二维PtTe2系列材料的金属铁电性研究进展 - 中国科学院物理研究所.pdf

RESEARCH ARTICLE Large Spin Hall Conductivity and Excellent Hydrogen Evolution Reaction Activity in Unconventional PtTe1.75 Monolayer Dexi Shao1,2, Junze Deng1,3, Haohao Sheng1,3, Ruihan Zhang1,3, Hongming Weng1,3, Zhong Fang1,3, Xing-Qiu Chen4,5, Yan Sun4,5*, and Zhijun Wang1,3* 1 *Address correspondence to: sunyan@imr.ac.cn (Y.S.); wzj@iphy.ac.cn (Z.W.) Two-dimensional (2D) materials have gained lots of attention due to the potential applications. In this work, we propose that based on first-principles calculations, the (2 × 2) patterned PtTe2 monolayer with kagome lattice formed by the well-ordered Te vacancy (PtTe1.75) hosts large and tunable spin Hall conductivity (SHC) and excellent hydrogen evolution reaction (HER) activity. The unconventional nature relies on the A1 @ 1b band representation of the highest valence band without spin–orbit coupling (SOC). The large SHC comes from the Rashba SOC in the noncentrosymmetric structure induced by the Te vacancy. Even though it has a metallic SOC band structure, the ℤ2 invariant is well defined because of the existence of the direct bandgap and is computed to be nontrivial. The calculated ℏ SHC is as large as 1.25 × 103 e (Ω cm)−1 at the Fermi level (EF). By tuning the chemical potential from ℏ EF − 0.3 to EF + 0.3 eV, it varies rapidly and monotonically from −1.2 × 103 to 3.1 × 103 (Ω cm)−1. e In addition, we also find that the Te vacancy in the patterned monolayer can induce excellent HER activity. Our results not only offer a new idea to search 2D materials with large SHC, i.e., by introducing inversion–symmetry breaking vacancies in large SOC systems, but also provide a feasible system with tunable SHC (by applying gate voltage) and excellent HER activity. Introduction In the past decade, many topological semimetals with various quasiparticle dispersions and fascinating properties have been proposed [1–5]. The layered noble transition metal dichalcogenide PtTe2 is extraordinary with heavily tilted type-II Dirac fermion [6]. It hosts unique properties, such as topological nontrivial band structure [6,7], ultrahigh electrical conductivity [8,9], and robustness of the remaining semimetal phase even down to just 2 triatomic layers [10,11]. Soon after, many PtTe2 derivatives have been proposed, including the monolayer, multilayer, doping, vacancy, heterojunction structures, and so on. For example, the Ir-doped PtTe2 (i.e., Pt1 − xIrxTe2) has realized the Fermi level (EF) tunability and superconductivity, which opens up a new route for the investigation of Dirac physics and topological superconductivity [12–14]. More recently, PtTe2based broadband photodetectors and image sensors have been fabricated, demonstrating tremendous potential application value in various photoelectric devices [15–17]. Very recently, Shao et al. 2023 | https://doi.org/10.34133/research.0042 Submitted 6 September 2022 Accepted 16 December 2022 Published 24 February 2023 Copyright © 2023 Dexi Shao et al. Exclusive Licensee Science and Technology Review Publishing House. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License (CC BY 4.0). the patterned monolayer with kagome lattice formed by one Te vacancy in a 2 × 2 supercell has been grown successfully [18], whose band topology and potential properties are unknown. The study of PtTe2 derivatives can not only reveal novel condensed matter physics but also facilitate the versatile development in device physics. In this work, we theoretically propose that the recently synthesized patterned PtTe2 monolayer with the Te vacancy (i.e., PtTe1.75) hosts large spin Hall conductivity (SHC) because of the Rashba spin–orbit coupling (SOC), where the Te vacancy breaks inversion symmetry ( ). The momentum offset and strength of the Rashba SOC are estimated, k0 = 0.12 Å−1 and αR = 0.8112 eV Å. The momentum offset k0 is very large and comparable with the largest one reported in the Bi/Ag(111) surface alloy in literature [19], which induces visible Rashba band splitting. Using the Kubo formula approach at the clean limit, we find the Rashba SOC will induce large SHC, as large as 1.25 × 103 ℏe (Ω cm)−1 at EF. Furthermore, the SHC changes rapidly and monotonically as the chemical potential evolving 1 Downloaded from https://spj.science.org on June 15, 2023 Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. 