Intrinsic Electric Field-Induced Properties in Janus MoSSe van der

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Intrinsic Electric Field Induced Properties in Janus MoSSe van der Waals Structures Fengping Li, Wei Wei, Hao Wang, Baibiao Huang, Ying Dai, and Timo Jacob J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03463 • Publication Date (Web): 18 Jan 2019 Downloaded from http://pubs.acs.org on January 21, 2019

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The Journal of Physical Chemistry Letters

Intrinsic Electric Field Induced Properties in Janus MoSSe van der Waals Structures

Fengping Li,1 Wei Wei,*,1 Hao Wang,1 Baibiao Huang,1 Ying Dai*,1 and Timo Jacob*,2

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School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

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Institute of Electrochemistry, Ulm University, Albert-Einstein-Allee 47, D-89081 Ulm, Germany

Corresponding authors: [email protected] (W. Wei) [email protected] (Y. Dai) [email protected] (T. Jacob)

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ABSTRACT Focusing on two-dimensional (2D) Janus MoSSe monolayers, we show that simultaneously existing in-plane and out-of-plane intrinsic electric fields causes Zeeman- and Rashba-type spin splitting, respectively. In MoSSe van der Waals (vdW) structures, intrinsic electric field results in a large interlayer band offset. Therefore, large interlayer band offset being the driving force for interlayer excitons endows ultra-long lifetimes to excitons and might dissociate excitons into free carriers. In comparison to its parent structure (i.e. MoS2) MoSSe vdW structures are rather appealing for new concepts in light–electricity interconversion. In addition, the Rashba effects could be tuned by changing the interlayer distances, due to the competition between intralayer and interlayer electric field. Due to the large band offset, valley polarization relaxation is markedly reduced, promising enhanced valley polarization and ultralong valley lifetimes. As a result, MoSSe vdW structures harbor strong valley-contrasting physics, making them competitive systems to their parent structures.

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In transition-metal dichalcogenides (TMDCs) MX2 (M=Mo, W; X=S, Se) directindirect band gap transition can be observed when moving from monolayers to multilayers or even the bulk phase. This behavior stems from the interlayer hybridization between the p orbital of components X and the d orbital of the metal atoms M.1-4 Combining this property with the weak van der Waals (vdW) interactions between the different sheets in layered TMDCs provides a fascinating platform for developing functional materials with new exciting phenomena.5-9 For instance, vdW heterostructures of type MX2 show an ultrafast transfer of interlayer excitons and accelerated photocurrent generation, effects caused by the spatially indirect geometry and type-II band alignment in these materials. This paves the way for applications in light emitting devices, solar cells and for light harvesting.10-13 It is widely accepted that the stacking sequence and twist angle between the monolayers strongly affect the electronic properties and the interlayer excitation transition within the vdW TMDCs.14-17 In addition, novel physical effects are also related to the stacking pattern, for example, valley-dependent spin polarization can be realized by varying the stacking sequence in MX2 bilayers (BLs) and trilayers (TLs).18-20 It is therefore conclusive that the interlayer coupling plays a crucial role in determining the electronic and optical properties of layered TMDCs. Recently, a new member to the family of 2D TMDCs, i.e. Janus MoSSe, has been successfully realized and draws increasing attention.21,22 It is reasonable that Janus MoSSe could inherit the unique electronic and optical properties of MX2 due to similarities in structure and chemical composition. It has been demonstrated that, for 3



instance, excitonic effects dominate the optical absorption of MoSSe, while a type-II band alignment has been predicted for MoSSe/WSSe bilayers.23 Regarding MoSSe, however, the very appealing feature is the intrinsic vertical electric field accompanied with its mirror asymmetry.21,22 In a MoSSe monolayer the vertical electric field causes a Rashba spin splitting, opening up new avenues for spintronics.24,25 Further, in these monolayers as well as MoSSe multilayers the vertical dipole moment leads to piezoelectric effects, which could be improved by a uniaxial or biaxial strain.26 In addition, valley polarization can be realized by magnetic doping, harboring an intriguing multi-valleyed band structure and strong spin-contrasting physics.27 In analogy to MX2 vdW structures, the stacking pattern and the interlayer coupling in MoSSe multilayers will have substantial influence on the overall properties. Therefore, the stacking-dependent electronic and optical properties are of crucial interest because of the mirror asymmetry of MoSSe monolayers. It could be expected that layered MoSSe vdW structures will bring peculiar electronic and optical properties due to the distinct interlayer interactions, opening up unprecedented opportunities for applications in optoelectronics and spin-valleytronics. Fundamental Properties of MoSSe vdW Structures. Figure 1a shows the structure of the Janus MoSSe monolayers, where Mo atoms are coordinated with S and Se atoms forming trigonal prisms with mirror asymmetry. This structure results in a net vertical electric field pointing from Se to S. In case of the simultaneous presence of an out-of-plane (𝑃" ) and in-plane (𝑃∥ ) electric dipole moments, in-plane Rashba-

