Flexible and Anisotropic Properties of Monolayer MX2 (M = Tc and Re

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Flexible and Anisotropic Properties of Monolayer MX (M = Tc and Re; X = S, Se) 2

Qiyi Zhao, Yaohui Guo, Yixuan Zhou, Xiang Xu, Zhaoyu Ren, Jin Tao Bai, and Xin Long Xu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07939 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 2, 2017

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The Journal of Physical Chemistry

Flexible and Anisotropic Properties of Monolayer MX2 (M = Tc and Re; X = S, Se) Qiyi Zhao, Yaohui Guo, Yixuan Zhou, Xiang Xu, Zhaoyu Ren, Jintao Bai, Xinlong Xu*

Shaanxi Joint Lab of Graphene, State Key Lab Incubation Base of Photoelectric Technology and Functional Materials, International Collaborative Center on Photoelectric Technology and Nano Functional Materials, Institute of Photonics & Photon-Technology, Northwest University, Xi'an 710069, China

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ABSTRACT: Flexible and anisotropic response of layered transition metal dichalcogenides MX2 (M = Tc and Re; X = S, Se) are important for wearable and polarized optoelectronics. Herein, the elastic, electronic, and optical dielectric properties of these two-dimensional (2D) materials have been investigated by density functional theory (DFT) with different van der Waals correction and Heyd-Scuseria-Ernzerhof hybrid functional. The Young’s modulus of these materials is low, which indicates that they are favorable for the flexible optoelectronic devices. The band gaps fall in between 1.70 eV and 2.12 eV with the d states of transition metal atoms playing an important role in conduction and valence bands. In addition, the appearance of band nesting implies that there are strong light-matter interactions in these materials, indicating they are suitable for photovoltaic and photocatalytic applications. Unlike the traditional 2D materials such as MoS2, the optical dielectric properties manifest highly in-plane anisotropic in the infrared and visible region, which is suitable for on-chip polarization manipulation with these materials. This work promotes the understanding of flexible and anisotropic response of these materials and their potential applications in new types of optoelectronic devices.

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1. INTRODUCTION

Flexible devices are important as wearable and consumer optoelectronics, and will afford humankind more flexibility in daily life. As such, displays1, thin-film transistors2, touch sensors3, photovoltaic devices4-5, and energy-storage devices6 have recently caughtmuch attention in the flexible format. Two-dimensional (2D) materials, especially 2D transition metal dichalcogenides (TMDs), have been paid wide attentions for their excellent performance in transparent and flexible electronics due to their high crystallinity in atomic thickness and their potential for different types of electronics and optoelectronics. To achieve flexibility, the materials must comply with bending to some degree without losing their function. The hunt for flexible materials suggests that Young’s modulus and shear modulus of them should be relatively small, while bulk modulus of them should be large. It has been reported that large scale molybdenum disulfide (MoS2) film is more suitable for transparent and flexible electronic compared to conventional amorphous silicon or organic films due to its high optical transparency, high electrical mobility and high on/off ratio7. Transparent and high flexible MoS2/hexagonal boron nitride/graphene heterostructures have been utilized in display logic circuits with high mobility and low power consumption8. The flexible and transparent thin film transistors and photodetector have also been achieved based on large-area tungsten selenide (WSe2) film9-10, which display high current on/off ratio. Anisotropic response is a physical property of crystal orientation dependence with different properties along different axes. This usually happens in one dimensional materials as the 3