2Department of Physics, Hangzhou Normal University, Hangzhou 311121, China. 3University of Chinese Academy of Sciences, Beijing 100049, China. 4Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Science, Shenyang 110016, Liaoning, China. 5School of Materials Science and Engineering, University of Science and Technology of China, Hefei, China. Citation: Shao D, Deng J, Sheng H, Zhang R, Weng H, Fang Z, Chen XQ, Sun Y, Wang Z. Large Spin Hall Conductivity and Excellent Hydrogen Evolution Reaction Activity in Unconventional PtTe1.75 Monolayer. Research 2023;6:Article 0042. https://doi.org/10.34133/ research.0042 in a wide range (E − E F ∈ [−0.3,0.3] eV), which benefits to the potential applications in spintronics. In the end, the variation of the Gibbs free energy for hydrogen adsorption progress is considered, which indicates that the PtTe1.75 mono­ layer exhibit an excellent hydrogen evolution reaction (HER) activity. Results and Discussion Electronic band structures Rashba SOC at Γ Because the Te vacancy breaks  in the patterned PtTe2 monolayer, the Rashba SOC band splitting will appear inevitably. As the projected band structures shown in Fig. 3C, the Te-pz dominated parabolic bands splits clearly near Γ. The [ℏ(k±k0 )]2 splitting bands near Γ can be well fitted by E = with 2M M = 2.02659 me (me denoting the free electronic mass) and k0 = 0.12 Å−1 (the momentum offset), as the 2 blue parabolas shown in Fig. 3C. The coupling strength of the Rashba SOC can be derived 2E ℏ2 k as 𝛼 R = k R = M 0 = 0.81 eVÅ. The estimated k0 is super large 0 in Fig. 3C, as large as the the Bi/Ag(111) surface alloy [19]. Large SHC effect To explore the intrinsic SHC in the patterned PtTe2 monolayer, the Wannier-based TB model under bases of the Te-p and Pt-d orbitals is extracted from the DFT calculations. As shown in 1 Te: bottom Te-px,y Te-pz Te: top Energy (eV) 0.5 Pt 0 –0.5 –1 Fig. 1. (Color online) (A)Crystal structure of the patterned PtTe2 monolayer (PtTe1.75). The pristine PtTe2 monolayer system in the kagome lattice contains 2 Te layers, with 4 Te atoms in both the bottom layer and the top layer of the (2 × 2) supercell. In addition, the PtTe1.75 system comes from the patterned PtTe2 monolayer with a well-ordered Te vacancy (schematized by “×” at the 1b Wyckoff site) at the top layer of the (2 × 2) supercell. Thus, there are 3 Te atoms (denoted by green ball) occupying the top layer, while there are 4 Te atoms (denoted by blue ball) occupying the bottom layer in the PtTe1.75 system. (B) The corresponding 2D bulk BZ and 1-dimensional projected BZ orthogonal to the (01) edge. Band structures of the PtTe1.75 system (C) without and (D) with SOC. The light green, blue, red, and gray zones in (D) indicate that there exist direct bandgaps between the corresponding adjacent bands. Thus, the time reversal ℤ2 can be defined and calculated to be 1, 1, 1, and 0 with (Ne − 4), (Ne − 2), Ne, and (Ne + 2) occupied bands. Shao et al. 2023 | https://doi.org/10.34133/research.0042 2 Downloaded from https://spj.science.org on June 15, 2023 The band structures of PtTe1.75 monolayer without and with SOC are presented in Fig. 1C and D, respectively. Comparing them, we notice that the band dispersions change dramatically. Each band splits into two nondegenerate bands in Fig. 1D. It is the Te vacancy in the monolayer that breaks  (and   ), inducing the visible Rashba band splitting. From the orbital-­ resolved band structures