Since graphene was first isolated through mechanical exfoliation from ghaphite sheets in 2004,^[1] two-dimensional (2D) materials such as transition metal dichacogenides, silicene, germanene, stananene, and phosphenene have been extensively studied^[2,3] over the past decade. Owing to the unique honeycomb structure, 2D materials exhibit extraordinary properties, including topological insulator effect,^[4] superconductivity,^[5] and thermoelectricity,^[6] which make them attractive for a wide range of applications in spintronics, optoelectronics, chemical sensors, and energy conversion or storage.^[2,7,8] Recently, two novel graphene-like 2D materials, namely asenene and antimonene, were predicted through first-principles calculations by Zhang et al.^[9] As the analogues of black phosphenene, asenene and antimonene have wide band gaps and high stability. To achieve multifunctional devices, it is crucial to tune the structural, electronic, and magnetic properties of 2D materials by various methods, including strain,^[10] doping,^[11,12] chemical functionalization,^[13] and external electric field,^[14] among which the chemical functionalization is an extremely effective way because of its high chemical reactivity.

Up to now, it has been reported that fully hydrogenated arsenene is a Dirac material and semi-hydrogenated arsenene exhibits significant magnetism.^[15] Moreover, fully halogenated arsenene^[16] and chemically decorated arsenene, AsX (X = CN, NC, NCO, NCS, and NCSe),^[17] were also found to be Dirac materials. However, as far as we know, functionalized antimonene has not been reported till now. In this work, we investigate the structural and electronic properties of fully hydrogenated (FH) antimonene and semi-hydrogenated (SH) antimonene using first-principles calculations.

First-principles calculations are performed within the framework of density functional theory (DFT) implemented in Quantum ESPRESSO package^[18,19] using a norm-conserving pseudopotentials^[20] and fully-relativistic ultrasoft pseudopotentials^[21] for calculations without spin–orbital coupling (SOC) calculations and with SOC calculations, respectively. Spin polarization is included throughout the calculation. The exchange–correlation functional is treated using generalized-gradient approximation (GGA) of Perdew–Burke–Eruzerhof (PBE).^[22] The unit cell optimization is terminated upon reaching the pressure cut-off of 0.01 kbar. The energy cutoff of the plane waves is set to 150 Ry in all computations except molecular dynamics (MD) simulation and nanoribbon. The energy criterion is set to 10⁻¹⁰ Ry for both electronic self consistency and structural optimization. A 20 Å vacuum layer is used to simulate the isolated sheet. The Brillouin zone integration is represented by the Monkhorst–Pack k-point scheme^[23] with 15 × 15 × 1 grid mesh. All the lattice constants and atom coordinates are optimized until the convergence of the force on each atom is less than 10⁻⁵ Ry/bohr. The SOC is included in the self-consistent calculations of electronic structure. Phonon dispersion is obtained by lattice dynamic calculations performed using density functional perturbation theory^[24] within linear response approach and by using the small displacement method^[25] for antimonene and hydrogenated antimonene, respectively. First-principles MD simulation is performed with a canonical (NVT) ensemble. The simulation time step is 1 fs and the simulation time is 1 ps. The 4×4 supercell containing 64 atoms is equilibrated at 300 K. The energy cutoff of the plane waves is set to 40 Ry in MD simulation and for nanoribbon.

Figure 1 shows the optimized crystal structures of pristine antimonene, fully hydrogenated antimonene, and semi-hydrogenated antimonene with the Sb–Sb bond length and buckling height. The key structural parameters are summarized in Table 1. We first check the equilibrium configuration of pristine antimonene. The calculated lattice constant, Sb–Sb bond length, and bond angle are 4.11 Å, 2.88 Å, and 91×, respectively, which agrees well with the previous work.^[9] As can be seen, pristine antimonene has a buckled honeycomb-like structure with a buckling height of 1.64 Å, which is mainly attributed to the mixing of sp² and sp³ hybridizations. After semi-hydrogenation, the buckling height decreases to 0.91 Å and the corresponding bond angle increases to 110.75°. Moreover, the buckling height of fully hydrogenated antimonene is dramatically decreased to 0.08 Å and results in the almost qusi-planar configurations with the bond angle of approximately 120°, indicating that a bonding is nearly an ideal sp² character. The Sb–H bond is 1.723 Å and 1.726 Å for semi-hydrogenated and fully hydrogenated antimonene, respectively, which reveals that hydrogen atoms are chemically absorbed in antimonene sheet. From our calculations, both the semi-hydrogenated and fully hydrogenated antimonene are nonmagnetic, though other semi-hydrogenated analogues of antimonene have been reported to be ferromagnetic.^[15,26,27]

Fig. 1.

