Janus Monolayer TMDs: Asymmetric 2D Materials
- Janus monolayer TMDs are two-dimensional crystals in which one chalcogen layer is replaced, breaking mirror symmetry to generate an intrinsic out-of-plane dipole.
- They exhibit Rashba-type spin splitting and orbital-selective band modifications that tailor optical gaps and enhance catalytic and spintronic functionalities.
- Diverse synthesis methods and defect engineering studies underpin their potential for high-mobility electronics, energy conversion, and quantum device applications.
Searching arXiv for recent and foundational work on Janus monolayer TMDs to ground the article in the current literature. Janus monolayer transition metal dichalcogenides (TMDs) are two-dimensional crystals of the form , in which a transition-metal plane is sandwiched between two inequivalent chalcogen planes and . In these monolayers, replacing one chalcogen layer of a parent sheet breaks the out-of-plane mirror symmetry that characterizes conventional symmetric TMDs and lowers the point-group symmetry to in the common 1H family, thereby generating a built-in out-of-plane dipole, Rashba-type spin splitting, and modified optical, transport, catalytic, and electromechanical responses (Zhang et al., 2017, Li et al., 5 Feb 2025). The field encompasses several structural polytypes and chemistries, including 1H group-VIB systems such as MoSSe and WSSe, 1T′-derived Janus monolayers such as WSeTe and WSTe, and lower-symmetry variants such as Janus rhenium dichalcogenides and vanadium dichalcogenides, whose reduced or altered symmetries enlarge the accessible phase space of band, spin, and collective-order engineering (Joseph et al., 2022, Zibouche et al., 2021, Xu et al., 2024).
1. Crystal chemistry, symmetry, and defining structural motifs
Janus monolayer TMDs extend the family of two-dimensional materials by replacing one of the two chalcogen layers in an sheet with a different chalcogen, yielding (Li et al., 5 Feb 2025). In the 1H phase, the structure is trigonal-prismatic, with a plane of transition-metal atoms sandwiched between two inequivalent chalcogen planes and ; because , out-of-plane mirror symmetry is broken, but in-plane 0 symmetry remains (Li et al., 5 Feb 2025). In conventional monolayer TMDs the point group is 1, whereas Janus 2 lowers the point-group symmetry to 3 by replacing the top chalcogen by a different species (Sayyad et al., 2024). This broken mirror symmetry produces a built-in dipole 4 per unit cell and an internal polarization field 5 along 6, with the details of the dipole set by the inequivalent metal-chalcogen bond lengths (Sayyad et al., 2024).
The same symmetry logic generalizes beyond the 1H family. In 1T′-derived Janus monolayers obtained from 7, replacing one Te layer by Se or S breaks out-of-plane mirror symmetry 8 and inversion 9, leaving only the in-plane mirror 0 (Joseph et al., 2022). In Janus VTeSe, replacing only the top Te with Se removes inversion and changes the point group from 1 to 2 (Xu et al., 2024). In low-symmetry rhenium dichalcogenides, in-plane anisotropy generates a much larger number of inequivalent Janus monolayers than in hexagonal TMDs, including 29 distinct 3 structures (Zibouche et al., 2021).
Several structural metrics recur across the literature. Ideal Janus 4 monolayers with 5 and 6 adopt a hexagonal lattice with 7, 8, and 9 (Sayyad et al., 2024). For specific materials, DFT gives 0, 1, and 2 (Zhang et al., 2017), while optimized values for freestanding WSe3 and WSSe are 4 and 5 (Sakano et al., 5 Oct 2025). In Janus SeMoS grown on Au, the AFM step height is 6, consistent with a single layer (Gan et al., 2022).
A frequent misconception is that all Janus TMDs are simply “polar versions” of ordinary hexagonal TMDs with otherwise unchanged physics. The literature instead shows that the consequences of symmetry lowering depend strongly on polytype and orbital character. In 1H WSSe, the dominant modification is a Rashba-type splitting and an upward shift of the 7-derived valence band, while the 8-valley valence bands remain nearly unchanged (Sakano et al., 5 Oct 2025). In 1T′-derived WSeTe and WSTe, by contrast, Janus asymmetry removes the parent quantum-spin-Hall inversion and produces a topologically trivial but strongly nonlinear-Hall-active state (Joseph et al., 2022).
