After graphene was discovered (Geim and Novoselov, 2010), it has frequently demonstrated some novel properties due to its very special monolayer structure (Butler et al., 2013; Kim et al., 2015; Xu et al., 2015; Wei et al., 2016; Gao et al., 2017; Zaminpayma et al., 2017; Zhang et al., 2018; Zhou et al., 2018; Sun and Schwingenschlögl, 2021a), which has attracted tremendous investigations to explore the other excellent characteristics and applications of two-dimensional (2D) materials (Li et al., 2014; Li et al., 2019; Li et al., 2021; Vahedi Fakhrabad et al., 2015; Keyte et al., 2019; Xu et al., 2020; Ren et al., 2021a; Ren et al., 2021b; Sun et al., 2021). For instance, biphenylene, a graphene-like material, was prepared, which is metallic, instead of dielectric (Fan et al., 2021). Biphenylene also possesses excellent electronic, mechanical, and catalytic properties (Luo et al., 2021). Two-dimensional MoSi₂N₄ was synthesized by chemical vapor deposition, suggesting a sandwiched structure; the exhibited semiconducting nature was also investigated, with a bandgap of about 1.94 eV (Hong et al., 2020). A novel 2D material of transition metal dichalcogenides (TMDs) has attracted considerable focus (Luo et al., 2019a; Luo et al., 2019b; Dongqi et al., 2021). For example, WSe₂ has been proved to be a semiconductor material with indirect bandgap, high carrier mobility, remarkable optical properties, and the responsivity of the field effect transistor of this material in the visible wavelength range is of 10⁻¹–10⁵A/W (Zhao et al., 2013; Allain and Kis, 2014; Jo et al., 2018). MoSe₂ is a layered material possessing a bandgap of 1.55 eV. It is found that MoSe₂ has strong light absorption capacity and photoelectric conversion efficiency (close to 10%) in the range of visible light and has a great application prospect in photovoltaic devices (Ma et al., 2011; Shi et al., 2013; Liu et al., 2016a). All these remarkable performances of the 2D materials present advanced applications in metal-ion batteries (Sun and Schwingenschlögl, 2020; Sun and Schwingenschlögl, 2021b), photocatalyst (Ong, 2017; Ren et al., 2019; Ren et al., 2021c; Sun et al., 2020; Agarwal et al., 2021), photodiode (Ouyang et al., 2021), light emitting devices (Ren et al., 2021d), etc.

Interestingly, these novel performances of the 2D materials can also be adjusted by suitable methods, such as external strain (Wang et al., 2019a; Shu, 2021; Zhao et al., 2021), electric field (Sun et al., 2017; Cui et al., 2021a), adsorption (Cui et al., 2021b), doping (Cui et al., 2021a), and defect (Sun et al., 2019). Recently, the synthesis of heterostructures demonstrates further properties and applications (Novoselov et al., 2016; Ang and Ang, 2019; Chen et al., 2020; Hidding and Guimarães, 2020). It is worth noting that a 2D heterostructure can be divided into a vertical heterostructure and a lateral heterostructure. The former can be obtained by artificial fixed-point transfer and chemical vapor deposition (CVD), and the latter is obtained by CVD epitaxial growth (Ding et al., 2018; Jiang, 2018). A vertical heterostructure is a structure that connects two or more layered materials through van der Waals (vdW) force, which can induce astonishing performances across the interface. For instance, the carrier mobility of a ZnO/BSe vertical heterostructure is as high as 2538.16 cm²·v⁻¹·s⁻¹, which is higher than that of original ZnO (360.88 cm²·v⁻¹·s⁻¹) and BSe (419.01 cm²·v⁻¹·s⁻¹) (Ren et al., 2020a). The Z-Scheme photocatalytic mechanism was discovered in the MoSe₂/HfS₂ heterostructure and is used as an efficient photocatalyst for water splitting (Wang et al., 2019b). Nevertheless, due to the weak vdW force between layers, the vertical heterostructure will be unstable at high temperature and other extreme conductance; thus, Duan et al. synthesized MoS₂/MoSe₂ and WS₂/WSe₂ lateral heterostructures by using the CVD epitaxial growth method and proved that the lateral heterostructure can be formed with remarkable current rectification behavior (Duan et al., 2014). The MoS₂/WSe₂ lateral heterostructure was studied that the fracture strength was determined by the mechanical properties of MoS₂. When the temperature increases from 50 to 500 K, the fracture strength and strain of MoS₂/WSe₂ vdW heterostructure are reduced by about 35 and 36%, respectively (Qin et al., 2019). More recently, the TMD material with a Janus structure, MoSSe, was successfully prepared (Lu et al., 2017), which exhibits novel electronic and optical properties (Ren et al., 2020b). WSSe with a Janus structure also have unexpected properties (Lou et al., 2021). WSSe with an armchair edge nanotube has strong oxidation ability, resulting in high conversion efficiency of solar hydrogen production (Guo et al., 2020). Considering that both monolayers MoSSe and WSSe have outstanding properties, and the MoSSe/WSSe heterostructure was also recently prepared (Trivedi et al., 2020), the lateral MoSSe/WSSe heterostructure was selected to explore the interesting performances and potential applications.

