Electronic and Optical Properties of Pristine and Vertical and Lateral

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Electronic and Optical Properties of Pristine and Vertical and Lateral Heterostructures of Janus MoSSe and WSSe Fengping Li, Wei Wei, Pei Zhao, Baibiao Huang, and Ying Dai J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02841 • Publication Date (Web): 24 Nov 2017 Downloaded from http://pubs.acs.org on November 25, 2017

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Electronic and Optical Properties of Pristine and Vertical and Lateral Heterostructures of Janus MoSSe and WSSe Fengping Li, Wei Wei,* Pei Zhao, Baibiao Huang, Ying Dai* School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

Corresponding Author: [email protected], (W. Wei) [email protected] (Y. Dai)

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ABSTRACT On the basis of electron-electron self-energy corrections, quasiparticle band structures of Janus MoSSe and WSSe are identified, and the excitonic effects are demonstrated to play a dominate role in the optical response. Combining together MoSSe and WSSe monolayers to form vertical heterostructures (VHTs) and lateral heterostructures (LHTs) rarely leads to a simple arithmetic sum of their properties, giving rise to novel and unexpected behaviors. In particular, Rashba polarization can be enhanced in VHTs due to improved out-of-plane electric polarity. In case of LHTs, photo-response and absorption coefficients show optical activity in a wide visible light range. It is of interest that both VHTs and LHTs reveal type-II band alignment, enabling the separation of excitons. Besides, grain boundaries (GBs) of large angle (60°) in Janus MoSSe due to chalcogen effects behave as one-dimensional (1D) metallic quantum wires, suggesting the possible formation of 1D electron or hole gas in such electronic heterostructures.

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Two-dimensional (2D) transition metal dichalcogenides (TMDCs) MX2 (M=Mo, W; X=S, Se) have attracted extensive attention in high-end electronics and optoelectronic devices.1-5 2D TMDCs indicate intrinsic in-plane asymmetry with direct band gaps of 1.1~1.9 eV, giant spin-orbit coupling (SOC) and favorable electronic and mechanical properties, which endow TMDCs great application potential in field-effect transistors (FETs), photonics and valleytronics.6-13 It has been demonstrated that the electronic and optical properties can be regulated through effective control of the alloy composition of the 2D TMDCs, such as in MoSxSe2-x, MoxW1-xS2 and WS2xSe2-2x.14-18 Recently, the organized Janus MoSSe in 2H phase has been successfully obtained, by fully replacing one of two the S (Se) layers with Se (S) atoms within MoS2 (MoSe2) at an applicable temperature mainly though the chemical vapor deposition (CVD) method.19,20 Different from 2D MX2 with mirror symmetry, Janus MoSSe reveals an intrinsic out-of-plane electric field due to the mirror asymmetry and thus demonstrates large Rashba band splitting and out-of-plane piezoelectricity.21-24 It has been extensively identified that combining distinct 2D materials to construct heterostructures can engineer the electronic properties and bring new exciting physical phenomena, which now is a central concept in nanoscale electronic and photovoltaic devices.25-31 As a consequence, the range of application of 2D TMDCs could be widely broadened by considering different stacking or combination patterns. In particular, 2D TMDCs can be vertically stacked layer by layer, forming the van der Waals (vdW) heterostructures.32-35 On the other hand, TMDCs can also be stitched 3

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seamlessly within the 2D plane to realize the lateral (in-plane) heterostructures (LHTs) with

the formation of

atomically

sharp one-dimensional (1D) interfaces

(interlines).36-40 Experimentally, the vertical heterostructures (VHTs) can be obtained through mechanical transfer, while the LHTs can be acquired though CVD approach.41-44 It has been found that VHTs and LHTs composed of 2D TMDCs manifest exciting novel properties. Inspired by this, in this work, we propose VHTs and LHTs composing of the polarized Janus MoSSe and hypothetical WSSe to investigate the unprecedented novel properties by means of the first-principles calculations (the computational details are described in the Supporting Information). Since the properties of WSSe are intrinsically similar with MoSSe, results for MoSSe are presented and discussed. In case of WSSe, dynamic and thermal stability have been verified by phonon spectrum and BOMD calculations. As shown in Figure S1, the phonon spectrum shows no imaginary frequency, and the BOMD results indicate small energy fluctuation, confirming the stability and thus the possibility of experimental realization. As indicated in Figure 1(a), Janus MoSSe presents in-plane asymmetry with two trigonal prismatic lattices while the mirror symmetry with respect to the Mo plane breaks. The hexagonal Mo plane is sandwiched in-between the S and Se layers with unequal distance. The lattice parameter is calculated to be 3.25 Å, and Mo-S and Mo-Se bond lengths are 2.42 and 2.53 Å, respectively. In consideration of the discrepancy in electronegativity for S and Se atoms, a vertical dipole moment of 0.25 Debye appears. The planar average of the electrostatic potential is indicated in Figure 1(b), and the energy difference of 0.5 eV is in fact the 4

