We theoretically evaluate the electronic band structures in carbon nanotubes with nanoscale periodic pores with a tight-binding approximation of π electrons, and demonstrate that band gaps of the carbon nanotubes with nanoscale periodic pores differ significantly from those of conventional carbon nanotubes. The band gaps of the carbon nanotubes with nanoscale periodic pores depend strongly on the size of pores and inter-pore distances. In some carbon nanotubes with nanoscale periodic pores, band gaps are constant as a function of their circumferences. In other ones, band gaps have the exact periodicity of three as a function of their circumferences. Those behaviors can be explained by taking properties of nanoscale periodic porous graphite into consideration. In some carbon nanotubes with relatively large nanoscale periodic pores, flat bands appear, which may cause singular properties about magnetism in one-dimensional porous carbon nanotubes.
Designer flat bands in quasi-one-dimensional atomic lattices