In this investigation, the Janus MoSSe and WSSe monolayers are selected to construct lateral heterostructures by armchair and zigzag edges as interfaces. The stability of the Janus MoSSe/WSSe heterostructure is addressed by using the molecular dynamics (MD) method. Then, electronic properties of the type-II band alignment of the MoSSe/WSSe heterostructure are obtained using first-principles calculations. Importantly, the structural symmetry and interface edge dependence for the thermal performance are further investigated.

For the first-principles calculations, the simulations were conducted by the Vienna ab initio simulation package (VASP) based on density functional theory (DFT) (Capelle, 2006). The generalized gradient approximation (GGA) and the projector augmented wave potentials (PAW) were used by the Perdew–Burke–Ernzerhof (PBE) functional for the exchange correlation functional (Kresse and Furthmüller, 1996; Perdew et al., 1996; Kresse and Joubert, 1999). The energy cutoff and the Monkhorst–Pack k-point grids were considered to be 550 eV and 17 × 17 × 1, respectively. The thickness of the vacuum energy level was employed by the 25 Å to prevent the interaction of the nearby layers. The studied heterostructures were fully relaxed by the Hellmann−Feynman force smaller than 0.01 eV Å⁻¹ for each atom. Furthermore, the convergence of the energy for the systems was controlled within 1 × 10^–5 eV. The density functional perturbation theory (DFPT) was used to obtain the phonon spectra of the investigated heterostructure by the PHONOPY code (Togo et al., 2008; Togo and Tanaka, 2015).

The MD calculations were performed by the LAMMPS package (Plimpton, 1995) in this work using parameterized Stillinger–Weber potential to demonstrate the covalent interaction between S, Se, Mo, and W atoms (Jiang, 2018). The time step of our MD simulation was set as 1 fs, and Newton’s equations of atomic motion were considered in the velocity Verlet algorithm. First, the studied heterostructure was relaxed for 10 ps under 300 K by the NPT (isothermal and isobaric) ensemble, and then, NVT ensemble was used to further optimize the structure of the system by Nosé–Hoover temperature sustaining 2000 ps. Next, the Janus heterostructure was equilibrated by the NVE (isovolumetric and isoenergetic) (Ren et al., 2020c).

The structure of the lateral MoSSe/WSSe heterostructure is constructed along two interfaces: armchair and zigzag edge. For the MoSSe/WSSe heterostructure with an armchair interface, asymmetric with a Janus structure, S and Se can be arranged on both sides of Mo (or W) atoms and the same layer, namely, arm-1 and arm-2, as shown in Figures 1A,B, respectively. Similarly, the zig-1 and zig-2 are shown in Figures 1C,D, respectively. Besides, the MoSSe and WSSe monolayers are also optimized by the lattice constants of 3.23 and 3.27 Å, respectively. The obtained bond lengths of the Mo–S, Mo–Se, W–S, and W–Se in the optimized monolayered MoSSe and WSSe are 2.41, 2.53, 2.43 and 2.54 Å, respectively, which are agreement with the experimental work, 2.58 and 2.41 Å for Mo–Se and Mo–S, respectively (Lu et al., 2017). Thus, the lattice mismatch of the MoSSe/WSSe heterostructure with armchair and zigzag edges is 3.7 and 2.8%, respectively. Furthermore, the calculated formation energies of arm-1, arm-2, zig-1, and zig-2 MoSSe/WSSe heterostructures are 0.136, 0.095, 0.364, and 0.050 eV, respectively.