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Figure 1 MoSSe monolayer (ML) and bilayers (BLs) structures as well as the Brillouin zones for MoSSe BLs. a Coordination structure of MoSSe ML, the dipole moments pointing from S (Se) to Mo are denoted as 𝑃$%&' (𝑃$(%&' ), the net in-plane (out-of-plane) dipole moments are indicated as 𝑃∥ (𝑃" ). b and c Schematics of Rashba and Zeeman-type valley spin splitting induced by out-of-plane and in-plane electric fields, respectively. d Schematic indicating how to obtain the 2H and 3R stacking orders from MoSSe ML, with the folding lines perpendicular and parallel to the mirror plane (MP), respectively. e and g Side views of AA′ (2H) and AA (3R) MoSSe BLs. f and h Illustration of first hexagonal Brillouin zones of 2H and 3R stacking orders, with spin configurations labeled. In 2H and 3R stacking orders, the Brillouin zone of upper ML is rotated 180º and 0º degree with respect to that of bottom ML, respectively.

type (α* ) and valley (λ,- ) spin splitting occur in MoSSe monolayer (as shown in Figures 1b and 1c). With respect to MX2 vdW structures,12,18 the observed stacking patterns are 2H (space group: P63/mmc) and 3R (space group: R3m). In accordance with the MX2 counterparts, we also adopt the 2H and 3R stacking orders in MoSSe vdW BLs and TLs. As for MoSSe BLs, five typical stacking orders with S/Se interface configurations are primarily taken into account:28 A′B, AA′ and AB in 2H pattern, and AB′ and AA in 3R phase. As shown in Table S1, total energy indicates that A′B and AA stacking orders are less stable than AA′, AB′ and AB stacking orders. 5



In experiments, however, these five stacking orders of MX2 could be obtained from the twisted MX2 BLs.14 Moreover, the valley and band structure engineering and second harmonic generation have also been realized in less stable AA MoS2.29,30 In order to clearly demonstrate the tunable Rashba effects and valley polarization via different stacking orders, MoSSe BLs of 3R stacking orders are also chosen for discussion. Figures 1e and 1g show the AA′ and AA stacking orders, while the other configurations are presented in Figure S1 (Supporting Information, SI). In particular, the origami rule can be used as reference for the 2H and 3R stacking orders. As illustrated in Figure 1d, the folding line of 2H stacking is perpendicular to the mirror plane, while that of 3R stacking is parallel to the mirror plane. As a result, 2H and 3R stacking orders correspond to 180º and 0º rotation of one of the monolayers with respect to the other one.29 Figures 1f and 1h show the first hexagonal Brillouin zones for 2H- and 3R-stacked MoSSe BL with 180º and 0º rotation. In contrast to 2H (Bernal stacking) MX2 BLs with inversion symmetry, both 2H- and 3R-stacked MoSSe configurations show the inversion asymmetry due to the net vertical intrinsic electric field. Consequently (as will be discussed later), in layered MoSSe valley contrasting properties can be expected, being promise for new aspects in spin/valley physics.

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Figure 2 Band structures and corresponding band alignments of MoSSe BLs and TLs. a and c Layer-projected band structures of AA (3R) MoSSe BL and 2H/2H-1 MoSSe TL, respectively. Red (LB), brown (LM) and blue (LT) dots represent contributions from bottom, middle and top layers, respectively. The insets are amplified valence band dispersions near Γ point, revealing the Rashba spin splitting. b and d Band alignments of 3R (AA) MoSSe BL and 2H/2H-1 MoSSe TL. ΔEV (ΔEV1, ΔEV2) and ΔEC (ΔEC1, ΔEC2) indicate the band offsets between two adjacent monolayers. The dashed ellipses demonstrate the interlayer exciton.