2. Synthesis routes and structural identification
Experimentally, Janus monolayers have been realized primarily through selective chalcogen exchange. The foundational demonstration of Janus SMoSe used controlled sulfurization of monolayer MoSe9: as-grown MoSe0 was placed in the furnace center at 1, sulfur powder was heated to 2, Ar at 3 carried 4 vapor to the MoSe5 surface, the reaction time was 30 min, and the selective reaction was maintained in the 6 window, below which no top-layer exchange occurs and above which full Se7S substitution happens in both layers (Zhang et al., 2017). The net reaction was written as
8
A distinct scalable route is one-pot chemical vapor deposition on Au foils. In that method, MoSe9 is first grown on polycrystalline Au foil and then sulfurized at 0, with the net exchange reaction
1
or more generally 2, with DFT-computed reaction energy 3 per formula (Gan et al., 2022). DFT on an 4 MoSe5/6 Au(111) supercell showed that 7 dissociation on Au(111) is exothermic with 8 per S atom, S adatoms diffuse with 9, removing a bottom-layer Se atom and binding it to Au costs only 0, whereas removing a top-layer Se costs 1, and the net replacement energy for bottom-layer Se by S is slightly exothermic 2 (Gan et al., 2022). These energetics explain why S atoms diffuse beneath the MoSe3 on Au and selectively exchange the bottom Se layer.
Room-temperature plasma or atomic-replacement strategies have also proved important. In monolayer WSSe, in-situ 4 plasma treatment at room temperature replaces the top Se layer with S, transforming Se–W–Se into S–W–Se; during the reaction the A-exciton PL peak shifts from 5 in WSe6 to 7 in WSSe over 8 min of plasma exposure (Sakano et al., 5 Oct 2025). In charge-tuneable Janus WSeS, the “Selective Epitaxial Atomic Replacement” (SEAR) method converts exfoliated 1L-WSe9 into Janus WSeS in situ at room temperature under controlled atmosphere, with time-resolved Raman spectroscopy used to stop conversion upon appearance of Janus signature modes (Feuer et al., 2022). Remote 0-plasma-assisted atomic-layer substitution has likewise been used to convert MoSe1 to MoSSe and MoS2 to MoSeS at room temperature within 5–15 min (Zhang et al., 28 Mar 2025).
Structural identification relies on spectroscopy and microscopy. In SMoSe, Raman-active Janus signatures include an out-of-plane S–Mo–Se mode at 3, an in-plane S–Mo–Se mode at 4, and an emergent 5 mode at 6, while TOF-SIMS depth profiling established the knockout sequence S7Mo8Se9SiO0, directly proving S–Mo–Se ordering (Zhang et al., 2017). In one-pot-grown SeMoS, Raman spectroscopy shows new peaks at 1 and 2, with 3, and angle-resolved XPS directly confirms Se on top, Mo in the middle, and S at the bottom (Gan et al., 2022). In WSeS, pristine WSe4 shows the 1L-WSe5 6 mode at 7, whereas fully converted Janus WSeS exhibits a single 8 mode at 9, with disappearance of WS0/WSe1 alloy peaks (Feuer et al., 2022). A later “Raman digital twin” library generalized these fingerprints: in 2H Janus TMDs the broken 2 activates four first-order Raman modes, two 3 and two 4, and in Janus WSSe the predicted frequencies are 5, 6, 7, and 8 (Kowalski et al., 10 Oct 2025).
3. Electronic structure, orbital asymmetry, and Rashba physics
The electronic hallmark of Janus monolayer TMDs is that broken out-of-plane mirror symmetry modifies bands in an orbital-selective manner. Direct micro-focused ARPES on an identical sample transformed from monolayer WSe9 to Janus WSSe provided a particularly clear case: both WSe00 and WSSe show nearly identical spin-orbit-split valence bands at 01, with the valence-band maximum pinned at 02 below 03, whereas at 04 monolayer WSe05 has a single spin-degenerate valence-band maximum at 06 and Janus WSSe exhibits two split branches with extrema at 07 (Sakano et al., 5 Oct 2025). The upward shift is therefore
08
that is, 09 10 (Sakano et al., 5 Oct 2025).
