Structural and electronic properties of α-, β-, γ-, and 6,6,18-graphdiyne sheets and nanotubes

α-, β-, γ- and 6,6,18-graphdiyne (GDYs) sheets, as well as the corresponding nanotubes (GDYNTs) are investigated systematically by using the self-consistent-field crystal orbital method. The calculations show that the GDYs and GDYNTs with different structures have different electronic properties. The α-GDY sheet is a conductor, while 2D β-, γ- and 6,6,18-GDYs are semiconductors. The carrier mobilities of β- and γ-GDY sheets in different directions are almost the same, indicating the isotropic transport characteristics. In addition, the electron mobility is in the order of 10⁶ cm² V^-1 s^-1 and it is two orders of magnitude larger than the hole mobility of 2D γ-GDY. However, α- and 6,6,18-GDY sheets have anisotropic mobilities, which are different along different directions. For the 1D tubes, the order of stability is γ-GDYNTs > 6,6,18-GDYNTs > β-GDYNTs > α-GDYNTs and is independent of the tube chirality and size. β- and γ-GDYNTs as well as zigzag α- and 6,6,18-GDYNTs are semiconductors with direct bandgaps, while armchair α-GDYNTs are metals, and armchair 6,6,18-GDYNTs change from semiconductors to metals with increasing tube size. The armchair β- and γ-GDYNTs are more favourable to transport holes, while the corresponding zigzag tubes prefer to transport electrons.