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work function difference between S and Se layers. On the basis of Bader charge analysis,45 S and Se atoms obtain 0.6 and 0.4 e, respectively, while Mo atom loses 1.0 e, which results in the net electric field pointing from Se to S. In Figure 1(b), charge density also demonstrates the less charge aggregation on Se atoms. Furthermore, the cohesive energy is calculated for MoSSe according to the following equation: Ec=

Et-µMo-uS-uSe, where Et, uMo, uS and uSe indicate the total energy of MoSSe monolayer, the chemical potential of Mo, S and Se atoms, respectively. The cohesive energy is -2.34 eV for MoSSe, which is comparable with that of MoS2 (-2.63 eV) and large enough to guarantee the stability. In the case of Janus WSSe, a vertical dipole moment of 0.24 Debye, work function difference of 0.6 eV and cohesive energy of -2.06 eV can be obtained. Band structures of MoSSe and WSSe obtained from many-body G0W0, screened hybrid HSE06 and PBE are presented in Figure S2 in the Supporting Information. It is clear that the direct band gaps at the K point at HSE06 level of theory are obviously larger than those from PBE, while smaller than those from G0W0 approximation. In the case of MoSSe, band gaps are 1.56 (PBE), 2.03 (HSE06) and 2.64 eV (G0W0), respectively. It should be pointed out that scissor rule is absent in the G0W0 corrections, and therefore dispersion relationship of the quasiparticle band structures has been obviously changed after considering the nonlocal exchange interactions in comparison with the PBE and HSE06 results. In respect to the optical absorption properties of the monolayers, e-h interactions can be taken into account with the BSE approach based on the quasiparticle corrections. As shown in Figure 1(c), the 5

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imaginary part of transverse dielectric constant ε1/2(ω) shows two obvious excitonic absorption peaks at 1.85 and 2.06 eV due to the strong SOC effects, which correspond to the two bound excitons of A1 and B1 found in MoS2.46-48 In particular, the excitation energy (1.85 eV) of the first exciton with a binding energy of 0.79 eV is in agreement with the experimentally measured optical gap of 1.68 eV. In Janus MoSSe and WSSe, the strong excitonic effects can be attributed to the reduced screening between excited electrons and holes. It is worth noting that the mirror symmetry breaking will certainly cause the in-plane Rashba as well as the out-of-plane valley spin polarizations.49 In order to better address the band splitting in MoSSe, orbital-projected band structures at PBE level considering SOC are shown in Figures 1(d) and 1(e). It can be observed that the conduction band minimum (CBM) at the K point is composed of out-of-plane Mo-dz2 states, while the valence band maximum (VBM) is mainly contributed by in-plane Mo-dx2-y2 and Se-px states. It also can be observed that Mo-dz2 and S-pz states play a dominant role in the in-plane Rashba spin splitting in MoSSe occurred at the Γ point. The symmetry for MoSSe is trigonal C3v, which is different from the space group of monolayer MX2 (D3h) owing to this out-of-plane asymmetry I (I≠Z→-Z). The band splitting Hamiltonian can be written as ‫ ܪ‬ሺkሻ = ‫ݒ‬௞ ൫݇௫ ߪ௬ − ݇௬ ߪ௫ ൯ + ߣ௞ ሺ3݇௫ଶ −

݇௬ଶ ሻ݇௬ ߪ௭ , k = ඥ݇௫ଶ + ݇௬ଶ , ‫ݒ‬௞ = ሺ1 + ߙ݇ ଶ ሻ . Where ߙ , ߪ௜ and ߣ௜ are the Rashba parameter, Pauli matrices and the warping parameter, respectively. The first and the second terms bring out the in-plane and out-of-plane band splitting at Γ and K points, respectively, as indicated in Figures S3(a) and S3(b). Furthermore, the out-of-plane 6