Figure 2a shows the layer-decomposed band structure of MoSSe BLs with AA stacking, while those for the other configurations can be found in Figure S2. As for these five MoSSe vdW stacks (see above), typical type-II band alignment can be found. As in MX2 heterobilayers, interlayer excitons (or charge transfer excitons) can be realized by virtue of the type-II band alignment in MoSSe homobilayers, as schematically depicted in Figure 2b. As shown in Figure S3, the partial charge density distributions for the valence band maximum (VBM) and conduction band minimum (CBM) at the Γ and K points confirms a type-II band alignment of the AAstacked MoSSe BL, which means VBM and CBM are located on opposite layers. In the case of type-II band alignment, excited electrons and holes will be separated into different monolayers, further the spatially indirect character of the excitons can largely reduce the rate of recombination. Consequently, MoSSe BLs deserve thorough considerations as photoelectric devices e.g., solar cells. As summarized in Table S1, it 7



is of importance that MoSSe BLs show a significantly larger band offset, which is the driving force for long-lived interlayer excitons (e.g., ΔEC = ΔEV = 0.62 eV for the AAstacked bilayer system). In contrast, for MX2 homobilayers the band offset is usually small, e.g., about 60 meV for VBM and CBM in MoS2 bilayers of 3R stacking while negligible in case of 2H stacking.31 Figure S4 shows the planar-average potential energy for stacked MoSSe BLs, revealing a large work function change (e.g., 1.1 eV for AA-stacked MoSSe BL) between both vacuum levels. In turn, the resulting work function change will give rise to an out-of-plane dipole moment according to Helmholtz’s equation. The vertical dipole moment (0.4 Debye for all stacking orders) is in fact a superposition from both individual MoSSe monolayers. Therefore, distinct larger band offset can be observed in MoSSe BLs as a result of the large interlayer vertical dipole moment, as further discussed later. In both AA- and A′B-stacked MoSSe BLs pronounced direct band gaps can be observed. As shown in Figure 2a as well as Figure S2, the direct band gap appears between the KV and KC points, while the indirect band gap (for AA′-, AB′- and ABstacked MoSSe BLs) arises between the ΓV and KC points. ΓV, KV and KC points are denoted in Figure 2a, and orbital contributions (in percent) to these points are summarized in Table S2. For all considered MoSSe BLs stacking orders, ΓV is mainly composed of out-of-plane orbitals (𝑑/ 0 of bottom Mo atoms and 𝑝/ of bottom S atoms), KV is dominated by in-plane orbitals (𝑑23 and 𝑑2 0 %3 0 of bottom Mo atoms), while KC is dominated by the 𝑑/ 0 orbitals of top Mo atoms. Figures S5a and S5b show the orbital-resolved band structures for the AA-stacked system, and Figure S3a 8


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displays the partial charge density at the ΓV point of the AA-stacked system, indicating the dominating contributions of the 𝑑/ 0 orbitals of the bottom Mo atoms (71%) and 𝑝/ orbitals of bottom S atoms (13.2%). According to the data summarized in Table S2, it is conclusive that changing the stacking order hardly influences the in-plane orbital contributions at KV (i.e. 𝑑23 and 𝑑2 0 %3 0 orbitals). In comparison to AA- and A′B-stacking orders, however, for AA′-, AB′- and AB-stacked bilayers the orbital contributions at ΓV (i.e. 𝑑/ 0 and 𝑝/ orbitals) decrease due to the apparent difference in interlayer distance. In particular, interfacial chalcogen atoms in AA- and A′B-stacked systems are aligned vertically, leading to a strong Coulomb repulsion between chalcogen atoms and therefore large interlayer spacing (3.7 Å for AA- and A′B-stacked systems, while 3.2 Å for AA′-, AB′- and AB-stacking orders, as listed Table S1). As a result, increased contributions from 𝑑/ 0 and 𝑝/ orbitals lower the band behavior at ΓV, which leads to the direct band gap in AA- and A′B-stacked MoSSe BLs. In other words, as a consequence of a weakened interlayer coupling in MoSSe BLs features of the band edge are approaching the behavior observed for the isolated monolayers. Rashba Effects in MoSSe vdW Structures. As a consequence of vertical stacking, MoSSe BLs undergo a breakage of inversion symmetry. It is of interest that, nevertheless, the Rashba effects only occur in AA- and A′B-stacked systems (see the insets in Figure 2a and Figure S2). The description of the Rashba and valley band splitting is provided in Note S1 (taking AA stacking with local k-space symmetry C3v at Γ point as an example). The Rashba strength is mainly controlled by the net vertical 9



electric field acting on the metal atoms, and can be described by the BychkovRashba.32,33 It is reasonable that the out-of-plane orbital (𝑝/ ) overlap between interfacial S and Se atoms will influence the Rashba effects. In order to confirm this, the Rashba coefficient (defined as 𝛼* =