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electrons or excitons have different mobility along the longitude and axial axes. Taking single-walled carbon nanotubes as an example, their anisotropic dynamic dielectric response can be used to control THz polarization11, which show great application in THz polarized devices12. 2D materials usually do not show the anisotropic response. However, there are some 2D materials which exhibit anisotropic properties due to their low symmetry. Black phosphorus (BP)， as the most stable allotrope of phosphorus, exhibits strong intrinsic in-plane anisotropy with different Hall mobility for holes along the light (x) and heavy (y) effective mass directions. BP thin films also exhibit large and anisotropic in-plane optical conductivity and on/off current ratio13. The calculated electron and hole effective masses show MX3 (M = Ti, Zr; X = S, Se, Te) have anisotropic conductive properties and monolayer TiS3 exhibits high anisotropy in the light absorption14. Unlike general TMDs such as MoS2 and zirconium sulfide (ZrS2), VIIB group TcX2 and ReX2 (X = S, Se) as a new family of 2D TMDs demonstrate an additional valence electron. This additional valence electron inTcX2 and ReX2 (X = S, Se) results in special electronic structures. Using ReS2 as an example, there is no charge couple between layers15, because the charge is confined by the additional valence electron in layers. As a consequence, ReS2 belongs to direct bandgap semiconductor no matter whether in bulk or in monolayer structures15-16. Hence, the special electronic properties and symmetry splitting caused by distorted phase make ReS2 a promising candidate for electron band engineering. The band gaps of TcX2 and ReX2 (X = S, Se) locate in the range of visible-infrared region and they have great applications in photovoltaics17-19. 4


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There are some theoretical calculations of VIIB-VIA 2D TMDs20-24, which mainly emphasize the investigation on the electronic properties, optical absorption, and Raman response. The optical absorption spectra and Raman spectra of monolayer ReX2 (X = S, Se) show in-plane anisotropic response. However, early works are short of an in-depth study on mechanical and optical dielectric properties of TcX2 and ReX2 (X = S, Se). On one hand, flexible electronics requires information of the Young’s modulus, shear modulus, and bulk modulus of the 2D materials. On the other hand, the dielectric functions of materials provide a bridge to connect macroscopic properties and microscopic electronic structures and have a profound effect on the optoelectronic applications of materials. In this paper, the mechanical properties and dielectric functions of VIIB-VIA 2D TMDs are investigated by hybrid density functional. Their elasticity modulus suggests they belong to flexible materials which could be used for flexible devices. Their band gaps mainly depend on d states of transition metal atoms. The band nesting phenomenon occurs in their energy bands manifest the strong light-matter interactions. Highly in-plane anisotropy is observed due to their special electronic structures and crystal structures, through observing the optical dielectric properties of materials.

2. COMPUTATIONAL METHOD

Mechanical, electronic, and dielectric properties of VIIB-VIA 2D TMDs have been performed through Vienna ab initio Simulation Package (VASP)25-26. The Green-Wannier (GW) version of 5



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the Perdew, Burke, and Ernzerh (PBE) parameterization has been used for the generalized gradient approximation (GGA)27-28. Projector augmented wave (PAW) pseudo-potentials29 act as exchange correlation and electron-ion interaction for all calculations. To obtain reasonable structures, three different kinds of van der Waals correction terms including van der Waals density functional (vdW-DF)30-32, van der Waals density functional dispersion correction (vdW-D3)33, and van der Waals Tkatchenko-Scheffler method with iterative Hirshfeld partitioning (vdW-TS/HI)34-37 are used to describe non-bonding interactions respectively. Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional38 is utilized for the calculation of optical dielectric functions within the framework of PAW method and band gap correction without changing the band character. Frequency dependent dielectric matrix contains the imaginary part of dielectric functions can be obtained after the electronic ground state is determined by hybridization calculations38-39. Afterwards, the real part of dielectric functions could be obtained through Kramers-Kronig relations40. The cut off energy of the plane-wave basis set is 650 eV. The energy relaxation is taken as 1.0 × 10-5 eV and the Hellmann-Feynman force between each atom is set to less than 0.01 eV/Å. In the k-points sampling routine, 5×5×5 and 5×5×1 Monkhorst−Pack grid41 are adopted for bulk and monolayer structures, respectively. In order to eliminate the spurious interaction between neighboring layers, a vacuum layer with a thickness of 3 nm is adopted for the calculation of monolayer structures. All the parameters meet the stability and accuracy criterions.

