Metallic behavior in low-dimensional honeycomb SiB crystals: A first-principles prediction of atomic structure and electronic properties

We present a detailed analysis of the atomic and electronic structure of a two-dimensional monolayer of boron and silicon elements within periodic density functional theory. The proposed h-SiB sheet is a structural analog of hexagonal boron nitride (h-BN) and exhibits a good structural stability, compared to the structure of silicene. The calculated cohesive energy of an infinite sheet of h-SiB is of 4.71 eV/atom, whereas the corresponding value for silicene is 4.09 eV/atom. However, h-SiB sheets are not able to be stacked into a three-dimensional graphitelike structure, leading to a new hexagonal phase. On the other hand, h-SiB is predicted to roll up into single-walled silicon boron nanotubes (SWSiBNTs) of which we examine the electronic properties of some zigzag and armchair tubes. The strain energy of the SWSiBNTs are four to five times lower than the strain energy of the corresponding carbon nanotubes. In contrast to more polar honeycomb monolayers, the h-SiB sheet is not semiconducting or semimetallic. It has a delocalized charge density like graphene, but the $\pi$ band and the two highest occupied $\sigma$ bands are only partly filled. This results in a high density of states around the Fermi level and a metallic behavior of the h-SiB sheet. Interestingly, all the low-dimensional h-SiB-based structures, including the smallest to the largest stable tubes studied here, are predicted to form metallic systems.

Figure 1

Cross sections of relaxed SWSiBNTs. Silicon and boron atoms are represented by yellow and blue spheres, respectively.

Figure 2

Strain energies of relaxed SWCNTs and SWSiBNTs versus their mean radii.

Figure 3

Temperature and cohesive energy versus time steps of the (5,5), (10,0), and (10,10) SWSiBNTs.

Figure 4

Snapshots of the SWSiBNTs after 1500 time steps (of 1 fs): (a) (10,10), (b) (10,0), and (c) (5,5). Silicon and boron atoms are represented by yellow and blue spheres, respectively.

Figure 5

Temperature and cohesive energy versus time steps (of 1 fs) of the (5,5) SWSiBNT.

Figure 6

The buckling parameter $\Delta$ is defined as the distance between the planes of two atom types. $\gamma$ is the angle between the lattice vectors in the plane.

Figure 7

Variation in the total energy of partly relaxed h-SiB with respect to the buckling parameter $\Delta$ (circles). The points denoted by $+$ correspond to sheets relaxed with the additional constraint of a fixed angle $\gamma$.

Figure 8

Probability density isosurfaces (at 50$\%$ of maximum grid value) of the $\pi$ orbital at the $\Gamma$ point of the h-SiB sheet. Silicon and boron atoms are represented by yellow and blue spheres, respectively.

Figure 9

Band structures, DOS and PDOS of h-BN, graphene, and h-SiB. The Fermi energy is plotted with a dashed line. The PDOS of $n{p}_{-1}$ is equal to $n{p}_1$, therefore it is not shown in the figures. Also, the PDOS of the $3d$ orbitals of silicon are excluded due to their minor contribution below and around the Fermi energy.

Figure 10

Band structure of planar and buckled sheets of silicene and h-SiB. Red (black) lines corresponds to the buckled (planar) structures. The more stable (buckled) $\beta$-silicene sheet has a $\Delta$ of 0.51 Å, while the unstable buckled h-SiB has a $\Delta$ of 0.70 Å.

Figure 11

The 2D Fermi surfaces (in slightly tilted 3D plots) of the planar stable h-SiB sheet (left) and the unstable buckled ($\Delta =0.70$ Å) h-SiB sheet (right).

Figure 12

Band structures of the zigzag (8,0) and (9,0) SWCNTs and the corresponding SWSiBNTs. The Fermi energy is indicated by a dashed line.