2𝐸* 9𝑘 , with 𝐸* and 𝑘* being the Rashba *

energy and momentum variation, respectively, see Fig. 1b) is calculated for these MoSSe BLs with variable interlayer distance. In the cases of AA- and A′B-stacking orders, the Rashba coefficient increases as the interlayer distance increases from their equilibrium distance (3.7 Å) (see Figure 3a). As the interlayer distance is larger than 5 Å, moreover, the Rashba coefficient will reach about 0.5 eV·Å, close to that of MoSSe monolayer. In this case, the overlap between the relevant atomic orbitals can be indeed neglected. For interlayer distances smaller than 3.7 Å (but larger than the intralayer S–Se vertical distance of 3.2 Å), however, Rashba effects disappear. This can be explained from the relationship between the vertical orbital overlap of S/Se atoms and the interlayer distance. In AA- and A′B-stacked systems, the overlap between the out-of plane 𝑝/ orbitals of interface S/Se atoms increases as interlayer distance decreases. In turn, the dipole moment pointing from top layer Se to bottom layer Mo decreases and compensates the dipole moment pointing from S to Mo in bottom layer. As a result, the net vertical electric field acting on bottom layer Mo vanishes.

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Figure 3 Rashba effects in MoSSe BLs. a Variation of the Rashba coefficient along with interlayer distance for MoSSe BLs of different stacking orders. b Variation of net vertical dipole moment in AA (3R) MoSSe BL as the interlayer distance (d) changes. c Variation of the local structure in MoSSe under compressive and tensile strains. d The valence band structures near Γ point with Rashba coefficient under strain of -4% – 4% for AA (3R) MoSSe BL. e Valence band splitting (lkv) under strain of -4% – 4% for AA (3R) MoSSe BL.

The Figure 3b shows the variation of the net vertical electric field acting on the Mo atoms in the AA-stacked system with changing interlayer distances (the behavior for A′B-stacking order is similar). As the interlayer distance decreases further, the direction of the net vertical electric field on Mo reverses due to the enhanced 𝑝/ overlap and the Rashba effects come into play again. Figure 3a clearly confirms this behavior for AA- and A′B-stacked systems (the interlayer distance is smaller than 3.2 Å). The explanation summarized above also holds true for MoSSe BLs of AA′-, ABand AB′-stacking orders, which becomes apparent by the Rashba effects as the 11



interlayer distance exceeds 3.7 Å due to reduced interlayer interactions (see Figure 3a). As the interlayer distance decreases, interactions between Mo 𝑑/ 0 orbitals and interfacial S 𝑝/ orbitals become dominating, as the interfacial S/Se 𝑝/ coupling. In this case, improved 𝑑/ 0 /𝑝/ and 𝑝/ /𝑝/ interactions suppress the net electric fields on Mo atoms and consequently Rashba spin splitting is absent. This behavior is shown in Figure 3a, showing zero Rashba coefficients for MoSSe BLs of AA′, AB and AB′ stacking orders. It is indicative that the interlayer atomic registry and the interlayer coupling strength play important role for Rashba effects, which can be tunable by stacking orders as well as interlayer distance. It can be expected that in-plane strain can also affect Rashba spin splitting, since the strain directly influences the net electric field acting on Mo atoms. Figure 3c shows the configurational changes in a MoSSe monolayer being influenced by an auxiliary strain, which provides an explanation for the variation of the Rashba effects. This supposition is confirmed in Figure 3d, where the variation of 𝛼; at ΓV as a function of the biaxial strain applied on the AA-stacked systems becomes apparent. In case of a compressive strain of –4%, a significantly large 𝛼; of 1.28 eV·Å can be obtained. As the strain increases to 2%, Rashba effects disappear. In comparison, under compressive strain an increased overlap between 𝑑/ 0 and 𝑝/ states leads to enhanced net vertical electric fields at the Mo atoms. In contrast, decreased out-ofplane orbital overlap due to the tensile strain will reduce the net vertical electric field experienced by Mo atoms, resulting in an absence of Rashba effects. It is therefore conclusive that in-plane strain provides an effective way to tune Rashba effects in 12