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band splitting λc at CBM and λv at VBM, the relevant Rashba parameters such as Rashba energy ER, momentum offset kR and Rashba coefficient αR have been calculated though PBE+SOC and G0W0+SOC approaches, and the results are summarized in Table 1. kR and ER are the shift of bands in the momentum space and the energy difference of the split state at Γ point are indicated in Figure S3(b). The trigonal C3v symmetry induces net electric diploe moment acting on Mo atoms, which plays an important role in the out-of-plane valley band splitting. Importantly, the broken mirror symmetry is certainly to facilitate the Rashba term due to the existing of the electric polarity. As summarized in Table 1, it is concluded that WSSe shows larger out-of-plane band splitting ((λc/λv)) and in-plane Rashba effects due to the heavy W atoms. It is known that vdW heterostructures play a crucial role in the novel optoelectronic and photovoltaic applications, in light of their unique electronic and optical properties. In order to obtain the possible stacking pattern between MoSSe and WSSe, five VHTs of high symmetry are checked, as shown in Figure S4. After relaxation, the interlayer distance is in a range from 3.06 to 3.70 Å. The stability of these configurations can be estimated by the binding energy, which can be calculated according to the following equation: Eb=Et-EMoSSe-EWSSe, where Et, EMoSSe and EWSSe represent the total energies of VHTs, isolated MoSSe and WSSe, respectively. The one having the lowest binding energy among the five configurations is the AB stacking, in which the chalcogen atoms of MoSSe are directly above the W atoms of WSSe and the Mo atoms are located above the hexagonal hole position. Additionally, the dynamic stability of 7

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VHTs has been verified by phonon spectrum that the all branches over the entire Brillouin zone demonstrate positive frequencies, as show in Figure S6(c). Consequently, the most stable AB stacking model is used for following discussion about the VHTs, see also Figure 2(a). The planar average of the electrostatic potential energy and the charge density difference are displayed in Figure 2(b). In this case, work function difference increases to 1.1 eV, and Bader charge analysis suggests an interlayer charge transfer of about 0.02 e from WSSe to MoSSe. The charge density difference shows that charge depletion is mainly located on the Se atoms of WSSe, and charge accumulation mainly occurs within the interface region. As shown in Figure 2(c), band structure manifests an indirect band gap of 1.08 eV and a direct band gap of 1.23 eV at K point for VHTs. It clearly illustrates a type-II band alignment, which will result in the separation of electrons and holes. The band-decomposed charge density for VHTs is provided in Figures S5(a) and S5(b), which reveal that the VBM and CBM are mainly constricted on Mo and W atoms, respectively. As shown in S5(c), electron localization function (ELF) indicates that nearly no electrons are localized in the interlayer region, illustrating the weak vdW interactions in the VHTs. In Figure 2(d), the band alignment is schematically demonstrated to show the formation of interlayer excitons. In particular, excited electrons from WSSe migrate to MoSSe while holes go oppositely owing to the band offset (∆Ec=0.91 eV, ∆Ev=0.76 eV), and the electrons and holes can be held together by strong Coulomb interactions. It is worth noting that for VTHs of AB stacking, it illustrates obviously larger Rashba coefficient αR comparing with isolated MoSSe and 8

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WSSe monolayers due to the enhanced vertical electric field, as shown in Table 1. As displayed in Figures 2(e), the CBM at K point is mainly composed of in-plane Mo

dx2-y2 orbitals, while VBM at Γ point is determined by in-plane W dx2-y2 with the Rashba spin polarization. Interestingly, indirect-direct band gap transition can be found by adjusting the interlay distance. As shown in Figures S6(a) and S6(b), the position of VBM at Γ point gradually decreases while at K point increases, leading to a direct band gap at K point when the interlayer distance is larger than 3.86 Å. In contrast to the weak vdW interactions within the VHTs, interfacial covalent bonds make LHTs hold robust electronic and optical properties. It is most likely to realize the LHTs with the formation of 1D interlines along the zigzag direction,41-44 and there is no intrinsic strain due to almost the same lattice parameters of the constituent MoSSe and WSSe. In our calculations, rectangular superlattice models are used to construct the LHTs. The length of LHTs n is defined as the number of Mo or W rows and, for example, LHTs with n=9 is shown in Figure 3(a). In this case, the Brillouin zone for calculating band structure is a rectangular one, see Figure 3(b). It should be noted that the band gap of LHTs decreases as n increases. As shown in Figure 3(c), the band gap decreases by 0.06 eV as n increases from 3 to 9, indicating decoupled interactions between two interlines. In Figure 3(d), band structure along Γ-X direction is presented for n=9 LHTs since the decisive features are along this direction. It can be found that a direct band gap of 1.53 eV exists at a k-point located at approximate two thirds way from Γ to X. The formation energy Ef can be calculated according to Ef= (Et-ƩiNiµi)/N, with Et being the total energy of the LHTs, Ni and µi 9

