Prompted by recent reports on $sqrt{3} times sqrt{3}$ graphene superlattices with intrinsic inter-valley interactions, we perform first-principles calculations to investigate the electronic properties of periodically nitrogen-doped graphene and carbon nanotube nanostructures. In these structures, nitrogen atoms substitute one-sixth of the carbon atoms in the pristine hexagonal lattices with exact periodicity to form perfect $sqrt{3} times sqrt{3}$ superlattices of graphene and carbon nanotubes. Multiple nanostructures of $sqrt{3} times sqrt{3}$ graphene ribbons and carbon nanotubes are explored, and all configurations show nonmagnetic and metallic behaviors. The transport properties of $sqrt{3} times sqrt{3}$ graphene and carbon nanotube superlattices are calculated utilizing the non-equilibrium Greens function formalism combined with density functional theory. The transmission spectrum through the pristine and $sqrt{3} times sqrt{3}$ armchair carbon nanotube heterostructure shows quantized behavior under certain circumstances.
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