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3. RESULTS AND DISCUSSION

3.1 Crystal Structure and Stability. It is known that the majority of TMDs belong to a hexagonal system with either D6h point-group symmetry or D3d point-group symmetry, while the VIIB-VIA 2D TMDs are triclinic structures with P 1 point-group symmetry. Their stable phases belong to distorted octahedral (T) phase. The chalcogen layers are buckled and the metal atoms form zigzag chains along the direction of lattice vector16. In exception to that, the triclinic unit cells of TcS2, TcSe2, and ReSe2 contain one sandwich which is constituted by four formula units. However, the unit cell of ReS2 contains two sandwiches which are related by a center of symmetry42. This suggests ReS2 has a unit cell with eight formula units. The VIIB atoms locate in a distorted octahedral coordination formed by VIA atoms42-43. Figure 1 illustrates the structures of MX2 and their flexibility.

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Figure 1. (a) Side view of MX2. (b) Top view of MX2. (c) MX2 on flexible substrate. The green represent chalcogenide atoms and gray represent transition metal atoms.

The most reasonable crystal structures compared with experimental data are used for the study on mechanical, electronic, and optical dielectric properties. The parameters of relaxed structures are listed in Table S1 in supporting information. The relaxed structures are different in different van der Waals correction terms. From Table S1, it could be found that the relaxed structures of TcS2 from vdW-D3 agree well with the experimental data, while the relaxed structures of ReS2 from vdW-TS/HI are in good agreement with the experimental data. 3.2 Mechanical Properties. The stability of structures under the influence of external 8


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distorting force has a deep influence on the flexible optoelectronics. Therefore, it is important to calculate the elastic constants Cij, which could build the bridge between mechanical and dynamical behavior of structures. In addition, there is a lot of other information, such as the Young’s modulus, Poisson’s ratio etc, could be obtained from the elastic constants. Hence, elastic constants play an important role in determining the stability and stiffness of the materials44-47.

Table 1. Calculated Elastic Constants for VIIB-VIA TMDs; Unit of each Value is GPa

TcS2

C1

C1

C1

C1

C1

C1

C2

C2

C2

C2

C2

C3

C3

1

2

3

4

5

6

2

3

4

5

6

3

4

25

53

36

-6.

12

4.

15

41

7.

58

-0.

56

-8.

29.

-9.

77.

-0.

27.

9

9

4

7

8

7

6

8

1.

14

-3.

11.

-1

65

-0.

22.

5

7

4

8

2

2

8

-5

24

0.3

-0.

-6.

90.

-2

-1.

8

0

7

2

4

5

2

-1.

-2.

-6.

76

-2

-1.

1

4

6

1

6

1 TcS

20

e2

3

ReS

20

2

9

ReS

17

e2

7

4 50

28

-1.

2.8

6 51

29

-5.

0.3

9 42

20

0 43

6.

1 41

9 12

-0.

37

3

2.

-6.

-1

3

3

3

-5.

-1.

-4

19

7.

1.

-7.

-1

8

4

8

7

3

4

3

2

33

11

C35

C3

C44

6

C4

C46

5

C5

C5

C6

5

6

6

39

-1

47

0 29

-1

36

0 19

0.

30

8 17

0.

25

7

As triclinic structures, VIIB-VIA 2D TMDs have 21 independent elastic constants. Table 1 shows the elastic constants of MX2. The eigenvalues of elastic constants matrixes are all positive and meet the stability criterion48 so that the structures would be stable under mechanical distortion. The elastic constants C11, C22, and C33 could indicate the resistance to linear compression from of a-, b-, and c-direction (Figure 1), respectively. Moreover, they also reflect sound propagation along these directions. Hence, it could be found that all VIIB-VIA 2D TMDs have large resistance to linear compression along a-and b-direction, which are larger than that of c-direction. In other words, the materials are stiffer for strain along the a- and b-direction than

