Nanotubes based on monolayer blue phosphorus

We demonstrate structural stability of monolayer zigzag and armchair blue phosphorus nanotubes by means of molecular dynamics simulations. The vibrational spectrum and electronic band structure are determined and analyzed as functions of the tube diameter and axial strain. The nanotubes are found to be semiconductors with a sensitive indirect band gap that allows flexible tuning.

Figure 1

Structures of $\beta -\mathrm{P}$ as well as zigzag $(10,0)$ and armchair $(10,10)\beta -\mathrm{P}$ nanotubes. The two atomic layers are distinguished by color.

Figure 2

Curvature energy as a function of the tube diameter. Fitting curves are given by green dashed lines.

Figure 3

Snapshots from the molecular dynamics simulation of the zigzag $(8,0)\beta -\mathrm{P}$ nanotube at increasing temperatures.

Figure 4

Left: Potential energy per atom as function of the temperature for zigzag (6,0), (8,0), (10,0) and armchair (6,6), (8,8), (10,10) $\beta -\mathrm{P}$ nanotubes. Right: Melting temperature as function of the tube diameter. The inset shows the temperature dependence of the potential energy of bulk phosphorus.

Figure 5

(Left) Vibrational spectrum and (right) electronic band structure of (top) zigzag and (bottom) armchair $\beta -\mathrm{P}$ nanotubes. Color is used to mark the breathing (red) and twiston (green) modes.

Figure 6

(Left) Vibrational spectrum and (right) electronic band structure of $\beta -\mathrm{P}$ in the hexagonal Brillouin zone.

Figure 7

(Left) Dependence of the band gap size on the nanotube diameter. The green dashed line refers to the band gap of $\beta -\mathrm{P}$ and the blue line is obtained by exponential fitting. (Right) Dependence of the band gap size on axial strain for the zigzag (8,0) and armchair (8,8) nanotubes.

Figure 8

Electronic band structure of the armchair (8,8) $\beta -\mathrm{P}$ nanotube under $-2\%$ (compressive) and $+2\%$ (tensile) axial strain. The valence and conduction band edges are marked by blue and red arrows, respectively.