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are the number and chemical potential of the ith atoms (i=Mo, W, S, Se), respectively, and N is the total number of the atoms in the heterojunctions. The chemical potential of metal is defined as the energy of a single atom in the bulk phase, while the chemical potential of chalcogen is referred to as the energy of a single atom in S8 (Se8) cluster. As n=9, Ef is -6.5 eV, which indicates the stability of the LHTs. In case of n=9, thermal stability by means of BOMD has been addressed and the result is shown in Figure S6(d), which reveals that the free energy oscillates slightly within a small range, further illustrating the stability. In addition, the electronegativity difference determines the strength connecting two constituents in LHTs. In Figure S7, the microscopy average of electrostatic potential indicates the difference between MoSSe and WSSe, and the Bader charge analysis also indicates the in-plane electric field pointing from MoSSe to WSSe. It is interesting that LHTs display type-II band alignment, with the CBM and VBM localized on MoSSe and WSSe, respectively, as shown in Figure 3(d). It is further confirmed by the charge densities of CBM and VBM, as indicated in Figures S5(e) and S5(f). As schematically plotted in Figure 3(e), ∆Ec of 0.23 eV and relatively small ∆Ev of 0.11 eV due to the hybridization between WSSe and MoSSe can be derived. As a consequence of the type-II band alignment, excitons generated near interlines could be separated into opposite sides. In short, in both cases of VHTs and LHTs, electron-hole separation has important significance for the conversion efficiency of solar energy in application in photovoltaics. In addition, the photo-responses with different polarization angle (θ) is also discussed to address the optical absorption ability for LHTs. In Figure 3(a), the 10

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schematic diagram for two probe devices is shown, in which the scattering region is illuminated by linearly polarized light. Upon illuminating, the excited electron-hole pairs propagate from the left anode to right cathode. The light polarization angle (θ) is defined as the intersection angle with y direction, in which y(e1) and z(e2) are set as the basis vector for the linearly polarized light. The absorption starts from 1.5 eV and the photo-response coefficient reaches 8 ܽ଴ଶ /photon (α0 stands for Bohr radius), which is much higher than the S-doped black phosphorus and the graphene p-n junction.50,51 Furthermore, Figure 3(g) shows a wide and intensive absorption in visible light range. It should be pointed out that defects are likely to appear during the growth of TMDCs. Especially, 60° grain boundaries (GBs) derived from chalcogen defects have been extensively discovered in TMDCs such as MoS2 and MoSe2.52,53 In the present work, we discuss the electronic characters of the 60° GBs for the Janus MoSSe. In Figure 4(a), the mostly observed 60° GBs in MoS2 and MoSe2 are presented for MoSSe. In our calculations, nanoribbons (NRs) models are adopted with the length

n=2, 5, 9 (n is defined as the number of Mo rows within half of the NRs), and the edges are terminated by Mo atoms. These NRs for 60° GBs display a slight bending due to the difference in the bond length of Mo-S and Mo-Se. The corresponding band structures are presented in Figures 4(b)-4(d), with the electronic contributions from the edge and boundary Mo atoms indicated by different colors. As n=2, strong interactions between the edge and boundary states can be seen, and the edge and boundary states turn to decouple when n increases to 5 and 9. As n increases from 5 to 9, therefore, change in band structures is small. It is of importance that, as unraveled 11