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MoSSe monolayer and layered structures. As a consequence of an auxiliary strain, the in-plane electric field will also be tuned and thus the valley splitting at band edges. This is confirmed by the VB splitting (λ,- ) at the K point, which increases when raising the strain from -4% to 4% (see Figure 3e). Valley-Contrasting Physics in MoSSe vdW Structures. In MX2 monolayers, local C3 symmetry at K/K′ point and the symmetric valence/conduction bands with respect to the mirror plane that contains the M atoms (hence the excitonic transitions between the VB and the CB are symmetry allowed) result in the valley-dependent optical selection rules for interband band transitions, enabling the possibility in spinvalleytronics applications.34-36 In natural, MX2 BLs of Bernal stacking with inversion symmetry, however, valley and spin polarizations are not achieved or negligible, which can be attributed to the strong interlayer hopping due to the small interlayer band offset. In order to obtain a large degree of polarization, strategies such as magnetic field,37 external electric field38 and structure symmetry engineering18,39 are adopted in MX2 BLs and/or heterobilayers, aiming at suppressing the valley mixing. However, challenges still exist, among which the relatively short valley lifetime is dominating.40 In different stacking orders, S-Se interfaces of MoSSe BLs will break the inversion symmetry. As shown in Table S1 spin–orbit coupling (SOC) leads to Zeeman-type spin splitting at KV and K′V in the order of approximately 170 meV for both constituent MLs. In Figure 4a and Figure S6a, the spin-resolved band structures indicate that for 3R-stacking the sign of valley-specific spin could be preserved in top 13



and bottom layers, but reversed in case of 2H stacking, with the spin polarization being almost 100%. As indicated in Figure 4b, the Berry curvature Ωz(k) shows obvious difference for 3R (AA, C3v) and 2H (AA′, C6v) stacking orders due to different symmetry. The result is similar with the case of MoS2 BLs, in which the interlayer contribution results in stacking dependence of the Berry curvature in 2H and 3R MoS2 BLs.31 As for the 3R MoSSe BL, Ω= (𝑘) can be as large as 128.4 Bohr2 (almost two times the Berry

Figure 4 Valley polarization in MoSSe BLs. a Spin-resolved band structure of AA (3R) MoSSe BL. Spin-up and spin-down states are presented by blue and red, respectively. b Berry curvature of the states in AA (3R) MoSSe BL along high symmetry lines (top) and in 2D k-plane (bottom). c Schematic of the interlayer valley exciton in AA (3R) MoSSe BL. Circularly polarized light are shown as 𝜎 A (right-handed) and 𝜎 % (left-handed). The spin-up and spin-down states are denoted by blue and purple. The vertical arrows indicate intralayer excitons and interlayer hopping is denoted by the black arrows. The dashed ellipses illustrate the interlayer valley polarization excitons.

curvature of MoSSe MLs of 63.9 Bohr2) at K and K′ points with opposite sign. The Berry curvature of the 2H-stacked MoSSe BL is shown in Figure S6b, indicating a negligible but nonzero value (1 Bohr2) due to the absence of inversion center. As a result, both electrons and holes that are excited by circularly polarized light will have 14


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an intrinsic concurrent contribution to the Hall conductivity or magnetization.35 Figures 1f and 1h schematically illustrate the spin configurations in typical 2H and 3R-stacked MoSSe, respectively. In MoSSe BLs, the valley-locked spin-up and spindown carriers can be selectively excited by right- (𝜎 A ) and left-handed (𝜎 % ) circularly polarized light, respectively, forming valley interlayer excitons as demonstrated in Figures 4c and S6c. In the light of large momentum mismatch at K and K′, intervalley hopping can probably be strongly inhibited, while intra-valley hopping of interlayer exciton turns out to be the dominant relaxation channel. In the case of 3R stacking, the spin is valley-locked, while the interlayer hopping is less effective in the 2H-stacked system due to the spin flip (spin-layer locking effects). As a consequence of this spin-valley locking behavior, valley polarization could be detected in all of the MoSSe BLs with different stacking orders, enriching the interaction of internal degrees of freedom including the spin and valley pseudospin of electrons and holes confined in different MLs. In consideration of the coupling of spin, valley as well as layer pseudospin degrees of freedom, spin/valley polarization can be realized at K (K′) in these proposed MoSSe BLs. It should be emphasized that the large band offset in both 2H and 3R-stacking orders (caused by the intrinsic vertical electric field) will more effectively separate the excited electrons and holes. Consequently, one might expect valley interlayer excitons with extended lifetimes. In this case, the valley polarization relaxation processes such as radiative recombination and exchange interactions should be markedly suppressed. Therefore, in comparison to native MX2 systems, MoSSe vdW structures could be 15