in Fig. 1C, we find that there exist visible band hybridizations between Te-px,y and Te-pz orbitals around EF. Using IRVSP [20], the irreducible representations of the high-­symmetry k points are calculated and labeled in Fig. 2A. Accordingly, the band representation (BR) analyses indicate that the 2 conduction bands belong to E @ 1b BR, while the highest valence band belongs to A1 @ 1b BR, suggesting the unconventional nature of the obstructed atomic limit [21–24]. SOC often plays important roles to engineering topological states, such as quantum spin Hall effect in graphene [25,26] and Ta2M3Te5 (M = Pd,Ni) compounds [27,28], 3D large-SOC-gap topological insulator in Bi2Se3 and NaCaBi families [29,30], and so on. In PtTe1.75, once including SOC, the Te-pz dominated band around Γ splits because of the Rashba SOC induced by the Te vacancy, as shown in Fig. 1D. To get more insights in the nontrivial band topology and Rashba SOC band splitting, we have explored how the band structure evolves with the increasing strength of SOC (denoted by λ) gradually in Fig. 2. We notice that the nontrivial band topology for Ne − 4 occupied bands is due to the SOC (can be infinitesimal)-induced bandgap at Γ without involving band inversion [31,32]. In addition, the nontrivial topologies for Ne − 2 and Ne occupied bands are due to a gap closing and reopening process as varing λ. Taking Ne − 2 occupied bands as an example, the critical Weyl band crossing between the (Ne − 2)th band and the (Ne − 1)th band appears on the M–K line with λ = 0.8, as highlighted by a red dashed ring in Fig. 2E. Similarly, the critical Weyl point (WP) between the Neth band and the (Ne + 1)th band appears on the K–Γ line with λ = 0.98, as the right inset shown in Fig. 2F. However, it becomes topologically trivial for Ne + 2 occupied bands because there are 2 nontrivial gap openings around both Γ and M. Because of the existence of R3z and M100 symmetries, the critical WPs abovementioned appear in sextuplet in the first BZ, as shown in Fig. 3A and B. Similar with WPs in 3D Weyl semimetals [33–36], these critical WPs also conform to the codimensional analysis. This can be deduced as follows. First, both the M–K (ky = π) and K–Γ (ky = 0) lines are M100 ∗ T invariant. In the 2-band k · p Hamiltonian depicting the Weyl band crossing, the combined antiunitary symmetry with [TM100]2 = 1 will reduce the number of the independent σ matrices in the k · p Hamiltonian to 2. Second, the kx value in both the TM100 invariant lines and the SOC strength λ are 2 tunable parameters to search a WP. Thus, the number of the independent σ matrices in the k · p Hamiltonian equals to the number of the tunable parameters, which indicates that a WP is stable in the 2D parameter space {kx, λ}. In other words, a topological phase transition can happen by tuning λ in the M100 ∗ T invariant lines. Through the gap closing and reopening process in the evolution, it becomes topologically nontrivial for Ne (Ne − 2) occupied bands. As a result, we can expect the existence of the helical edge states of the patterned PtTe2 monolayer. The edge spectra are presented in Fig. S3B and D (in Section C of the SM). Fig. S2A and B, the fitted Wannier-based TB bands can reproduce the DFT bands perfectly. On the basis of this Wannierbased TB model, we have employed the Kubo formula approach at the clean limit [37–41] to calculate the SHC of the patterned PtTe2 monolayer, e∑ dk f (k)Ω𝛾𝛼𝛽;n (k), 𝜎 𝛾𝛼𝛽 = ℏ n �BZ (2𝜋)2 n ⟨ ⟩⟨ ⟩ 𝛾 ukn |�J 𝛼 |ukm ukm |� v 𝛽 |ukn ∑ Ω𝛾𝛼𝛽;n (k) = 2iℏ2 , (1) ( )2 n m m≠n 𝜀 k − 𝜀k changes rapidly and monotonically in a wide energy window ranging from EF − 0.3 eV to EF + 0.3 eV. At E − EF =  −0.3 eV, the SHC changes the sign and becomes −1.2 × 103 ℏ (Ω cm)−1, e while at E − EF = 0.3 eV, the SHC nearly triples and becomes 3.1 × 103 ℏe (Ω cm)−1. In general, the chemical potential can be tuned by applying gate voltage or