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in band structures with dispersive bands crossing the Fermi level, 60° GBs are characterized in metallic. As shown in Figure S8 of the charge density distribution near the Fermi level for 60° GBs (n=9), it further confirms the 1D metallic quantum wires. In this case, 1D electron or hole gas can probably be realized. It is of interest that, as n increases from 5 to 9, energy bands of edge Mo atoms shift upward, while those of the boundary Mo atoms shift downward. In other words, electrons will migrate from edges to the GBs as the length increases. This phenomenon results from the polar discontinuity, which leads to the potential difference between edge and GBs. In turn, the built-in in-plane electric field promotes electrons (holes) to migrate to the edge (GBs), giving rise to the 1D metallic wires within the instead semiconducting TMDCs.54 Further evidence for the electric filed induced by the polar discontinuity is presented in Figure 4(e), which displays the macroscopic average of the electrostatic potential energy ‫ݒ‬෤ (x). It is found that the slop of ‫ݒ‬෤(x) reduces while the potential energy difference ∆V increases as the length increases, which explains the presence of polarization charge.55 The formation of the 1D metallic GBs in electronic heterostructures of Janus TMDCs indicates great potential in electronic applications. In conclusion, many-body effects (e-e and e-h interactions) have been identified in Janus MoSSe and WSSe monolayers, that is, quasiparticle corrections strongly change the bands dispersion relationship and the excitonic effects dominate the optical response. VHTs and LHTs composing of Janus MoSSe and WSSe have been proposed in this work, bringing new properties and great potential in applications in such as electronics, spintronics and optoelectronics. In particular, both VHTs and LHTs 12

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illustrate type-II band alignment, which is beneficial to exciton dissociation and thus highly desirable for energy conversion. In case of VTHs, larger Rashba spin polarization can be expected due to the enhanced out-of-plane electric dipole in comparison to isolated single layers. In addition, interlayer charge transfer and tunable electronic properties are addressed in VHTs. In case of LHTs, a wide range visible absorption and appreciable photo-response intensity can be detected. It is interesting to find that 60° GBs in MoSSe show metallic properties, behaving as 1D metallic quantum wires and suggesting the formation of 1D electron or hole gas in such electronic heterostructures. These findings are of interest in exploring novel electronic, spintronic and optoelectronic nanodevices.

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (No. 11404187, 11374190 and 21333006), the Taishan Scholar Program of Shandong Province, and the Young Scholars Program of Shandong University (YSPSDU).

ASSOCIATED CONTENT Supporting Information Available: The computational details and the relevant electronic properties for MoSSe/WSSe and the vertical and lateral heterostructure. REFERENCES (1) Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L. J.; Loh, K. P.; Zhang, H. The Chemistry of Two-Dimensional Layered Transition Metal Dichalcogenide 13

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(11) Kou, L. Z.; Tang, C.; Zhang, Y.; Heine, T.; Chen, C. F.; Frauenheim, T. Tuning Magnetism and Electronic Phase Transitions by Strain and Electric Field in Zigzag MoS2 Nanoribbons. J. Phys. Chem. Lett. 2012, 3, 2934–2941. (12) Long, R.; Guo, M.; Liu, L. H.; Fang, W. H. Nonradiative Relaxation of Photoexcited Black Phosphorus Is Reduced by Stacking with MoS2: A Time Domain Ab Initio Study. J. Phys. Chem. Lett. 2016, 7, 1830–1835. (13) Ye, Z. L; Cao, T.; O'Brien, K.; Zhu, H. Y.; Yin, X. B; Wang, Y.; Louie, S. G.; Zhang, X. Probing Excitonic Dark States in Single-Layer Tungsten Disulphide.

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(18) Lin, Z.; Thee, M. T.; Elías, A. L.; Feng, S. M.; Zhou, C. J; Fujisawa, K.; Perea-López, N.; Carozo, V.; Terrones, H.; Terrones, M. Facile Synthesis of MoS2 and MoxW1-xS2 Triangular Monolayers. APL Mater. 2014, 2, 092514. (19) Lu, A. Y.; Zhu, H. Y; Xiao, J.; Chu, C. P.; Han, Y. M.; Chiu, M. H.; Cheng, C. C.; Yang, C. W.; Wei, K. H.; Yang, Y. M; et al. Janus Monolayers of Transition Metal Dichalcogenides. Nat. Nanotechnol. 2017, 12,744–749. (20) Zhang, J.; Jia, S.; Kholmanov, I.; Dong, L.; Er, D. Q.; Chen, W. B.; Guo, H.; Jin, Z. H.; Shenoy, V. B.; Shi, L.; et al. Janus Monolayer Transition-Metal Dichalcogenides. ACS Nano 2017, 11, 8192–8198. (21) Yao, Q.-F.; Cai, J.; Tong, W.-Y.; Gong, S.-J.; Wang, J.-Q.; Wan, X.; Duan, C.-G.; Chu, J. H. Manipulation of the Large Rashba Spin Splitting in Polar Two-Dimensional Transition-Metal Dichalcogenides. Phys. Rev. B 2017, 95, 165401. (22) Cheng, Y. C.; Zhu, Z. Y.; Tahir, M.; Schwingenschlögl, U. Spin-Orbit–Induced Spin Splittings in Polar Transition Metal Dichalcogenide Monolayers. EPL

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One-Dimensional Half-Metallic Interfaces of Two-Dimensional Honeycomb Insulators. Phys. Rev. B 2013, 88, 161411.

