_{2}, Janus ReSSe, and ReSe

_{2}Monolayers

Monolayers of transition metal ReX_{2} and ReSX (X=S, Se) have been proposed as new electronic materials for nanoscale devices. In this paper, there are three structures: ReS_{2}, Janus ReSSe, and ReSe_{2}. Based on the first-principles theory, we analyzed the structures, electronic properties, and Fermi speed. Remarkably, we studied the stability of structures of ReS_{2}, Janus ReSSe, and ReSe_{2} monolayers under biaxial tensile and compressive strain by density functional approach. It is worth noting that when the strain changes, not only the band gap changes but also the band gap properties (direct and indirect) also change. The bond gaps decrease with the increase of tensile strain and compressive strain; Moreover, when the strain is greater than 0, the bond angle decreases as the strain increases, and when the strain is less than 0, the bond angle increases as the strain increases.

It has been proposed that the transition metal dichalcogenide (TMD) [_{2} is expected to become the next generation of new electronic materials due to the inherent electron bandgap. This led to studies on the physical and chemical properties of such structures, such as ReS_{2}, ReSe_{2}, WS_{2}, WSSe, and WSe_{2} [

In multilayer 2D materials, physical properties can be regulated by external electrical/magnetic field, stress, structural modification, and heterostructure [_{2}, but more sensitive to a multilayer structure [

When studying the electronic and optical properties of materials, the regulation of biaxial strain is more practical than that of external E-field [

At present, there is great interest in a ReX_{2} TMD monolayer system. One sulfur element, X, is replaced by another sulfur element, Y, which forms a single layer of ReXY, which is called the Janus layer and this paper is called the Janus structure [_{2} TMD, but the crystal symmetry is reduced from D_{3h} to C_{3v} [_{2}, Janus ReSSe, and ReSe_{2}, including bond lengths, and analyzed the changes under tensile and compressive strains [

Our calculation is based on a density functional theory [

In the monolayers of ReS_{2} and ReSe_{2}, the atoms are arranged symmetrically in the shape of triangular prism S-Re-S and Se-Re-Se, respectively. The symmetrical arrangement of atoms in the triangular prism shows a symmetry of D_{3h}. Moreover, ReS_{2} and ReSe_{2} are typical “sandwich” structures, although they are monolayers, with the same two layers of atoms holding the Re atoms sandwiched between them [

Figure _{2}, ReSe_{2}, and Janus ReSSe. For the ReS_{2} monolayer, the optimized lattice parameters are _{2} lattice parameters are _{2} and ReSe_{2} are 2.36 Å and 2.49 Å, respectively. In the monolayer of Janus ReSSe, the bond lengths of Re-S and Re-Se are 2.36 Å and 2.49 Å, respectively. The bond angles ∠ReSRe and ∠ReSeRe in the ReS_{2} and ReSe_{2} monolayers are approximately 75.49° and 74°, respectively. These angles have changed significantly in the monolayer of Janus ReSSe; ∠ReSRe is about 84.06° and is larger than the corresponding point of view in the ReS_{2} monolayer, and ∠ReSeRe is about 79.32° and is smaller than the corresponding point of view in the ReSe_{2} monolayer. The reason for the change in bond angles is that the radius of the constituent atoms in the Janus ReSSe monolayer is different.

Side view of (a) ReS_{2} monolayer, (b) Janus ReSSe monolayer, (c) ReSe_{2} monolayer, and (d) the hexagonal Brillouin zone of unit cell.

The energy band structure and Fermi velocity of these monolayers were calculated. The electron band structure is plotted above. Figures _{2}, Janus ReSSe, and ReSe_{2}, respectively, indicating that all these monolayers are direct bandgap materials. The band gap of _{2}, Janus ReSSe, and ReSe_{2} monolayers calculated by GGA is 1.43 eV, 1.32 eV, and 1.25 eV, respectively.

(a) Electronic band structure and total density of states and (b) partial density of states of ReS_{2} monolayer.

(a) Electronic band structure and total density of states and (b) partial density of states of ReSeS monolayer.

(a) Electronic band structure and total density of states and (b) partial density of states of ReSe_{2} monolayer.

We also calculated the partial density of the state, and the energy results of the ReS_{2}, Janus ReSSe, and ReSe_{2} monolayers at -2 to 2 eV are summarized in Figures _{2} monolayer VBM is mainly contributed by Re-d_{x}^{2}_{-y}^{2} and Re-d_{x}^{2} orbitals, while the CBM is contributed by Re-d_{x}^{2}; however, the S atom does not contribute to the Fermi energy. Similarly, the Janus ReSSe monolayer CBM is dominated by Re-d_{yz}, and Re-d_{x}^{2}_{-y}^{2} has a partial contribution. However, the VBM state is attributed to the Re-d_{x}^{2} orbit. A similar contribution was observed for ReSe_{2}, where the CBM consisted of Re-d_{yz} orbitals and the state in the VBM was dominated by the Re-d_{z}^{2} orbit, Figure _{2} band produced a split.