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that along the c-direction. This is the reason there exists strong ionic bonds in a- and b-direction, while only weak interaction in c-direction. Besides, the C11 of TcS2 and TcSe2 is bigger than C22 of TcS2 and TcSe2, respectively. While C11 of ReS2 and ReSe2 is lower than C22 of ReS2 and ReSe2, respectively. These suggest that TcX2 (X = S, Se) are easy to slip along the b-direction, while ReX2 (X = S, Se) are easy to slip along the a-direction. The elastic constant C44 plays the most important role in governing the indentation hardness of a material. This parameter reflects the ability of resisting the monoclinic shear distortion in (1 0 0) plane, and the parameter C66 presents the resistance to shear in the direction. It could be found that the C44 of TcS2 and ReS2 is higher than that of TcSe2 and ReSe2, respectively. Besides, the C66 of TcS2, TcSe2, ReS2 and ReSe2 decreased in turn. The resistance of VIIB-VIA 2D TMDs to linear compression along basis vector of lattices is similar to that of MoS245. While the resistance of VIIB-VIA 2D TMDs to shear in direction is lower than that of MoS2, it suggests that VIIB-VIA 2D TMDs are more likely to produce elastic deformation than MoS2. It is known that Young’s modulus (Y), bulk modulus (B), shear modulus (G) and Poisson’s ratio ( ν ), which are regarded as the most concern elastic properties for applications, especially for the investigation on the hardness of polycrystalline materials. The computational process is presented in supporting information. The values of Y, B, G and ν of VIIB-VIA 2D TMDs are listed in Table 2.

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Table 2. Calculated Bulk Modulus (B in GPa), Shear Modulus (G in GPa), Young’s Modulus (Y in GPa) and Poisson’s Ratio ( ν ) for VIIB-VIA TMDs from Single Crystal Elastic Constants ν B G Y B/G TcS2 50.591 39.309 93.804 0.193 1.287 TcSe2 50.355 30.510 76.151 0.248 1.650 ReS2 50.736 36.974 89.243 0.207 1.372 33.667 28.524 66.727 0.170 1.180 ReSe2 Young’s modulus is utilized for the measurement of the stiffness of materials, which is defined as the ratio of stress and strain. Compared with other 2D materials, the Young’s modulus of VIIB-VIA 2D TMDs is far lower than that of MoS2 (199.525 GPa)45, but similar to that of BP (70.3 GPa) 49 and bismuth sulfide (Bi2S3) (106.9GPa)50. It has been reported that MoS2 could be used in transparent and flexible electronic devices7-8. Therefore, the VIIB-VIA 2D TMDs, which are more flexible than MoS2, also have potential applications in flexible optoelectronics. Poisson’s ratio is used to reflect the degree of directionality of the covalent bonds. For the covalent materials, the Poisson’s ratio is relatively small ( ν = 0.1) and the typical value of ν for ionic materials is 0.2551. The Poisson’s ratio of VIIB-VIA 2D TMDs is about 0.2, which is lower than those of BP and Bi2S349-50. It means that ionic contribution plays a major role in inter-atomic bonding for VIIB-VIA 2D TMDs. The bulk modulus (B) as the resistance to fracture and shear modulus (G) represents the resistance to plastic deformation. Pugh used the ratio of B and G to measure the ductility52. A material is brittle if B/G is less than 1.75. Contrarily, the material is ductile. 3.3 Electronic Properties. In order to describe the optical dielectric properties accurately, the accurate description of electronic properties of structures should first be obtained. The electronic 11



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band structures of monolayer VIIB-VIA 2D TMDs are calculated in Brillouin zones (BZ) along the lines connecting high-symmetry points Γ, X, S, X1, Y, X2 , Y1, Γ in the k-space, whose coordination are shown in Figure S1 in supporting information. Figure 2 shows the band structures of monolayer VIIB-VIA 2D TMDs calculated by PBE method.

