Single-layer crystalline phases of antimony: Antimonenes

The pseudolayered character of 3D bulk crystals of antimony has led us to predict its 2D single-layer crystalline phase named antimonene in a buckled honeycomb structure like silicene. Sb atoms also form an asymmetric washboard structure like black phospherene. Based on an extensive analysis comprising ab initio phonon and finite-temperature molecular dynamics calculations, we show that these two single-layer phases are robust and can remain stable at high temperatures. They are nonmagnetic semiconductors with band gaps ranging from 0.3 eV to 1.5 eV, and are suitable for 2D electronic applications. The washboard antimonene displays strongly directional mechanical properties, which may give rise to a strong influence of strain on the electronic properties. Single-layer antimonene phases form bilayer and trilayer structures with wide interlayer spacings. In multilayers, this spacing is reduced and eventually the structure changes to 3D pseudolayered bulk crystals. The zigzag and armchair nanoribbons of the antimonene phases have fundamental band gaps derived from reconstructed edge states and display a diversity of magnetic and electronic properties depending on their width and edge geometry. Their band gaps are tunable with the widths of the nanoribbons. When grown on substrates, such as germanene or Ge(111), the buckled antimonene attains a significant influence of substrates.

Figure 1

Results of ab initio calculations on the 3D bulk crystal of Sb with trigonal and hexagonal lattice. (a) Side and top views of the optimized atomic configuration and structural parameters. Pseudolayered character of the crystal is highlighted by atomic layers exhibiting ABCABC… stacking. Inlayer and interlayer bonding is depicted by isosurface and contour plots of the total charge density. (b) Calculated dispersion relations of bands of vibrational frequencies. The Brillouin zone is shown by inset. (c) Electronic energy bands calculated within PBE. The correction by HSE is shown by green-dashed lines. The zero of energy is set to the Fermi level. (d) Total and orbital projected densities of states. For illustrative purposes, the zero of the vertical axis is shifted for each projected density of states.

Figure 2

2D, single-layer structures of antimony. (a) The equilibrium 2D crystalline structure of buckled honeycomb structure, i.e., B-antimonene, with hexagonal lattice. The primitive unit cell has two Sb atoms. Optimized values of the structural parameters, such as lattice constants, bond lengths, and bond angles, are also shown. Bonding between Sb atoms is depicted by the isosurfaces and contour plots of the total charge density. $\mathrm{\Delta }$ is the buckling, where Sb atoms on the corners of the hexagon alternatively move up and down. (b) Same for 2D, symmetric washboard structure, i.e., W-antimonene, having 2D rectangular lattice. Rectangular primitive unit cell has four Sb atoms. In the side view one deduces two atomic planes. (c) Same for 2D, asymmetric washboard structure, i.e., aW-antimonene, with rectangular lattice. The primitive unit cell has four Sb atoms; single-layer structure is composed of four atomic planes.

Figure 3

Ab initio calculations of the bands of vibrational frequencies. The Brillouin zones and their symmetry directions are shown by insets. (a) B-antimonene. (b) W-antimonene with imaginary frequencies as $\mathbf{k}\to 0$. (c) aW-antimonene.

Figure 4

The electronic band structure together with the total and orbital projected densities of states of the single-layer antimonene phases. Zeros of the band energy are set at the maximum of the valance bands. Bands corrected by HSE are shown by green-dashed lines. Bands calculated by including spin-orbit coupling are shown by insets. (a) B-antimonene. (b) W-antimonene. (c) aW-antimonene. For illustrative purposes, the zero of the vertical axis is shifted for each projected density of states.

Figure 5

(a) The optimized atomic structure and binding interaction of B-antimonene grown on germanene surface (i.e., graphene-like structure of Ge atoms). The registry of Sb and Ge atoms are shown by inset. (b) Corresponding electronic energy band structure. (c) Total and partial densities of states (DOS) projected on Sb and Ge atoms. The comparison of the total density of states of free B-Sb single-layer structure with the density of states projected on the Sb atoms grown on germanene indicates significant substrate influence. (d)–(f) Same for B-antimonene grown on the Ge(111) substrate. The zero of energy is set to the Fermi level shown by dash-dotted line.

Figure 6

(a) Minimum-energy AB stacking geometry of the B-antimonene bilayer and the variation of its total energy with the distance $z$ between the layers. The total energies are given relative to $z \to$ infinity. (b) Energy band structure of bilayer corresponding to the equilibrium spacing. Calculations using HSE presented by green dashed lines. (c) Same for trilayer of B-antimonene in ABC stacking. The first minimum of the total energy occurs at $z=3.65\text{Å}$. Upon overcoming an energy barrier the second minimum occurs at $z=2.5\text{Å}$. The variation of the optimized total energy of the periodic 3D structure as a function of $z$, which exhibits a single minimum at $z=2.37\text{Å}$ corresponding to the pseudolayered 3D bulk crystal. (d) The energy band structure of the trilayer in the first minimum at $z=3.65\text{Å}$. (e) Minimum-energy AA stacking geometry of aW-antimonene bilayer and the variation of its total energy with the distance $z$ between layers. Top and side views of atomic structures are shown by insets. (f) Energy band structure of aW-antimonene bilayer in (e).

Figure 7

(a) The primitive unit cell, optimized atomic configuration, and energy band structure of the armchair B-antimonene nanoribbon. The variation of band gap with $n$ and charge density isosurfaces of specific band states at the edges of conduction (C) and valence (V) bands are also shown. Energy bands corrected using HSE are shown by dashed lines. (b) Same for the zigzag B-antimonene nanoribbon. Structure optimization and band calculations are performed using $2\times 1$ unit cell. The zero of energy is set at the top of the valence band. Spin-up and spin-down bands are shown by red and blue lines, respectively. Spin-up and spin-down bands corrected using HSE are also shown by dashed red and blue lines, respectively.

Figure 8

(a) The primitive unit cell having $n$ Sb atoms, optimized atomic structure, and the energy band structure of the armchair aW-antimonene nanoribbon. The variation of band gap with $n$ and charge density isosurfaces of specific band states at the edges of conduction (C) and valence (V) bands are also shown. Energy bands calculated by HSE are shown by dashed lines. The zero of the energy is set at the top of the valence band. (b) Same for the zigzag aW-antimonene nanoribbon, where due to the reconstructions of edges calculations are performed using $2\times 1$ unit cell. Spin-up and spin-down bands are shown by red and blue lines, respectively. The zero of energy is set at the Fermi level.