Near 11, Janus WSSe realizes a Rashba-type splitting because the 12 crystal lacks horizontal mirror symmetry. The effective Hamiltonian is
13
leading to
14
From 15-ARPES along 16-M, the splitting at 17 is 18, which yields 19 (Sakano et al., 5 Oct 2025). Fully relativistic PBE-GGA calculations reproduce a Rashba splitting of 20 at 21 in WSSe, no Rashba splitting in WSe22, and an upward shift of 23 at 24 in WSSe versus WSe25, traced to the larger S 26 versus Se 27 weight, with projected 28 (Sakano et al., 5 Oct 2025). This is the paper’s “chalcogen-orbital engineering.”
The persistence of the 29-valley bands alongside strong 30-point reconstruction is not accidental. In WSSe, the 31-valley invariance is attributed to the dominant in-plane W 32 orbital character at 33, which is insensitive to 34 breaking, together with Fermi-level pinning by the graphite substrate (Sakano et al., 5 Oct 2025). This orbital selectivity recurs in model treatments. A low-energy tilted massive Dirac Hamiltonian has been used to describe Janus TMD monolayers lacking inversion symmetry,
35
with the tilt parameter 36 breaking inversion symmetry but preserving time reversal (Joseph et al., 2022, Quintela et al., 2022). In the excitonic analysis of inversion-broken TMDC monolayers, once 37 the conduction-band minimum and valence-band maximum shift in opposite directions in 38-space, making the gap indirect, and for 39 the spectrum becomes semimetallic with electron and/or hole pockets (Quintela et al., 2022).
Broken symmetry also reshapes orbital and spin textures. In non-Janus monolayers, the wavefunctions at the valence and conduction bands are dominated by 40, 41, and 42 orbitals, but in Janus systems the internal electric field intermixes these states with 43 and 44, producing a robust orbital texture around the valleys 45, 46, and 47 (Sahu et al., 13 Nov 2025). Near each valley 48, the in-plane orbital texture is parametrized by
49
and spin-orbit coupling not only generates a chiral spin texture but also reverses the chirality of one orbital branch (Sahu et al., 13 Nov 2025). In WSeTe, a six-band tight-binding model further gives a Rashba term with 50 and conventional Ising SOC 51 (Kameda et al., 10 May 2025).
A plausible implication is that “Janus band engineering” is best understood not as a uniform shift of all band edges, but as symmetry- and orbital-selective perturbation: weak at valleys dominated by in-plane 52 orbitals, strong where 53 and 54 admixtures are substantial, and especially consequential near avoided crossings or 55-derived states.
4. Optical transitions, excitons, and magneto-optical response
Janus monolayer TMDs retain direct-gap optical transitions in several experimentally relevant cases while simultaneously introducing dipolar and spin-split excitonic structure. In charge-tuneable Janus WSeS, DFT including SOC confirms that the system is direct-bandgap at the 56 points, with both the conduction-band minimum and valence-band maximum at 57 (Feuer et al., 2022). The measured neutral exciton appears in both PL and reflectance contrast at
58
with the narrowest PL full width at half maximum 59 and average 60 across the device (Feuer et al., 2022). Gate tuning resolves two negatively charged trions: 61 at 62, 63 below 64, and 65 at 66, 67 below 68, giving an exchange splitting 69 (Feuer et al., 2022). At high 70-doping 71, a lower-energy feature 72 appears at 73 and red-shifts by 74 as carrier density increases (Feuer et al., 2022).
The same WSeS work attributes the out-of-plane dipolar character of neutral excitons to the asymmetric chalcogen environment. DFT predicts for the neutral exciton in WSeS a dipole moment 75, with an estimated Stark shift
76
(Feuer et al., 2022). Magneto-optic measurements indicate that monolayer WSeS has a direct bandgap at the 77 points, and at 4 K the measured exciton 78-factors are 79 for 80 in PL, 81 in reflectance contrast, 82 for 83, 84 for 85, and 86 for 87 (Feuer et al., 2022).