To assess the thermal stability of such a lateral MoSSe/WSSe heterostructure, molecular dynamics simulations were employed. After complete relaxation of the lateral MoSSe/WSSe heterostructure at a Nosé–Hoover temperature of 300 K, the structures of arm-1, arm-2, zig-1, and zig-2 lateral MoSSe/WSSe heterostructures are demonstrated in Figures 2A–D, respectively. The whole optimization process took about 4000 ps for the lateral MoSSe/WSSe heterostructure, and one can find that the structures of these heterostructures are still intact. Interestingly, at the interface of the arm-1 and zig-1 of the lateral MoSSe/WSSe heterostructure, a bending phenomenon occurred because of the asymmetric atomic arrangement pattern of the S and Se atoms. In detail, this natural folding phenomenon is also caused by the uneven stress of bonds at the interface.

The projected band structure of arm-1, arm-2, zig-1, and zig-2 lateral MoSSe/WSSe heterostructures is shown in as Figures 3A–D, respectively. It can be seen that arm-1 and arm-2 lateral MoSSe/WSSe heterostructures possess similar band structures with the semiconductor characteristic with a direct bandgap of 1.57 and 1.58 eV, respectively, suggesting the conduction band minimum (CBM) and valence band maximum (VBM) located at K point. The zig-1 and zig-2 lateral MoSSe/WSSe heterostructures also have a direct bandgap of 1.56 and 1.56 eV, respectively, with the CBM and VBM at Γ point. Importantly, the red, blue, cyan, and yellow marks represent the band contributions of the Mo, S, W, and Se atoms, respectively, which show that these four Janus lateral heterostructures possess type-II band alignment and that the CBM and VBM resulted from MoSSe and WSSe layers, respectively. Besides, the obtained bandgaps are comparable with those of the reported MoSSe/WSSe heterostructure (about 1.53 eV) (Li et al., 2017).

The obtained type-II band structure of the lateral MoSSe/WSSe heterostructure provides the ability to separate the photogenerated electrons and holes continuously. As Figure 4 shows, taking the arm-1 MoSSe/WSSe heterostructure as an example, the energy positions are also demonstrated. When the MoSSe/WSSe heterostructure is inspired by light, the photogenerated electrons of the MoSSe and WSSe layers can be stimulated to the conduction band (CB), and the photogenerated holes will result in the valence band (VB). Then, the photogenerated electrons at the CB of the WSSe layer and the photogenerated holes at the VB of the MoSSe layer transfer to the CB of the MoSSe layer and the VB of the WSSe layer by the power of the conduction band offset and valence band offset, named conduction band offset (CBO) and valence band offset (VBO) in Figure 4, respectively. Thus, the separated photogenerated electrons at the CB of the MoSSe layer and holes at the VB of the WSSe layer can induce the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER), respectively, suggesting these four lateral MoSSe/WSSe heterostructures can act as a potential photocatalyst for water splitting. In particular, if the photogenerated electrons at the CB of the MoSSe layer and the photogenerated holes at the VB of the WSSe layer develop recombination, the HER and the OER are induced at the CB of the WSSe layer and the VB of the MoSSe layer, respectively, and the Z-scheme photocatalytic mechanism is promoted (Xu et al., 2018; Ren et al., 2020d).

To investigate the heat conduction properties of the lateral MoSSe/WSSe heterostructure with different symmetries and interface edges, the non-equilibrium molecular dynamics (NEMD) method was adopted. A temperature gradient is constructed with MoSSe and WSSe acting as cold and hot baths, respectively. The schematic diagram of the temperature gradient of these four heterostructures arm-1, arm-2, zig-1, and zig-2 MoSSe/WSSe is shown in Figures 5A–D, respectively, suggesting heat flux flow from the MoSSe layer to the WSSe layer. Besides, NEMD simulations can explain the temperature interaction between atoms. The temperature distribution can also be demonstrated by NEMD calculations across the interface. In MD simulation work Nose–Hoover and Langevin are popular heat baths that can account for different experimental factors (Hu et al., 2020). The Nose–Hoover and Langevin can induce different temperature profiles, and in this NEMD investigation, the temperature jump across the interface of the MoSSe/WSSe heterostructure is critical. Therefore, the Nose–Hoover heat bath was selected. We fixed the ends of the MoSSe and WSSe and set the temperature at 80 and 100 K, respectively. We obtained the time-independent heat flux with enough relaxation time to build a non-equilibrium status. The heat flux (J) was calculated as follows: J = 1 V [ ∑ i N ε i v i + 1 2 ∑ i j ; i ≠ j N ( F i j ⋅ v i ) r i j + 1 6 ∑ i j k , i ≠ j ≠ k N ( F i j k ⋅ v i ) ( r i j + r i k ) ] , (1) where ε i is the energy; v i represents the velocity of an atom i; r _ij is the interatomic distance between atoms i and j; F _ij and F _ijk are two-body and three-body forces, respectively; and V represents the volume of the investigated MoSSe/WSSe heterostructure. Furthermore, the calculated thickness of MoSSe and WSSe is 3.243 and 3.230 Å, respectively.

