Stimulated by the fascinating properties of graphene,^[1] great efforts have been devoted to discovering and synthesizing more two-dimensional (2D) materials.^[2–8] Compared to group-VI transition metal dichalcogenides (TMDs) (especially MoS₂ and WS₂), platinum dichalcogenides (PtS₂, PtSe₂, and PtTe₂), as one of the group-X TMDs, are still in their infancy.^[9–11] Experimental research of few layered PtS₂ and monolayer PtSe₂ has made great progress,^[12–16] and several novel physical phenomena have also been found in bulked PtTe₂.^[17,18] However, so far there has been no available experimental data about monolayer PtTe₂. Despite the sporadic calculation reports on binary-phased Pt-Te nanosheets,^[19,20] systematical theoretical investigations and potential applications for platinum and tellurium binary monolayer are still lacking and necessary.

To extend 2D materials’ potential and to widen their applications, an advanced method is engineering pristine structures at atomic scales.^[21–24] In fact, engineering surface atoms is a promising way to design catalysts for hydrogen evolution reaction (HER) in TMDs.^[25–31] Except for the catalytic performance at the edges,^[32,33] an inert basal plane of monolayer MoS₂ could further be used as HER catalysis by introducing sulfur vacancies or strain.^[34,35] Vacancies in 2D TMDs are ubiquitous and play crucial roles in understanding electronic, optical, and catalytic properties and tailoring them for desirable applications.^[36,37] Bulk PtTe₂ can be transformed from a chemically inert material into a catalyst in stable adsorption of hydroxyl groups after the introduction of defects and surface functionalization,^[38] while the atomic level functionalization of PtTe₂ monolayer has not yet been reported.

In this paper, based on density functional theory (DFT) calculations, we screened the structural and electronic properties of platinum and tellurium binary structured nanosheets systematically, and found a stable structured 1T-PtTe₂ monolayer, namely Pt₄Te₇. Pristine 1T-PtTe₂ monolayer is an indirect band semiconductor with a gap of 0.67 eV. In contrast, Pt₄Te₇ monolayer is a mini-gap semiconductor, whose bandgap is only 28 meV. Its thermal and dynamical stability has also been confirmed by formation energy, ab initio molecular dynamics and phonon dispersion analysis. The electronic structure of Pt₄Te₇ makes it excellent catalytic performance for HER distinguished from its pristine plane 1T-PtTe₂ monolayer. The Gibbs free energy, a widely used descriptor for catalytic activity, is less than 0.07 eV for Pt₄Te₇, which is better than the best cathode material for HER, Pt bulk surfaces (–0.09 eV).^[39] The stable void-containing structured 1T-PtTe₂ monolayers predicted in this study could be a benefit for searching other functionalized TMD materials.

Density functional theory (DFT) calculations were carried out using the projector-augmented wave approach (PAW)^[40] and the Perdew–Burke–Ernzerhof (PBE) developed exchange-correlation functional,^[41] as implemented in the VASP.^[42] The band structure calculation of Pt₄Te₇ is employed Heyd–Scuseria–Ernzerhof (HSE) hybrid functional. The cutoff energy was chosen at 500 eV, and the Brillouin zone was sampled using k-points of 7 × 7 × 1. The convergence thresholds for energy and atomic forces were set as 1 × 10^–5 eV and 0.01 eV/Å, respectively. The distance of vacuum space was set to larger than 20 Å. The phonon spectrum was computed with density functional perturbation theory (DFPT)^[43] and post-treated by Phonopy code.^[44] Molecular dynamic simulations were performed using the (4 × 4) PtTe₂ supercell and the NVT ensemble, and lasted for 10 ps with a time steps of 1.0 fs, which was controlled by the Nosé–Hoover method.^[45]

It is reported that bulk and layered PtTe₂ is stable in the octahedral 1T structure.^[18] Similar to other TMD materials, the electronic properties of PtTe₂ are also thickness dependent.^[10,11] Bulk 1T-PtTe₂ is semi-metallic, and monolayer PtTe₂ exhibits an indirect semiconducting feature with bandgap of 0.67 eV. The lattice parameters of 1T PtTe₂ were optimized to be a = b = 4.0 Å. We modified the monolayer structure of PtTe₂ by introducing voids at the atomic scale.

Different types of void-containing 1T-PtTe₂ monolayers are firstly investigated. A 2 × 2 supercell is selected for structural modification at atomic level. According to the number and location of missing Te atoms, we investigate four different structured monolayers as shown in Fig. 1. In one case, one Te atom is removed. The stoichiometry is Pt₄Te₇ (as shown in Fig. 1(a)). In the other three cases, one Te atom is removed from the first layer and one Te atom is removed from the third layer. The three structures are named as α-Pt₄Te₆, β-Pt₄Te₆ and γ-Pt₄Te₆ (Figs. 1(b)–1(d)). The optimized lattice constants of Pt₄Te₇ monolayer are a = b = 7.8 Å at the PBE level, which is slightly smaller than that of the perfect 1T-PtTe₂ monolayer (2a = 2b = 8.0 Å). The optimized lattice parameters of the other three Pt₄Te₆ are 7.7 Å, 7.8 Å, and 8.0 Å, respectively.

Fig. 1.