introducing chemical doping at the vacancy. As shown in Fig. S5A to C, we can find that the absorption of Tl/Pb at the vacancy behaves as electron dopings, which will increase the EF with negligible changes in the band structure. We think our results will be benefitial to the potential applications in spintronics. { } 𝛾 v 𝛼 ,̂s𝛾 is the spin current operator, with ̂s denoting where ̂J 𝛼 = 12 ̂ Excellent HER activity � According to the new principle for active catalytic sites [23,42,43], the obstructed bulk states in the patterned monolayer (which can be seen as the limit of obstructed surface states) may bring measured catalytic activity. By exposing undercoordinated atoms as the active sites, vacancy engineering is an important strategy to optimize the HER performance of the basal planes in 2D materials [44,45]. As the acidic HER of the PtTe1.75 is schematized in Fig. 4A, protons (H+) in solution generate adsorbed H atoms (H∗) as intermediate and then the H atoms on the catalyst surface are desorbed to produce hydrogen (H2), which can be formulized as 1 H + + e− + ∗ → H∗ → H2 + ∗ . 2 (2) Fig. 2. (Color online) Band structures of PtTe1.75 monolayer with the strength of SOC (A) λ = 0 (without SOC), (B) λ = 0.2, (C) λ = 0.4, (D) λ = 0.6, (E) λ = 0.8, and (F) λ = 1.0 (with actual SOC). For the case without SOC shown in (A), the 2 conduction bands schematized by 2 blue lines belong to E @ 1b BR, while the highest valence band schematized by the red line belongs to A1 @ 1b BR. There exists a WP along the M–K line below EF when λ = 0.8. Bands near EF undergoes a gap closing and reopening progress when the strength of SOC evolves from 0.0 to 1.0, which gives a topological nontrivial bandgap with SOC (λ = 1.0). The critical transition occurs at λ = 0.98 (right inset in the λ = 1.0 panel), which gives another WP along the K–Γ line. Shao et al. 2023 | https://doi.org/10.34133/research.0042 3 Downloaded from https://spj.science.org on June 15, 2023 𝜕H the spin operator, � denoting the velocity operator, and v 𝛼 = ℏ𝜕k 𝛼 n α, β, γ = {x, y, z}. fn(k) is the Fermi–Dirac distribution. � uk ⟩ and n 𝜀k are the eigenvectors and eigenvalues of the TB Hamiltonian, ∑ x respectively. The distributions of N (k) ≡ N n=1 Ωyz;n (k) for N = Ne − 1 and Ne occupied bands are presented in Fig. 3D and E, respectively. As the calculated SHC as a function of the chemical potential shown in Fig. 3G, one can find that the calculated SHC is as large as 1.25 × 103 ℏe (Ω cm)−1 at E = EF. The corresponding distribution at E = EF is presented in Fig. 3F, which indicates that the large contribution of the SHC at K comes from the SOC band splitting. In addition, the SHC Fig. 3. (Color online) The 6 symmetry-related (R3z and M100) WPs formed by band crossings (A) between the (Ne − 2)th band and the (Ne − 1)th band with λ = 0.8 as well as (B) the Neth band and the (Ne + 1)th band with λ = 0.98. (C) The Te-pz projected band structures with SOC, and the 2 blue lines depict the parabolically asymptotic behavior of the ( ) ( ) Rashba SOC induced splitting bands near the Γ point. The distribution of (D) Ne −1 k and (E) Ne k in the 2D BZ. (F) The distribution of 𝜎 zxy at EF. (G) The calculated SHC vs. the chemical potential (ranging from EF − 0.5 eV to EF + 0.5 eV). Conclusion We find that the PtTe1.75 not only hosts the unique band structure with 3 lower-energy bands belonging to (A1 + E) @ 1b Shao et al. 2023 | https://doi.org/10.34133/research.0042 BRs at an empty site but also exhibits large and tunable SHC and excellent HER performance. First, we have calculated the time reversal invariant ℤ2, which indicates the 2D topological insulator nature in the patterned PtTe2 monolayer. We demonstrate that the topological phase can be deduced by a gap closing and reopening process with the evolution of the strength of SOC from λ = 0 to λ = 1.0. The critical phase transition occurs at λ = 0.98, which gives a