilst maintaining
its excellent electronic transport properties. Among the proposed mechanisms to
explain this effect is the suggestion that long-range inter-impurity
interactions mediated by the conduction electrons of graphene may give rise to
the asymmetry between sub-lattice occupations. Electron-mediated interactions
are known to be prevalent not only between N atoms but also between impurities
that are adsorbed to a specific location within the hexagonal structure, namely
to the top of the carbon atom. Furthermore, this interaction is known to become
more long-ranged as the dimensionality of the system is lowered. For that
reason, in this paper we investigate whether a similar sub-lattice asymmetry
appears in the case of metallic carbon nanotubes doped with Hydrogen adatoms.
Our results indicate that similar sub-lattice asymmetries are observable and
even more pronounced in small-diameter CNTs with a dilute concentration of
adsorbates, diminishing with increasing diameter or impurity concentrations.