Figure 2. Band structures of (a) monolayer TcS2, (b) monolayer TcSe2, (c) monolayer ReS2, (d)

monolayer ReSe2. The Fermi level is indicated as the dash line at E=0.0 eV. 12


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It can be found that the monolayer TcS2, TcSe2, and ReSe2 are all indirect gap semiconductors. The CBM of them are between Γ and X of high symmetry k-points and their VBM are between X1 and Y of high symmetry k-points. The ReS2 exhibits a direct gap at Γ. These results are consistent with previous works22-24. Then HSE06 hybrid exchange-correlation (XC) functional is adopted for the correction of band gaps. Table 3 shows the band gaps of monolayer VIIB-VIA TMDs calculated by PBE, PBE with spin-orbit coupling (SOC) and HSE06. Table 3. Calculated Band Gaps in eV for Monolayer VIIB-VIA TMDs PBE PBE-SOC TcS2 1.34 1.28 TcSe2 1.22 1.02 1.46 1.36 ReS2 ReSe2 1.28 1.18

HSE06 1.87 1.70 2.12 1.78

As shown in Table 3, the band gaps of monolayer materials decrease a little bit when SOC is included. The reason is that spin-orbit splitting occur in valence band. While their band gaps increase significantly when the band gaps are corrected by HSE06 hybrid functional. These characteristics are similar to other TMDs such as MoS2, ZrS2 and so on53-55. Besides, the values of band gaps we obtained by HSE06 hybrid functional are similar to previous references24, 56. On account of the fact that band gap defines the threshold of photon absorption, which is related to the electron transition from the valence band to the conduction band. However, the largest absorption usually does not appear at band-gap edge. Therefore, in order to learn about the significant optical response, band nesting of materials is investigated. In 2D materials, the band nesting means the divergence of the joint density of states (JDOS), which implies high optical conductivity57.

According

to

the

definition,

band

nesting

would

appear

once

13



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∇k ( Ec − E v )

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1 ( 2π a ) ( 2π a is the modulus of the reciprocal lattice vector). The lines

connecting high-symmetry points of all structures are searched for exploring the scope where the band nesting occurs. Figure 3 illustrates the modulus of gradient of difference between conduction band and valence band for VIIB-VIA TMDs. The lowest unoccupied band, the highest occupied band, and the second highest occupied band of materials are symbolized by Ec1, Ev1, and Ev2, respectively.

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Figure 3. Modulus of gradient of difference for monolayer (a) TcS2, (b) TcSe2, (c) ReS2 and (d) ReSe2. The scopes where the band nesting occurs are summarized in Table S2 in supporting information. It could be found that the band nesting mainly occurs between X and Y1 of the high symmetry k-points. Because of the difference of materials, scopes are slightly different. It means there exist singularities of JDOS in the scopes that embody strong light-matter interactions and high optical conductivity in monolayer structures. Besides, the total and partial densities of states of monolayer VIIB-VIA TMDs are calculated and the results are displayed in Figure 4 and Figure 5 for the understanding of the contribution of different atoms to the band structures of materials.

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Figure 4. (a, b) DOS of TcS2 and TcSe2; (c, d) DOS of S atoms and Se atoms of monolayer TcS2 and TcSe2; (e, f) DOS of Tc atoms of monolayer TcS2 and TcSe2. It could be found that the highest occupied valance bands and the lowest unoccupied conduction bands are mainly dominated by Tc d states for monolayer TcS2 and TcSe2 in Figure 4.

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Figure 5. (a, b) DOS of ReS2 and ReSe2; (c, d) DOS of S atoms and Se atoms of monolayer ReS2 and ReSe2; (e, f) DOS of Tc atoms of monolayer ReS2 and ReSe2. In Figure 5, the obvious difference for monolayer ReS2 and ReSe2 is that the highest occupied valance bands are dominated by p states of chalcogenide atoms and d states of Re atoms. The lowest unoccupied conduction bands are dominated by d states of transition metal atoms, which are similar to TcS2 and TcSe2. Compared with Figure 4, the electronic properties of VIIB-VIA 17



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TMDs could provide information for the manipulating electron band.

3.4 Optical Dielectric Properties. Optical dielectric properties of monolayer VIIB-VIA TMDs are relatively less reported in literatures. However, they are important for the investigation on other optical properties of materials such as absorption spectrum, photoconductivity and so on. Figure 6 illustrates the imaginary part of dielectric functions of monolayer VIIB-VIA TMDs. Because of the in-plane anisotropy, the imaginary part of dielectric functions are indicated by

ε 2 ⊥ XY , ε 2 ⊥ X and ε 2 ⊥ Y , repectively. They indicate imaginary part of dielectric function perpendicular to the plane (the plane defined by the X-axis and Y-axis and as shown in Figure S1 in the supporting information), X-axis, and Y-axis respectively. The peaks of dielectric function are related to the Van Hove singularity of the high symmetry k-points and high symmetry lines, which are listed in Table S3 in supporting information.