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Fig. 1. Atomic structures of void-containing 1T-PtTe2 monolayer. (a) Top and side view of Pt4Te7, in which one Te atom in the first atomic layer is removed in a 2 × 2 supercell, making the first layer looks like a Kagome pattern. (b) Top and side view of α-Pt4Te6, in which one Te atom from the first layer and one nearest-neighbor Te atom from the third layer are removed in a supercell. (c) Top and side view of β-Pt4Te6, in which two Te atoms from the first layer are removed in a supercell. (d) Top and side view of γ-Pt4Te6, in which one Te atom from the first layer and one next nearest-neighboring Te atom from the third layer are removed in a supercell. The supercell is shown in a black box. The Te atoms in the first and third atomic layers are represented by light orange and dark orange, respectively. The Pt atoms in the second atomic layer are represented by blue. For clarity, the atoms in the first atomic layer magnified, while the side view only shows the nearby atoms containing voids.

The stability of the structured 1T-PtTe₂ monolayers is checked by calculating the formation energy which indicates the energy difference during the formation of the 2D material from its constituent elements at 0 K and 0 atm. The equation for the energy changes of formation of the structured PtTe₂ monolayer is

Fig. 2.

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Fig. 2. Stability of void-containing 1T-PtTe2 monolayer. (a) Formation energy of void-containing 1T-PtTe2 monolayer. The black square indicates the formation energy of bulk structures and are connected by blue lines. The bulk Pt–Te binary has multiple structures,[46] chemical components from left to right are Pt, PtTe, Pt3Te4, Pt2Te3, PtTe2, Te, respectively. The orange triangles represent formation energies of 2D structures. (b)–(c) Phonon dispersion of monolayer Pt4Te7 and α-Pt4Te6 along the high-symmetry directions of the Brillouin zone. (d) Snapshots of the equilibrium structure of Pt4Te7 monolayer at 400 K at the end of 10 ps first-principles molecular dynamics simulation.

The kinetic stability of these structured 1T-PtTe₂ monolayers is further studied by checking the existence of imaginary frequency in the phonon dispersion, which is widely used to test the structural stability.^[50] For Pt₄Te₇ monolayer, as shown in Fig. 2(b), the absence of imaginary modes in the entire Brillouin zone confirms its dynamical stabilities. For the Pt₄Te₆ monolayer, there are imaginary frequencies for β- and γ-Pt₄Te₆, indicating that these two structures are not stable. For α-Pt₄Te₆, the phonon dispersion is shown in Fig. 2(c). There is no imaginary frequency indicating its kinetic stability. Through the verification of the stability, we can obtain two stable novel structured monolayer materials, namely, Pt₄Te₇ and α-Pt₄Te₆.

Moreover, we carried out first-principles molecular dynamics simulations to check the structural stability at finite temperature (400 K). Figure 2(d) is a snapshot for a 4 × 4 Pt₄Te₇ supercell after 10 ps MD run. The structure remains intact throughout the whole MD run, indicating that monolayer Pt₄Te₇ is thermodynamically stable. On the other hand, α-Pt₄Te₆ is screened out because the structure becomes disorder in the MD simulation.

After confirming the stability of Pt₄Te₇, we explored its electronic properties. As shown in Fig. 3(a), Pt₄Te₇ monolayer exhibits semiconductor character with a mini-gap of 28 meV. This nearly metallic feature may exhibit feasible physical properties in electrode candidate materials.

Fig. 3.

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	Fig. 3. Energy band structures and HER catalytic performance of Pt4Te7. (a) The energy band structure of monolayer Pt4Te7, which show a band gap of 28 meV at HSE06 level. The inset shows the Brillouin zone with high-symmetry points. (b) The Gibbs free-energy profile of HER for monolayer Pt4Te7.

Therefore, we investigate the hydrogen evolution reaction (HER) catalytic performance of monolayer Pt₄Te₇. For HER catalytic performance, Δ G_H is known to scale with activation energies and has been successfully used as a descriptor for correlating theoretical predications with experimental measurements of catalytic activity for various systems.^[26] For the pristine monolayer 1T-PtTe₂, Δ G_H is about 1 eV (Fig. 3(b)), indicating that the monolayer 1T-PtTe₂ is inert for HER. When periodic Te atom vacancies are introduced (i.e., the structured monolayer Pt₄Te₇), the Δ G_H decreases to 0.06 eV. We attribute this significant improvement to the small bandgap of Pt₄Te₇. As already demonstrated in other TMD materials,^[34] such as MoS₂, the improvement of HER catalytic performance can be achieved by the semiconducting-to-metallic transition. Compared to the pristine PtTe₂ which has a bandgap of 0.5 eV, the band gap of Pt₄Te₇ monolayer is only 28 meV, which is very closely metallic.

In summary, we have modified the 1T phase monolayer PtTe₂ at the atomic level and found a structured void-containing monolayer, Pt₄Te₇, based on comprehensive DFT calculations. According to our results, Pt₄Te₇ is a stable 2D monolayer material which is verified by the calculation of formation energy, phonon dispersion and ab initio molecular dynamics simulations. This void-containing Pt₄Te₇ is predicted to have excellent HER catalytic performance due to the exposure of Pt atoms in the sandwiched structure. These findings open new perspectives for the functionalization of 2D TMD materials at the atomic level.