Tunable electronic structures, Rashba splitting, and optical and photocatalytic responses of MSSe-PtO2 (M = Mo, W) van der Waals heterostructures

Binding energies, AIMD simulation and phonon spectra confirm both the thermal and dynamical stabilities of model-I and model-II of MSSe-PtO2 (M = Mo, W) vdWHs. An indirect type-II band alignment in both the models of MSSe-PtO2 vdWHs and a larger Rashba spin splitting in model-II than in model-I provide a platform for experimental design of MSSe-PtO2 vdWHs for optoelectronics and spintronic device applications. Transfer of electrons from the MSSe layer to the PtO2 layer at the interface of MSSe-PtO2 vdWHs makes MSSe (PtO2) p(n)-type. Large absorption in the visible region of MoSSe-PtO2 vdWHs, while blue shifts in WSSe-PtO2 vdWHs are observed. In the case of model-II of MSSe-PtO2 vdWHs, a further blue shift is observed. Furthermore, the photocatalytic response shows that MSSe-PtO2 vdWHs cross the standard water redox potentials confirming their capability to split water into H+/H2 and O2/H2O.


Introduction
Although the rst 2D Janus material is graphone prepared using graphene through hydrogenation via DFT, 1,2 Lu (Zhang) et al. 3,4 have selenized (sulfurized) MoS 2 (MoSe 2 ) through the chemical vapor deposition (CVD) technique and named the resultant product MoSSe with MXY (M = Mo, W; (X s Y) = S, Se) as the general formula.The space group of MoS 2 is D 3h which also changed to C 3v for MXY monolayers with broken symmetry. 5,6][10] Employing many-body Green's function perturbation theory, substantial excitonic effects are exhibited in the MoSSe monolayer used in optoelectronic devices. 11ecently, Paul et al. 12 studied Janus PtXY (X, Y = S, Se, or Te) and observed that Rashba splitting is around the M point.They also investigated whether the band gaps and the strength of the Rashba effect could be further tuned through biaxial strain.
Another 2D material, PtO 2 , produced by exfoliation from bulk a-PtO 2 , survives at high temperature with better thermomechanical stability and superior optical absorption and carrier mobility. 37,38The PtO 2 monolayer has been shown to be very closely matched with TMDCs to form vdWHs. 38 It has been shown that PtO 2 -MoS 2 (ZnO-PtO 2 ) vdWHs with indirect (direct type-II) band alignment can be used in photocatalysis (photodetector) applications. 38,39Experimentally synthesized Ni(OH) 2 -PtO 2 nanostructured arrays indicate enhanced hydrogen evolution reaction. 40ndeed, the small lattice mismatch, identical symmetry and high energetic feasibility of MSSe (M = Mo, W) and PtO 2 led to the design of MSSe-PtO 2 vdWHs.Two models of MSSe-PtO 2 (M = Mo, W) vdWHs with four possible stacking congurations based on two different chalcogen atoms are fabricated.Both models of MSSe-PtO 2 vdWHs with specic conguration are energetically, dynamically and thermally stable at 300 K. Furthermore, a detailed study is conducted to explore the electronic structure, Rashba spin splitting, work function, and optical and photocatalytic properties of the most stable congurations.Interestingly, we observed type-II band alignment in both models with considerable Rashba spin parameters and good photocatalytic response.These ndings raised potential applications of MSSe-PtO 2 vdWHs in nanoscale electronics, photovoltaics and photocatalysis.