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Figure 6. Imaginary part of optical dielectric functions of monolayer (a) TcS2, (b) TcSe2, (c) ReS2 and (d) ReSe2. Compared with the imaginary part of optical dielectric functions of monolayer MoS258, imaginary part of optical dielectric functions of monolayer VIIB-VIA TMDs shows obvious in-plane anisotropy after 2.5 eV. What is noteworthy is that TcS2 and TcSe2 tend to be in-plane isotropic in the relatively high energy range (> 5 eV), while ReS2 and ReSe2 always show 19



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in-plane anisotropic. Table S3 in the supporting information shows the transition of each peak modes for MX2. In monolayer MoS2, the band transition is from valence bands of S p states to conduction bands of Mo d states. While for TcS2 and TcSe2, the transition is from valence bands of Tc d states to conduction bands of Tc d states. However, for ReS2 and ReSe2, the transition is from valence bands of Re d states and p states of chalcogenide atoms to conduction bands of Re d states. Figure 6 also shows that VIIB-VIA TMDs have excellent absorption properties in visible range. Hence, they could be regarded as promising candidates for the third generation solar cell. Through Kramers-Kronig relations40, the real part of dielectric functions could be obtained and the results are displayed in Figure 7.

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Figure 7. Real part of optical dielectric functions of monolayer (a) TcS2, (b) TcSe2, (c) ReS2 and (d) ReSe2. The real part of optical dielectric functions of monolayer VIIB-VIA TMDs shows relatively highly in-plane isotropic except the energy range between 2 eV and 3 eV. The complex dielectric constant can be expressed as ε ⊥ (ω) = ε1⊥ (ω ) + i ε2⊥ (ω ) and ε (ω) = ε1 (ω) + i ε2 (ω) , from which absorption, conductivity, transmission, and reflection could be obtained. Compared with 21



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the bulk materials, the dielectric functions difference is bigger than those of lithium niobate and kalium niobate with the photon energy below 4 eV59. The anisotropy suggests they could be used for the on-chip wave plate, polarizer, and other polarization sensitive devices.

4. CONCLUSION

In summary, we study the structural, electronic, mechanical and optical dielectric properties of the VIIB-VIA 2D TMDs utilizing the ab initio approach. As one kind of new 2D materials that contains in-plane anisotropy, VIIB-VIA 2D TMDs is much more flexible than most studied common TMDs such as MoS2, which have been applied in flexible devices. Therefore, they could be regarded as ideal candidates for flexible electronics. In addition, the band gaps and band nesting of VIIB-VIA monolayer TMDs indicate that they could be the ideal materials for third photovoltaic applications and photo-catalysis. Besides, through the analysis of total and partial densities of states, it could provide guidance for tuning electronic properties of materials. Finally, the optical dielectric functions are obtained. Their highly in-plane anisotropic in the infrared and visible region suggests they could be utilized for on-chip polarization manipulation. The results pave the way for the flexible and anisotropic optoelectronic devices with VIIB-VIA 2D TMDs.

AUTHOR INFORMATION Corresponding Author * Corresponding author: [email protected]. 22


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Supporting Information Lattice constants of relaxed structures, computational formulas of elasticity modulus, Brillouin zones with high symmetry k-points, band nesting regions, transitions and peak positions in dielectric functions spectra

ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (No. 11374240, 11774288, 61605160), Natural Science Foundation of Shaanxi Province (2017KCT-01, 2016JQ1010), Natural Science Research Plan of Shaanxi Education Department (16JK1781), Young Talent Plan from Institute of Science and Technology of University in Shaanxi Province (20160114).

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Flexible and Anisotropic Properties of Monolayer MX2 (M = Tc and Re

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