sextuplet of critical WPs. Second, the Te vacancy breaks  and induces Rashba SOC band splitting. The estimated momentum offset is super large with k0 = 0.12 Å−1. Third, we find that the SHC is as large as 1.25 × 103 ℏe (Ω cm)−1 at E F. Furthermore, the SHC varies quickly and almost monotonically from −1.2 to 3.1 × 103 ℏe (Ω cm)−1, indicating that the SHC in the patterned PtTe2 monolayer can be conveniently tuned for various applications. Last, we also find the Te vacancy in the patterned monolayer can induce excellent HER activity. These results not only offer a new idea to search 2D materials with large SHC, i.e., by introducing inversion–symmetry breaking vacancies in large SOC systems, but also provide a feasible system for the potential application in spintronics and HER catalysts. Materials and Methods The pristine PtTe2 crystallizes in the CdI 2-type trigonal (1T) structure with P3m1 space group (SG). It hosts the layered structure stacking along the z axis and can be easily tuned by strain, which indicates that it can be grown under various substrates. The patterned monolayer with kagome lattice formed by one Te vacancy in the 2 × 2 supercell has been successfully grown on the Pt(111) surface [18]. As shown in Fig. 1A, the patterned PtTe2 monolayer contains 2 Te layers: 4 Te atoms (blue balls) in the bottom layer and 3 Te atoms (green balls; with one vacancy schematized by “×” at 1b Wyckoff site) in the top layer. The distance between the bottom and top layers is d0 = 2.7253 Å. The Te vacancy breaks , resulting in a noncentrosymmetrical structure with the p3m1 layer group (LG 69; corresponding to SG P3m1 excluding translational symmetry along the z axis). Thus, the Rashba SOC-induced band splitting is inevitable. The lattice parameters and atomic positions are listed in Table S1 of the Supplementary Materials (SM). 4 Downloaded from https://spj.science.org on June 15, 2023 Here “*” denotes some site on the surface, i.e., a “*” by itself denotes a free site, while H* denotes a hydrogen atom absorbed on the surface. Te vacancy-induced states near EF give PtTe1.75 monolayer larger electrical conductivity than pristine PtTe2 monolayer, which will effectively facilitate electron transfer for HER. We used a 2 × 2 PtTe1.75 supercell to simulate the basal plane. Compared with the fully coordinated Te atoms, H atoms are more likely to be adsorbed near the undercoordinated Pt atoms, just as the most stable and metastable structures shown in Fig. 4B and C. Details of screening stable adsorption sites can be found in the SM. It is well known that the change of Gibbs free energy induced by hydrogen adsorption (ΔGH∗) is an important descriptor of HER activity [46–48], and an ideal catalyst for HER should host a near-zero ΔGH∗, which can effectively maintain the balance between adsorption and desorption steps [47]. As shown in Fig. 4D, unlike the pristine PtTe2 mono­ layer with a large positive ΔGH∗ due to its extremely inert basal plane, the PtTe1.75 monolayer hosts an optimal ΔGH∗ (0.08 eV), which is slightly superior to the benchmark material Pt (ΔGH∗ = −0.09 eV) [46]. Details of the free energy correction can be found in the SM. Here, we noted that the effect of the size on the ΔGH∗ is negligible, which can be deduced from Table S2. Thus, the active Pt sites induced by Te vacancy greatly optimize hydrogen adsorption in the intermediate, which will significantly improve HER performance [49]. According to Nørskov et al. [46], the theoretical exchange current density (i0) as a function of ΔGH∗ is calculated. As shown in Fig. 4E, the PtTe 1.75 monolayer approaches the volcanic peak from the right with i0 = 0.68 mA cm−2, which is comparable to commercial Pt/C catalyst (i0 = 1.2 mA cm−2) [50]. In addition, as shown in Fig. S4A and B, the energy pathways and corresponding energy barriers of the (a) Heyrovsky and (b) Tafel reactions to release hydrogen in HER