Computational details
DFT with Grimme 41 correction, a cut-off energy of 500 eV, a convergence criteria of 10 −3 eV Å −1 (10 −4 eV) for forces (energy), a k-mesh of 6 × 6 × 1 (12 × 12 × 1) and the PBE 42 functional in the VASP 43,44 are used for geometric relaxation (electronic structure calculations).Starting with converged PBE wave functions, the HSE06 functional 45 without rening the kmesh is also used for electronic band structure calculations.A 20 Å vacuum layer (to prevent the artifacts of the periodic boundaries along the z-axis) and the effect of SOC are also considered. 46Furthermore, using HSE06 wave functions, the Bethe-Salpeter equation was solved in the GW 0 approach to study the imaginary part of the dielectric function. 47IMD 48 were performed using the Nose thermostat algorithm (with 300 K and a 1 fs time interval) to investigate the thermal stabilities of the above mentioned vdWHs.Dynamical stability of these systems was investigated by using density functional perturbation theory in the phonopy code, in which the harmonic interatomic force constant is used as the input 49,50

Results and discussion
In agreement with ref. 51 and 52, optimized lattice constants (MoSSe ∼ 3.25 Å, WSSe ∼ 3.26 Å and PtO 2 ∼ 3.17 Å) and bond lengths (M-S ∼ 2.411 Å, M-Se ∼ 2.39 Å and Pt-O ∼ 2.31 Å) show the reliability of our computational approach.MSSe and PtO 2 have the same hexagonal lattice symmetry with a small and experimentally achievable lattice mismatch (MoSSe-PtO 2 ∼ 2.46% and WSSe-PtO 2 ∼ 2.27%), showing the possibility for experimental fabrication of vdWHs based on MSSe and PtO 2 monolayers, i.e., MSSe-PtO 2 (M = Mo, W). 53 As the interfacial properties are very sensitive to the layer congurations and connected atoms at the interface of vdWHs, in the case of the MSSe monolayer, two chalcogen atoms (S and Se) that terminate the surface are available for making vdWHs with the PtO energy and small interlayer distance, which shows higher energetic stability and strong physical and vdW interaction between MSSe and PtO 2 layers.Slightly small vertical distances and high energetic feasibilities in model-II are due to the larger covalent radius of Se than the S atom at the interface which results in more attractive energy by making these stacking congurations, see Table 1.A small lattice mismatch induces minor strain in the corresponding monolayers (compressed Pt-O, while stretched M-S and M-Se bond lengths) of MSSe-PtO 2 vdWHs, in agreement with ref. 26.
AIMD simulations for the most stable stacking conguration ((a) stacking) of MoSSe-PtO 2 vdWHs in model-I, in Fig. 2(a), show a small variation in the total energy, while no distortion was found in the structure aer 6 ps, hence conrming the thermal stability at 300 K.The phonon band structure of the same vdWH for model-I, in Fig. 2 1.It is important to address that a R for MSSe-PtO 2 vdWHs is smaller than that of the corresponding isolated monolayer, 26 which may be due to the intrinsic electric eld. 55 1 for model-I and model-II, differentiate the excitonic behavior of free-standing monolayers from the corresponding vdWHs, which helps promote photogenerated carrier (electrons and holes) separation.Quantitative charge transfer is also investigated by Bader charge analysis, which shows that about 0.086e (0.097e) and 0.075e (0.91e) are transferred from the MoSSe and    .High (smaller) carrier mobility (effective mass) is preferable for electronic and optoelectronic devices. 57From Table 1 it's clear that WSSe-PtO 2 (M-I) has miniaturized effective masses, hence sponsors high charge carrier mobility, and therefore, shows good response towards high performance device applications. 57e have further explored the optical response of MSSe-PtO 2 vdWHs in terms of 3 2 (u), directly associated with the band structure and the bandgap values, 58,59 shown in Fig. 7.The optical absorption range for MoSSe and WSSe monolayers is about 2 to 5.0 eV, 27 while for Mo(W)SSe-PtO 2 vdWHs in model-I and model-II it is from 2.5 (3.0) to 7.0 (8.0) eV.Broader absorption in the visible region of MoSSe-PtO 2 than WSSe-PtO 2 vdWHs is due to the smaller bandgap of the former, while a blue shi is observed in the latter.A further blue shi in model-II than in model-I of MSSe-PtO 2 vdWHs may be due to the selective atom of chalcogen atom at the interface.Although there is a blue shi in the absorption spectrum of MSSe-PtO 2 vdWHs from model-I to -II, the qualitative behaviour of the peak is similar for both models.High optical absorption requires a wide range peak, which may occupy a large number of states near the Fermi level.Broadened optical absorption of vdWHs is due to high carrier density (compared to parent monolayers). 60Obviously, the fabrication of vdWHs is an effective way to understand the modulation of absorption performance of 2D layered materials.We predict that MoSSe-PtO 2 vdWHs for model-I (-II) have good optical absorption in visible regions, which makes them suitable for practical applications in nanoelectronics and optoelectronic devices. 61n photocatalytic activity, illumination of solar light on semiconductors separates charge carriers in conduction and valence bands.Using Mulliken electronegativity (c) 62 and standard electrode potential on the hydrogen scale (E elec = 4.5 eV), energies of

