Geometry, electronic structures and optical properties of phosphorus nanotubes.

Using a first principles approach, we investigated the geometry, electronic structures, and optical properties of phosphorus nanotubes (PNTs). Two possible 1D configurations, the so-called α-PNTs and β-PNTs, are proposed, which are structurally related to blue and black phosphorus monolayers, respectively. Hereby, we predict that both armchair and zigzag geometries can be synthesized in α-PNTs, but the zigzag form of β-PNT is highly unfavorable because of large strain and conformation energies. The band gap of α-PNTs is expected to be ∼2.67 eV, and this is insensitive to the chirality when the tube's inner diameter is larger than 1.3 nm, while the armchair β-PNTs have a much smaller band gap. Interestingly, we find nearly flat band structures in the zigzag α-PNT system. This may indicate that an excited particle-hole pair has a huge effective mass. We also find asymmetric optical properties with respect to the polarization direction. The armchair α-PNT for parallel polarization shows a large refractive index of 2.6 near the ultraviolet wavelength, and also we find that the refractive index can be even smaller than 1 in certain frequency ranges. The zigzag tubes show very weak reflectivity for parallel polarization, while the armchair tube displays high reflectivity.