One-pot-grown SeMoS monolayers exhibit similarly strong optical quality. Low-temperature PL on hBN-encapsulated SeMoS reveals a free-exciton peak at 88 with 89 at 5 K, visible up to room temperature, and a lower-energy localized peak near 90 appearing only below 150 K (Gan et al., 2022). The exciton energy follows the O’Donnell–Chen form
91
with 92, 93, and 94, while the linewidth broadening is described by
95
with 96 and 97, indicating stronger exciton-phonon coupling than in MoSe98 and MoS99 monolayers (Gan et al., 2022). Under circularly polarized excitation, the free exciton shows 00 up to 100 K; in Faraday geometry up to 9 T, the Zeeman splitting is 01 at 02, corresponding to 03 (Gan et al., 2022).
Theory has pushed the excitonic perspective further. For inversion-broken TMDC monolayers described by a tilted massive Dirac Hamiltonian, solving the Bethe–Salpeter equation with a Rytova–Keldysh interaction gives 04 binding energies of 05 in hBN and 06 in quartz for representative parameters 07, 08, and 09 (Quintela et al., 2022). An excitonic instability occurs when 10; numerically, the crossing occurs at 11 in hBN and 12 in quartz (Quintela et al., 2022). In the optical conductivity, only excitons with angular momentum 13 or 14 are active, and the 15 resonances carry oscillator strengths more than two orders of magnitude larger than the 16 transitions (Quintela et al., 2022).
These results clarify a second common misconception: broken mirror symmetry does not necessarily destroy the bright 17 optical transitions of monolayer TMDs. In WSeS, magneto-optic data and charge-tunable spectroscopy are explicitly consistent with direct-gap transitions at 18 (Feuer et al., 2022), while in SMoSe the gap becomes slightly indirect, with 19 and 20, producing PL quenching by 21 and a blue shift to 22 (Zhang et al., 2017). The optical consequences are therefore material specific rather than universal.
5. Topology, Berry curvature, nonlinear Hall response, and collective ordering
In 1T′-derived Janus monolayers, inversion breaking can change not only spin splitting but also band topology. With SOC, monolayer WTe23 is a quantum-spin-Hall insulator with a direct gap 24 and inverted band ordering near the 25-X line, whereas WSeTe and WSTe remain gapped but lose band inversion because of the asymmetric crystal field introduced by the Janus structure (Joseph et al., 2022). The 26 invariant determined from the Wannier charge-center flow is 27 for WTe28 and 29 for WSeTe and WSTe, and ribbon spectra confirm that only the parent WTe30 hosts helical edge states crossing the gap (Joseph et al., 2022). The direct gap along X–31 decreases from 32 in WTe33 to 34 in WSeTe and 35 in WSTe (Joseph et al., 2022).
Despite being topologically trivial, these Janus monolayers exhibit large Berry curvature dipoles. For a 2D system,
36
and the Berry curvature dipole is
37
With only 38 symmetry, the only nonzero component is 39 (Joseph et al., 2022). First-principles calculations show that 40 concentrates near band anticrossings along 41-X, its magnitude increases as the gap shrinks from WTe42 to WSeTe to WSTe, and the computed 43 at the Fermi level is roughly ten times larger in WSTe than in WTe44 (Joseph et al., 2022). In time-reversal-invariant but inversion-broken crystals, this yields a second-order Hall-like response 45 (Joseph et al., 2022).
Janus asymmetry can also alter collective electronic order. In monolayer Janus VTeSe fabricated by surface selenization of VTe46, low-temperature STM at 4.5 K reveals a rhombic 47 supercell with side length 48 and cell angle 49 (Xu et al., 2024). The charge modulation can be written as
50
with 51 (Xu et al., 2024). DFT finds that Fermi-surface nesting and nonmagnetic phonon instabilities both point to a 52 modulation rather than the observed 53 state, whereas in the 54 supercell the pronounced flat PDOS peak at 55 splits and shifts away, lowering the total energy by 56 per unit cell (Xu et al., 2024). The proposed mechanism is therefore charge modulation in the Janus VTeSe beyond the conventional electron-phonon picture (Xu et al., 2024).