more appropriate candidates for valley-contrasting physics and valleytronics. Regarding MoSSe trilayers (TLs), six stacking orders are considered on the basis of MoSSe BLs (see Figure S7). In these TLs, direct band gaps (between KV and KC) and Rashba effects can be found in 2H/2H-1, 2H/3R-1 and 3R/3R-1 stacking orders, while indirect band gaps (between ΓV and KC) and no Rashba effects in 2H/2H-2, 2H/3R-2 and 3R/3R-2 stacking orders (see Figure S8 and Note S2). It is of importance that MoSSe TLs can realize a step-like band alignment with a large band offset (as large as approximate 0.6 eV for all considered stacking orders, see Table S4), as schematically illustrated in Figures 2c and 2d. In this case, excited electrons can be promoted into the top layer with holes staying in the bottom layer, that is, the excitons are spatially separated by the central layer. Further, the reduced exciton binding energy will lead to extended exciton lifetimes. In a recent work,41 such a step-like band alignment has been demonstrated experimentally in MX2 vdW heterostructures, although with relatively small interlayer band offset. In the presence of large band offsets induced by the intrinsic electric field, the bound excitons may dissociate into free charge carriers. As a result, the MoSSe vdW structures conceal tremendous potential for applications in photovoltaics and light harvesting, for example, as well as new physical phenomena like Bose-Einstein condensation42 and superfluidity.43 It is worth mentioning that in MoSSe TLs with different stacking orders diverse interlayer valley polarization exciton formation and relaxation mechanisms could be imagined, as demonstrated in Figure S10. It is expected that the vertical dipole moment will cancel each other if the BLs have 16


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the S–S or Se–Se interface. As a consequence of a net zero dipole moment in total (or zero work function change), the band offset between two MLs should vanish, which can be seen in the band structures and potential energies shown in Figure S11 as well as Table S5. It can also be inferred that the Berry curvature will vanish on account of the simultaneous presence of inversion and time reversal symmetries. As indicated in Figure 5 and Table S5, the eliminated band offset due to the zero vertical dipole moment is also occurring in MoSSe TLs, i.e., 3R/3R-I (Se–S and Se–Se interfaces), 3R/3R-II (Se–Se and S–S interfaces) and 3R/3R-III (Se–Se and S–Se interfaces). It clearly demonstrates that the vertical net electric field in MoSSe vdW structures plays a significant role in the large band offset driving the formation and transfer of interlayer excitons. It is reasonable to imagine that the above results could be applied in other Janus-type MXY (M=Mo, W; X, Y=S, Se, Te) counterparts. In these cases, interlayer band alignment turns out to be tunable by selecting constituent MLs to promote interlayer exciton formation, hopping and dissociation, to finally obtain the desired Rashba and spin-valley splitting properties.

Figure 5: Band structures and band alignments of MoSSe TLs. a, b and c: 3R-3R-I, 3R-3R-II, 3R-3RIII stacking orders, respectively.

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All first-principles calculations were performed on the basis of density functional theory (DFT) as implemented in the Vienna Ab Initio Simulation Package (VASP).44,45 The electron exchange correlation was treated with the Perdew–Burke– Ernzerhof (PBE) in the framework of generalized gradient approximation (GGA).46 The DFT Kohn–Sham equations were resolved by the projector augmented wave (PAW) through the plane wave basis set. The cutoff energy of 500 eV was chosen for plane-wave expansion of wave functions and Monkhorst–Pack (MP) scheme for kpoint sampling was employed for the integration over the first Brillouin zone.47 The 13×13×1 k-point mesh was used for 1×1 MoSSe cells and other van der Waals structures. They were relaxed until the atomic forces on each ionic were less than 0.01 eV/Å-1 and the electron relaxation convergence criterion was 10-4 eV in two consecutive loops. In order to mimic the isolated layers, a vacuum space was set to 25 Å. In order to correctly describe the band edge splitting, SOC effects are considered, which roots in the heavy 4d states of Mo atoms. In order to cover dispersive interactions, DFT-D2 vdW corrections are included.48,49

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (No. 51872170 and 21333006), the Taishan Scholar Program of Shandong Province, the Young Scholars Program of Shandong University (YSPSDU), and the 111 project (B13029). This work was funded by the Deutsche Forschungsgemeinschaft DFG (TRR234 “CataLight“, Projects A5 and B6). 18


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Intrinsic Electric Field-Induced Properties in Janus MoSSe van der

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