Electronic band structure of (a) ReS_{2}, (b) ReSSe, and (c) ReSe_{2} monolayers after considering spin orbit coupling.

Figure _{2}, Janus ReSSe, and ReSe_{2} monolayers under compression and tensile strain [

The variation of bond angle and bond length under the compressive and tensile strain of (a) ReS_{2}, (b) Janus ReSSe, and (c) ReSe_{2} monolayers.

The physical properties of these monolayers have changed under both compression and tensile strain. We calculated the bond length and bond angle changes of ReS_{2}, Janus ReSSe, and ReSe_{2} monolayers under different Janus ReSSe, which are summarized in Figures

Under the control of compressive strain and tensile strain, the electronic band structures of the three monolayers have changed. Not only does the band gap change, but also the band properties shift between the direct band gap and the indirect band gap [

Effect of compressive and tensile strain on band gap, D stands for direct gap and ID stands for indirect band gap.

In order to see the electronic phase transition more accurately, we considered more points in the strain interval [_{2} monolayer showed a direct to indirect bandgap transition at 2% compressive strain and 6% tensile strain, as shown in Figures _{2} monolayer also exhibits a direct to indirect bandgap transition at 2% compressive strain and 9% tensile strain, as seen in Figures _{2}, as shown in Figures

Electronic band structure of (a) the ReS_{2} monolayer at 2% compressive strain, (b) the ReS_{2} monolayer at 6% tensile strain, (c) the Janus ReSSe monolayer at 2% compressive strain, (d) the Janus ReSSe monolayer at 9% tensile strain, (e) the ReSe_{2} monolayer at 2% compressive strain, and (f) ReS_{2} monolayer at 6% tensile strain.

In order to visually see the change trend of the band gap under the compressive strain and tensile strain and the mutual conversion trend between the direct band and gap indirect band gap, we draw a trend chart. Purple represents the trend of ReS_{2}, orange represents the trend of Janus ReSSe, and green represents the trend of ReSe_{2}. As shown in Figure _{2} decreases with the increase of compressive strain and decreases with the increase of tensile strain. The maximum band gap appears at 2% compressive strain. When the compressive strain is greater than 2% and the tensile strain is greater than 6%, the band gap exhibits indirect band gap, in which case the ReS_{2} monolayer is a kind of indirect band gap semiconductor. And the trend of the band gap of the Janus ReSSe monolayer and the ReSe_{2} monolayer with strain is similar to that of the ReS_{2} monolayer.

What is more, the strain phase transition point of the direct band gap and the indirect band gap of the ReSe_{2} monolayer is the same as that of the ReS_{2} monolayer. However, the direct band gap and the indirect band gap strain phase transition point of the Janus ReSSe monolayer occur when the compressive strain is 2% and the tensile strain is 9%.

The ReS_{2} single layer shows that the band gap changes are not obvious when the tensile strain and compressive strain are 0~4% and the band gap changes are not obvious when the compressive strain is greater than 4%; then the band gap changes are not obvious when the tensile strain is greater than 4%. The orange lines are shown in the figure. The band gap variation of the Janus ReSSe single layer and ReSe_{2} single layer is relatively stable, and the change of the band gap of Janus ReSSe shows a linear change, which shows a linear decrease with the increase of compressive strain and tensile strain.

The Janus ReSSe single-layer electronic band structure exhibits a direct bandgap semiconductor behavior similar to the MoSSe single layer. The band gap of the Janus ReSSe single layer is located between the band gap values of the ReS_{2} and ReSe_{2} monolayers. Under the influence of spin-orbit coupling, the energy band structure of ReS_{2} and Janus ReSSe did not change, and the energy band structure of ReSe_{2} was split. The effects of biaxial strain on the stability and electronic properties of ReS_{2}, Janus ReSSe, and ReSe_{2} monolayers were investigated by a density functional theory. It is found that under the influence of stress, the bond length, and bond angle of the three structures change, the bond angle decreases with the increase of tensile stress, and as the compressive stress increases, it also increases. The tensile strain increases and decreases as the compressive stress increases. Moreover, under biaxial strain, these single layers undergo a transition between direct and indirect band gaps. These findings will provide a theoretical basis for future research and experiments.

Readers can find our structural parameters from the computational methods and corresponding basic data. Moreover, the corresponding basic data has been added to the new document, and readers can repeat our calculation. If you have any questions, please contact us any time.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61571210, 61172028, and 11434006).

_{2}, Janus WSSe and WSe

_{2}monolayers

_{2}

_{2}/WS

_{2}heterostructures

_{2}-WSe

_{2}and WS

_{2}-MoSe

_{2}

_{2}/MoS

_{2}monolayers

_{2}

_{2}and WSe

_{2}n-MOSFET

_{2}under elastic strain