Conclusion
In summary, using rst principles calculations, electronic structures, Rashba splitting, and optical and photocatalytic Fig. 1 Model-I; stacking configuration of MSSe-PtO 2 vdWHs.
(b), is free from imaginary frequency, hence conrming the dynamic stability of MSSe-PtO 2 (M = Mo, W) vdWHs.Similar trends were also found for other vdWHs in both model-I and model-II.Generally, in DFT, the choice of the functional (conventional or hybrid) affects the band structure and bandgap values.Therefore, we have used both PBE and HSE06 functionals to calculate the electronic band structure of MSSe-PtO 2 vdWHs, see Fig.3.In both models, the VBM (CBM) is pinned at the K (M-G)-point of the rst BZ and hence reveals the indirect bandgap nature of MSSe-PtO 2 vdWHs.The bandgap values calculated by the HSE06 method are larger than those obtained by the calculations at the PBE level, which are further decreased by including the SOC effect due to the VBM/CBM spin splitting and mirror symmetry breaking in MSSe monolayers, see Table1and Fig.4(a)-(h).The bandgap values also decrease from Mo to W and also from model-I to model-II which may be due to the different chalcogen atoms attached to PtO 2 layers in MSSe-PtO 2 vdWHs.Replacing one of the similar chalcogen atoms in the MX 2 monolayer by a different one, with vertical stacking in vdWHs, breaks the inversion symmetry, due to which an electric eld is produced and generates Rashba spin splitting at the G-
Furthermore, the a R values increase from model-I to -II and also from MoSSe-PtO 2 to WSSe-PtO 2 vdWHs which is due to the selective atom of chalcogen atom and heavier W atom than the Mo atom.Hence, MSSe-PtO 2 vdWHs with considerable a R values set a platform for practical application in spintronic devices.Partial band structures of MSSe-PtO 2 (M = Mo, W) vdWHs, depicted in Fig. 5, show that the M-d xy (Pt-d xy ) state of the MSSe (PtO 2 ) layer mainly contributes to the VBM (CBM) of MSSe-PtO 2 vdWHs.Localization of the VBM and CBM from the isolated MSSe and PtO 2 layers conrms type-II (staggered) band alignment in MSSe-PtO 2 vdWHs, responsible for charge carrier separation. 35,36Hence in the case of MSSe-PtO 2 vdWHs, photogenerated carriers move from different layers (electrons (holes) move from the MSSe (PtO 2 ) layer to the PtO 2 (MSSe) layer), which may decrease their recombination rate and hence play an important role in photocatalysis and solar cell application.Average electrostatic potential (Fig. 6(a)-(d)) and the charge density difference (CDD) (Fig. 6(e)-(h)) are also calculated to understand both the qualitative and quantitative behaviour of the transfer of charge among the layers of MSSe-PtO 2 (M = Mo, W) vdWHs.One can see that the PtO 2 layer has deeper potential than the MSSe layer, indicating that electrons are moving from the MSSe layer to the PtO 2 layer at the interface of MSSe-PtO 2 vdWHs.The CDD in Fig. 6(e)-(h) conrms the charge transfer from the MSSe layer to PtO 2 ; hence the MSSe (PtO 2 ) monolayer becomes p(n)-doped aer stacking.The deeper potential of S than Se is due to the electronegativity difference.Potential drops between MSSe and PtO 2 layers, presented in Table