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	Fig. 1. Top view (left) and side view (right) of optimized (a) pristine antimonene, (b) fully hydrogenated antimonene, and (c) semi-hydrogenated antimonene.

Table 1.

Table 1.

Table 1. Structural parameters calculated for pristine antimonene, fully hydrogenated antimonene, and semi-hydrogenated antimonene. Lattice constants a, buckling height Δ, bond angle θ, Sb–Sb bond length lSb−Sb, and Sb–H bond length lSb−H are given. . a/Å Δ/Å θ/(°) lSb−Sb/Å lSb−H/Å Sb 4.11 1.64 91.00 2.88 – FH-Sb 5.27 0.08 119.92 3.04 1.723 SH-Sb 4.83 0.91 110.75 2.93 1.726

Table 1. Structural parameters calculated for pristine antimonene, fully hydrogenated antimonene, and semi-hydrogenated antimonene. Lattice constants a, buckling height Δ, bond angle θ, Sb–Sb bond length lSb−Sb, and Sb–H bond length lSb−H are given. .

To verify the structural stability of pristine antimonene and hydrogenated antimonene, we perform phonon dispersion calculations. Figures 2(a) and 2(b) show the phonon dispersion along the highly symmetric points in the Brillouin zone of pristine antimonene and FH antimonene. Both the phonon spectra do not have imaginary frequencies, which means they own high stability. Moreover, we carry out first-principles MD simulations in canonical ensemble to examine the thermal stability of the FH antimonene at room temperature. A 4×4 supercell containing 64 atoms is used and MD simulation is performed at T = 300 K. Figure 2(c) shows the snapshot of FH antimonene taken at 1 ps. It can be clearly seen that the framework of FH antimonene is well kept as its initial equilibrium structure at T = 300 K. As we know, free-standing antimonene has been obtained in the experiment.^[28] Our results indicate that FH antimonene has highly dynamic stability even at room temperature, and could also be synthesized in the experiment in the future.

Fig. 2.

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	Fig. 2. Phonon band dispersions of (a) pristine antimonene and (b) FH antimonene. (c) Snapshot of FH antimonene structure in MD simulation at 300 K after 1 ps.

Antimonene is a semiconductor with an indirect band gap of 1.24 eV in our calculations. The band structure with and without SOC and the corresponding total density of states (TDOS) and projected density of states (PDOS) of FH and SH antimonene are presented in Fig. 3. For FH antimonene without SOC, it is found that two energy bands cross linearly at the K point, forming an obvious Dirac cone that lies exactly at the Fermi level. The linear dispersion indicates that the carriers in FH antimonene are massless Dirac fermion. According to linear spectrum E = ℏv_Fk, Fermi velocities v_F of FH antimonene is calculated to be in the order of 10⁶ m/s, indicating an excellent electronic transport feature. A sizeable band gap of 425 meV opens up at Dirac cone when the SOC is turned on. Thus, FH antimonene is a quantum spin Hall (QSH) insulator, which was first proposed by Kane and Mele in graphene.^[29] Because the space inversion symmetry is present in FH antimonene, the Z₂ invariant can be calculated following the parity method proposed by Fu and Kane.^[30] We find the Z₂ of FH antimonene is 1, indicating that it is a QSH insulator, which is similar to some other systems.^[31,32] While for SH antimonene, it exhibits a typical metallic character with a band across the Fermi level. In order to analyze the origin of Dirac cone in FH antimonene, the corresponding TDOS and PDOS are calculated. It is evident that the Dirac cone originates from the Sb-p orbital. As a matter of fact, the Sb atom has five valence electrons. It is assumed that three of them form the covalent σ bonds with three Sb atoms, while another one is saturated by hydrogen atom, leaving an extra unbonded electron. Obviously, this yields a graphene-like structure which only has sp² hybridization. This can be further verified by projecting the component of bands of FH antimonene. From Fig. 4, it can be seen that Dirac cone mainly comes from Sb-p_x,y orbitals, as illustrated by the size of circles near the Fermi level. In this case, it is the Sb-p_x,y orbitals that form σ bonds between Sb–Sb atoms, demonstrating an in-plane Dirac cone feature. Such Dirac states composed of p_x,y orbitals are refered to as σ-type Dirac cone, which has been reported in several 2D systems including fluoridated tin films and functionalized germanene.^[33,34] From Fig. 3(b), in the energy region (−1,1) eV, the contribution to TDOS mainly comes from p obital of Sb atom, indicating that the conduction band is mainly attributed to p orbital of Sb atom.

