High Stability of Faceted Nanotubes and Fullerenes of Multiphase Layered Phosphorus: A Computational Study

We present a paradigm in constructing very stable, faceted nanotube and fullerene structures by laterally joining nanoribbons or patches of different planar phosphorene phases. Our ab initio density functional calculations indicate that these phases may form very stable, nonplanar joints. Unlike fullerenes and nanotubes obtained by deforming a single-phase planar monolayer at substantial energy penalty, we find faceted fullerenes and nanotubes to be nearly as stable as the planar single-phase monolayers. The resulting rich variety of polymorphs allows us to tune the electronic properties of phosphorene nanotubes and fullerenes not only by the chiral index but also by the combination of different phosphorene phases. In selected phosphorene nanotubes, a metal-insulator transition may be induced by strain or by changing the number of walls.

Figure 1

(a) Atomic structure of $\alpha \text{−}\mathrm{P}$, $\beta \text{−}\mathrm{P}$, $\gamma \text{−}\mathrm{P}$, and $\delta \text{−}\mathrm{P}$ in top view and the side view of zigzag and armchair edges. The orthogonal lattice vectors ${\overrightarrow{a}}_1$ and ${\overrightarrow{a}}_2$ define the unit cells or supercells used in this study. Schematic and atomic structure of (b) an armchair and (d) a zigzag PNT, with the different structural phases distinguished by color and shading. The cross sections of (c) an armchair and (e) a zigzag nanotube illustrate the symmetry and the distribution of phases along the perimeter.

Figure 2

Phosphorene-based fullerene structures with (a)–(c) octahedral and (d)–(f) icosahedral symmetry. The structural models in (a) and (d) indicate how triangular facets of $\beta \text{−}\mathrm{P}$ are connected by $\gamma \text{−}\mathrm{P}$ along the edges. The stick models of ${\mathrm{P}}_{72}$ in (b), ${\mathrm{P}}_{200}$ in (c), ${\mathrm{P}}_{80}$ in (e), and ${\mathrm{P}}_{180}$ in (f) depict the relaxed atomic structures of octahedral and icosahedral fullerenes.

Figure 3

Stability and electronic structure of faceted nanotubes and fullerenes. (a) Average strain energy per atom $\mathrm{\Delta }E/n$ in PNTs of different radius $R$ with respect to a planar $\beta \text{−}\mathrm{P}$ monolayer. The shaded region indicates the range of stabilities of different planar phases and contains most data points for multicomponent faceted nanotubes. For the sake of comparison, we also present data points for pure-phase PNTs obtained by rolling up $\beta \text{−}\mathrm{P}$ and $\gamma \text{−}\mathrm{P}$ to a tube. (b) Strain energy per atom in octahedral (o) and icosahedral (i) fullerenes of radius $R$. The dashed lines in (a) and (b) represent the $1/R^2$ behavior based on continuum elasticity theory for pure-phase nanostructures. (c) Fundamental band gaps $E_g$ in faceted a-PNTs and z-PNTs. The horizontal lines depict $E_g$ values in pure planar phosphorene monolayers and help to rationalize the separation between large gap values in a-PNTs and small gap values in z-PNTs. (d) HOMO-LUMO gaps in o- and i-fullerenes. o-fullerenes have consistently larger band gaps than i-fullerenes.

Figure 4

(a) Cross section and (b) DOS of the double-wall z-PNT (5,0,5,0)@(9,0,9,0). The solid line in (b) shows the total DOS and the dashed line depicts the superposition of the densities of states of the isolated nanotube components. The Fermi level $E_F$ is set at 0. (c) Perspective view of the a-PNT(3,0,9,0) and (d) dependence of the gap energy $E_g$ on axial strain.