Fig. 4 A
Fig. 4 A sample texture for (a-h) bandgap and (i) Rashba spin splitting.
are efficient for formation of the interface and charge transfer.One can observe that the values of f increase from model-I to model-II and also from MoSSe-PtO 2 to WSSe-PtO 2 vdWHs, which may be due to the selective atom of chalcogen atom and heavier W atom than the Mo atom.Fabrication of MSSe-PtO 2 (M = Mo, W) vdWHs modulates the band structure of the corresponding monolayers, hence the effective masses.Therefore, we have calculated the effective mass of MSSe-PtO 2 (M = Mo, W) vdWHs by using parabolic tting to the band edge, given in ref.

Fig. 6
Fig. 6 Electrostatic potential in model-I (a(b)) and in model-II (c(d)) and the charge density difference in model-I (e(g)) and in model-II (f(h)) of MSSe-PtO 2 vdWHs, where (i) represents the calculated work function of the corresponding materials.
VBM ) and conduction (E VBM ) band edge potentials at pH = 0 are E VBM = c − E elec − 0.5 E g and E CBM = E VBM − E g .Standard water redox potentials are −4.50 (−5.73) eV for reduction (oxidation) i.e., H + /H 2 (H 2 O/O 2 ), 23,63 which show that the size of the bandgap and energy of the band edge potentials are the basic criteria to facilitate water splitting reactions.Both E VBM and E CBM of MSSe-PtO 2 (M = Mo, W) vdWHs in model-I and model-II are presented in Fig. 8.In the case of model-I of MSSe-PtO 2 vdWHs, both E VBM and E CBM cross the standard redox and oxidation potential at pH = 0, and hence show the capacity for full water splitting.In model-II of MSSe-PtO 2 vdWHs, E VBM crosses standard redox potential, hence having the ability to reduce water at H + /H 2 but failing for oxidation (O 2 /H 2 O).It is clear from the above discussion and Fig. 8 that photocatalytic water splitting activity is very sensitive to the order of chalcogen atoms attached at the interface of vdWHs.Similar photocatalytic water splitting is also demonstrated in ref. 29.
properties of MSSe-PtO 2 (M = Mo, W) vdWHs are investigated.Binding energies, AIMD simulation and phonon spectra conrm the thermal and dynamical stabilities of MSSe-PtO 2 vdWHs in model-I and model-II.Electronic band structures show that MSSe-PtO 2 vdWHs are indirect type-II semiconductors.Interestingly Rashba spin splitting observed in both model-I and model-II of MSSe-PtO 2 vdWHs, with larger Rashba parameters in model-I than in model-II, provides a platform for experimental design of MSSe-PtO 2 vdWHs for optoelectronics and spintronic device applications.Transfer of electrons from the MSSe layer to the PtO 2 layer at the interface of MSSe-PtO 2 vdWHs makes the MSSe (PtO 2 ) monolayer p(n)doped aer stacking.Broad absorption occurs in the visible region of MoSSe-PtO 2 vdWHs and a blue shi is observed in WSSe-PtO 2 vdWHs.A further blue shi is also observed in model-II than in model-I of MSSe-PtO 2 vdWHs.MSSe-PtO 2 vdWHs in model-I are also found to be exciting materials for water splitting and suggested for low cost hydrogen production.PaperNanoscale Advances

Table 1
Binding energies (E b in eV), interlayer spacing (d spacing in Å) for possible stacking configuration, lattice constant (a in Å), bond length (Pt-O, M-S, and M-Se in Å), bandgap (E g in eV), Rashba parameter (a R in eV), work function (f in eV), potential drop (DV in eV), and effective mass (m * e and m * h ) for MSSe-PtO 2 vdWHs