are exhibited, from which we can find that the Tafel reactions to release hydrogen is preferred. Therefore, Te vacancy can greatly stimulate the catalytic activity of PtTe2 basal plane and produce excellent HER performance. We performed the first-principles calculations based on the density functional theory (DFT) using projector augmented wave method [52,53] implemented in the Vienna ab initio simulation package (VASP) [54,55]. The generalized gradient approximation with exchange–correlation functional of Perdew, Burke, and Ernzerhof for the exchange–correlation functional [56] was adopted. The kinetic energy cutoff was set to 500 eV for the plane wave bases. The thickness of the vacuum layer along z axis was set to >20 Å. The brillouin zone (BZ) was sampled by Γ-centered Monkhorst–Pack method with a 12 × 12 × 1 k-mesh for the 2-dimensional (2D) periodic boundary conditions in the self-­consistent process. The Wilson loop technique [57] was used to calculate the ℤ2 topological invariant. In addition, the electronic structures near EF were doubly checked by the full-potential local-orbital code [58] and fully consistent with those from VASP. To compute SHC, a Wannier-based tight-binding (TB) model under bases of the Te-p and Pt-d orbitals is extracted from the DFT calculations. Acknowledgments Funding: This work was supported by the National Natural Science Foundation of China (grant no. 12204138, no. 11974395, no. 12188101, no. 52188101, and no. 51725103), the Strategic Priority Research Program of Chinese Academy of Sciences Shao et al. 2023 | https://doi.org/10.34133/research.0042 (grant no. XDB33000000), and the Center for Materials Genome. Competing interests: The authors declare that they have no competing interests. Data Availability The datasets used in this article are available from the corresponding author upon request. Supplementary Materials Section A. Lattice parameters of the patterned PtTe2 monolayer with a Te vacancy. Section B. The calculated weak topological invariant Z2. Section C. Topological surface states of the patterned PtTe2 monolayer. Section D. Releasing hydrogen in HER. Section E. Screening adsorption sites and the correction of Gibbs free energy. Section F. Band structures vs. dopping. Table S1. Crystal structures of the patterned PtTe2 monolayer in terms of SG P3m1 (SG 156). Table S2. The Gibbs free energy correction terms of the most thermodynamically stable PtTe1.75 adsorption structures with 5 Downloaded from https://spj.science.org on June 15, 2023 Fig. 4. (Color online) (A) Schematic diagram of HER process on PtTe1.75 monolayer. Top and side views of (B) the most stable (PtTe1.75-I) and (C) metastable (PtTe1.75-II) structures after H atom adsorption. The red ball denotes the absorbed H atom. (D) Variation of the Gibbs free energy for hydrogen adsorption (ΔGH∗) to different compounds. (E) Volcano plot depicting the relationship between exchange current density (i0) and ΔGH∗, in which cases of Pt(111) [46], Rh [46], Pt/C [50], PtTe2 with ordered trigonal Te vacancies (PtTe2-VTe) [44], MoS1.76 [45], and 2H-1T phase boundaries of MoS2 (MoS2-PBs) [51] are also included for comparison. 1 × 1, 2 × 2, 3 × 3, and 4 × 4 supercell, including adsorption energies of hydrogen (ΔEH*), the change of zero-point energy (ΔZPE), enthalpy correction (Δ∫CpdT), entropy correction (ΔTS), and Gibbs free energy (ΔGH*). Fig. S1. (Color online) The calculated weak topological invariant Z2 for (A) 80, (B) 82, (C) 84, and (D) 86 occupied bands, respectively. Fig. S2. (Color online) DFT vs. Wannier bands (A) without SOC and (B) with SOC. Fig. S3. (Color online) The projected edge states along (01) direction (A) without SOC and (B) with SOC in the upper edge. Fig. S4. (Color online) Energy pathways of the (A) Heyrovsky and (B) Tafel reactions on PtTe1.75 monolayer to release hydrogen. Fig. S5. 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