After obtaining the steady state for the systems, the temperature profile of the lateral MoSSe/WSSe heterostructure with an armchair and zigzag interface edge is demonstrated in Figures 6A,B, respectively. Reflection, transmission, and mode conversion occur by phonons travelling across the interface of the MoSSe/WSSe heterostructure, suggesting a temperature jump, which can further result in interfacial thermal resistance. Linear fitting and extrapolation were explored to calculate a more reasonable temperature jump (Yu and Zhang, 2013). As Figure 6 shows, a significant temperature jump (ΔT) is characterized at the interface of the lateral MoSSe/WSSe heterostructure. Such a temperature jump is also obtained by other reported heterostructures, such as graphene/h-BN (Liu et al., 2016b), phosphorene/graphene (Liu et al., 2018), and MoS₂/WSe₂ (Qin et al., 2019). The heat flux of the arm-1, arm-2, zig-1, zig-2 MoSSe/WSSe heterostructures is calculated as 5.48 × 10⁹, 6.21 × 10⁹, 3.70 × 10⁹, and 4.28 × 10⁹ W m⁻², respectively. Besides, the temperature jump of the arm-1, arm-2, zig-1, and zig-2 MoSSe/WSSe heterostructures is obtained at 18.77, 14.66, 17.43 and 13.67 K, respectively. The interfacial thermal resistance (ITC) of the lateral MoSSe/WSSe heterostructure was decided as follows: λ = J Δ T . (2)

Therefore, pronounced ITC across the interfaces of the arm-1, arm-2, zig-1, and zig-2 MoSSe/WSSe heterostructures is 2.92 × 10⁸, 4.24 × 10⁸, 2.12 × 10⁸, and 3.13 × 10⁸ W K⁻¹·m⁻², respectively, which is comparable with that of graphene/BP (2.5 × 10⁸ W K⁻¹·m⁻²) (Liu et al., 2018). More importantly, the obtained ITC, 4.24 × 10⁸ W K⁻¹·m⁻², of the arm-2 MoSSe/WSSe heterostructure is also larger than lateral heterostructure MoS₂/WSe₂ (3.65 × 10⁸ W K⁻¹·m⁻² and 3.76 × 10⁸ W K⁻¹·m⁻² along armchair and zigzag directions) (Qin et al., 2019). It is worth noting that the heat flux of arm-2 (or zig-2) is larger than that of the arm-1 (zig-1) MoSSe/WSSe heterostructure, which is suppressed by the interface bending in arm-1 (or zig-1).

In particular, it is observed that the heat flux of the arm-1 (arm-2) heterostructure is also higher than that of the zig-1 (zig-2) heterostructure. The phonon scattering spectrums of lateral MoSSe/WSSe heterostructures with armchair and zigzag interfaces are demonstrated in Figures 7A,B, respectively, obtained by the density functional theory by the unit cell, as shown in Figure 1. It is worth noting that the slope of the acoustic branch in the arm-1 (or arm-2) heterostructure is steeper than that in the zig-1 (or zig-2) heterostructure in Figure 7A (or Figure 7B), which illustrates that the acoustic branches can be suppressed by the zigzag interface in the MoSSe/WSSe heterostructure, resulting in a lower group velocity. Thus, the heat flux in the MoSSe/WSSe heterostructure with an armchair interface is higher than that of the zigzag interface.

First-principles calculations and MD simulations were carried out to explore the electronic and thermal properties of the lateral Janus MoSSe/WSSe heterostructure. Four different structures of the Janus MoSSe/WSSe heterostructures were constructed by different symmetry and interface edges. These MoSSe/WSSe heterostructures possess direct type-II band structures, which can provide the ability to separate the photogenerated electrons and holes as a photocatalyst for water splitting. More interestingly, the asymmetric arrangement of S and Se in the Janus MoSSe/WSSe heterostructure can decrease the heat flux because of interface bending, while the lower heat flux and ITC of the Janus MoSSe/WSSe heterostructure with a zigzag interface is mainly due to the suppressed acoustic branches. The studied lateral Janus MoSSe/WSSe heterostructure in our work will provide theoretical guidance for the designing the 2D heterostructure to be used for future nano-devices.