Band structure and optical properties of wurtzite semiconductor nanotubes

We develop a comprehensive theoretical model for the band structure of single-crystal faceted nanotubes of wurtzite semiconductors based on the tight-binding approach. We focus on the GaN nanotube grown along the [0001] direction and surrounded by the equivalent surfaces {1 1̄ 00}. We first calculate the band structure of the wurtzite slab of finite thickness grown along the axis [1 1̄ 00]. We show that dangling bonds on two surfaces of the slab cause surface bands, which form the conduction and valence bands of the slab. Analyzing the symmetry of the single-crystal faceted nanotubes, we conclude that their band structure can be calculated from that of the slab with the help of cyclic boundary conditions. We show that the spectrum of the nanotubes depends both on the thickness of nanotube walls and on the radius. We further study the absorption coefficient of the nanotubes. We demonstrate that, with decreasing wall thickness, the contribution of surface states to the absorption spectrum becomes more pronounced.