Table 1 Band gap Eg (eV), valence band splitting λkv (meV) at VBM, conduction band splitting λkc (meV) at CBM, momentum offset kR (Å-1), Rashba energy ER (meV), and Rashba parameter αR (eV Å). The Rashba coefficient can be expressed as αR = 2ER/kR.

Eg

VHTs

λkc

kR

ER

αR

(eV) (meV) (meV)

(Å-1)

1.47

170

13

0.005

1.4

0.53

G0W0+SOC 2.69

179

26

0.004

1.3

0.65

PBE+SOC

1.42

444

31

0.010

3.6

0.72

G0W0+SOC 2.59

478

33

0.007

2.5

0.71

PBE+SOC

0.61

446

14

0.005

3.1

1.22

G0W0+SOC 1.83

454

21

0.004

1.9

0.95

MoSSe PBE+SOC

WSSe

λkv

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(meV) (eV Å)

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Figure Captions Figure 1 Top and side views of MoSSe monolayer (a), and bond lengths are labeled. The planar average of electrostatic potential energy (navy line) and the planar average of charge density (red line) perpendicular to the MoSSe surface (b). Imaginary part of the macroscopic dielectric function of MoSSe monolayer from G0W0+BSE+SOC, A1 and B1 indicate the two low-energy bound excitons (c). Orbit-projected band structures of MoSSe near the Fermi level from PBE+SOC (d) and (e), the bigger the dot size is, the more the orbitals contribute to the wave functions at various k points, and the Fermi level is set to zero.

Figure 2 Side view of the VHTs composed of MoSSe and WSSe monolayers, the layer distance and the intralayer (I) and interlayer exciton (II) are denoted (a). Upper panel: planar average of electrostatic potential energy (navy line) and planar average of charge density (red line) of the VHTs composed of MoSSe and WSSe. Bottom panel: planar average of charge density difference of the VHTs composed of MoSSe 22

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and WSSe, and the inset shows spatial charge redistribution (b). Orbit-projected band structure of VHTs, and contributions from MoSSe and WSSe are distinguished by the peach and azure dot lines, respectively (c). The schematic diagram of the type-II band alignment, and the intralayer and interlayer exciton are denoted (d). Orbit-projected band structure of CBM (upper) and VBM (bottom) of the VHTs from PBE+SOC (e), the bigger the dot size is, the more the orbitals contribute to the wave functions at various k points, and the Fermi level is set to zero.

Figure 3 Atomic configuration of the LHTs composed of MoSSe and WSSe for the two probe device (a). Hexagonal and rectangular Brillouin zones (b). Variation of band gap as the length of LHTs changes (c). Orbit-projected band structure of n=9 LHTs, and the contributions from MoSSe and WSSe are distinguished by peach and azure dot lines, respectively (d), the bigger the dot size is, the more the orbitals contribute to the wave functions at various k points, and the Fermi level is set to zero. Schematic diagram of the type-II band alignment with band offsets denoted (e). Photo-response coefficient for n=9 LHTs (f). Absorption coefficient (g).

Figure 4 Side views of the 60° GBs in MoSSe with n=2, 5, 9 (a). Corresponding band structures of the MoSSe with 60° GBs as n=2 (b), n=5 (c) and n=9 (d), contributions from edge and boundary Mo atoms are indicated by azure and peach dot lines, respectively. The bigger the dot size is, the more the orbitals contribute to the wave functions at various k points, and the Fermi level is set to zero. Macroscopic average 23

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of the electrostatic potential energy (solid lines) along the direction perpendicular to the GBs for MoSSe with n=2 (green), n=5 (peach) and n=9 (azure), and the planar average of the electrostatic potential energy (dashed line) along the direction perpendicular to the GBs for MoSSe with n=9 (e).

Fig. 1

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Fig. 2

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Fig. 3

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Fig. 4

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