Fig. 3.

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	Fig. 3. Band structure with and without SOC and the corresponding TDOS and PDOS of (a) FH and (b) SH antimonene.

Fig. 4.

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	Fig. 4. Projected band structure of FH antimonene with contribution from s, px+py, and pz orbitals represented by red, green, and blue dots, respectively.

One of the prominent features of QSH insulators is the existence of gapless edge states that are helical with the spin-momentum locked. In order to explicitly demonstrate the edge states for FH antimonene, a zigzag nanoribbon (ZNR) with space inversion symmetry is constructed with the edges passivated by hydrogen atoms, as shown in Fig. 5(a). For avoiding interaction between the edge states, FH antimonene ZNR with width of N = 7 (3.24 nm) is selected, where N is classified by the number of zigzag chains across the ribbon width. The calculated bandstructure of FH antimonene ZNR is presented in Fig. 5(b). We can clearly see one pair of helical edge states cross at the X point, exhibiting the topological nontrivial property. Figure 5(c) shows the localized density of states (LDOS) plots of ZNR of FH antimonene. As expected, ZNR of FH antimonene are metallic and the density of states (DOS) near the Fermi level is mainly attributed to edge atoms. The charge density distribution of edge states near the Fermi level is depicted in Fig. 5(d), which clearly shows that they are localized along the edge of the ribbon. All the above results consistently indicate that FH antimonene is a QSH insulator.

Fig. 5.

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	Fig. 5. (a) Top view of zigzag nanoribbon of FH antimonene with width of N = 7 (3.24 nm). (b) Band structure of ZNR for FH antimonene with (red) and without (blue) SOC. (c) The LDOS plots of ZNR. (d) Charge density distribuion in real space of the edge state near Fermi level.

To see what would happen to Dirac cone in FH antimonene when the in-plane tensile strain is applied, we investigate the structural and electronic properties of FH antimonene under a biaxial strain. Here, a biaxial strain is defined as ε = (a−a₀)/a₀, where a and a₀ are the lattice constants of the strained and the equilibrium unit, respectively. The band structure of FH antimonene with and without SOC under different strains are shown in Fig. 6. We can see that Dirac cone in FH antimonene without SOC still exits even under 30% biaxial strain. And in all cases, band gap opens at Dirac cone when SOC is turned on. It means that FH antimonene as a QSH insulator is robust to tensile strain, which provides a good reference for the design of future nanoelectronic devices.

Fig. 6.

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	Fig. 6. Band structure of FH antimonene without (blue) and with (red) SOC under different biaxial strain.

In summary, we have explored the hydrogenated antimonene by first-principles calculations. FH antimonene is a QSH insulator with a band gap of 425 meV. Moreover, FH antimonene has high dynamic stability even at room temperature, indicating that it could be obtained in experiments. We have revealed that Dirac cone in FH antimonene is related to Sb-p_x,y orbitals, which is robust to tensile strain. SH antimonene is found to be a non-magnetic metal. We expect the experimental realization of FH antimonene and its great potential in next-generation high-performance devices.