Magnetic Janus TMDs add yet another sector. In vanadium-based Janus monolayers 57, first-principles calculations predict that the built-in electric field 58 of order 59 generates Rashba-like spin-orbit effects, while heavier chalcogens enhance magnetic exchange and anisotropy (Smaili et al., 2020). The extracted Rashba coefficients are 60 for VSSe, 61 for VSeTe, and 62 for VTe63, with exchange 64 and anisotropy 65 per V in VSeTe (Smaili et al., 2020). Kubo–Bastin transport calculations on a 66 tight-binding supercell give an overall spin-orbit torque efficiency 67 up to 68 and a zero-temperature critical switching current density 69 (Smaili et al., 2020).
6. Stability, defects, and materials optimization
A central issue for Janus monolayer TMDs is why some compounds are realized experimentally while many predicted ones are not. A systematic electronic-structure analysis of 1H-phase JTMDs identifies a group dependence of stability, with Group-VIB-based monolayers exhibiting robust stability, as evidenced by the successful synthesized MoSSe and WSSe (Li et al., 5 Feb 2025). The underlying competition is between metal-ligand ionic bonding and ligand-ligand covalent bonding, together with high-energy 70-electron orbital splitting near 71 (Li et al., 5 Feb 2025). In trigonal-prismatic 72 coordination, the five 73 orbitals split into 74, 75, and 76, and the authors classify JTMDs using an 77 scheme based on occupied antibonding states and unoccupied bonding states (Li et al., 5 Feb 2025). Across 84 computed 78 systems, 45 are stable in 1H, including 32 from groups IVB and VIB (Li et al., 5 Feb 2025). Prototype values are 79 and 80 per formula unit for MoSSe, and 81 and 82 for WSSe, both dynamically stable (Li et al., 5 Feb 2025).
High-throughput thermodynamic characterization similarly shows that stable Janus ordering at room temperature is not generic. In a survey of 72 TMD alloys using cluster expansion and Monte Carlo, the only alloys with stable out-of-plane Janus ordering at 300 K are the X-site mixed Ti- and Zr-based systems: T-TiSTe, T-TiSeTe, H-TiSTe, H-TiSeTe, T-ZrSTe, T-ZrSeTe, H-ZrSTe, and H-ZrSeTe (Linderälv et al., 2022). Their mixing enthalpies at 83 are negative, ranging from 84 per MX85 for T-TiSTe to 86 for H-ZrSeTe (Linderälv et al., 2022). This suggests that thermodynamic favorability of ordered Janus stacking is highly chemistry dependent even within the broader TMD family.
Defects are another decisive factor. High-resolution STEM, DFT, and cryogenic spectroscopy on Janus 87 monolayers identify the most energetically stable point defects as single chalcogen vacancies 88 and 89, the double vacancy 90, interstitial defects 91, and metal impurities 92 (Sayyad et al., 2024). Under elemental chemical potentials, the neutral formation energies are 93 for 94, 95 for 96, 97 for 98, and 99 for 00 and 01 (Sayyad et al., 2024). The defect complex 02 has a binding energy 03, making it slightly more favorable than two isolated single vacancies (Sayyad et al., 2024). In-gap Kohn–Sham levels appear at 04 for 05, 06 for 07, and 08 for 09, with SOC splittings of 210–300 meV (Sayyad et al., 2024). In hBN-encapsulated Janus WSeS at 4 K, these correlate with narrow bound-exciton lines at 10, 11, and 12 (Sayyad et al., 2024).
Synthesis-related nanoscale defects have also been resolved directly. Cross-correlated AFM and TERS imaging of MoSSe and MoSeS monolayers shows that bilayer nanoislands in the precursor crystals lead, after Janus conversion, to Janus/TMD vertical heterostructure islands of 13 lateral size, while the precursor bilayer patches themselves are 14 across (Zhang et al., 28 Mar 2025). Strain transfer from growth substrate and conversion pathway strongly affects morphology: for MoSe15MoSSe on SiO16/Si, the net strain is 17 tensile, producing fragmentation into 18 domains with a defect density of 19 cracks/cm20, whereas for MoS21MoSeS on SiO22/Si the net strain is 23 compressive, producing 24-high wrinkles with 100–200 nm spacing but no fragmentation (Zhang et al., 28 Mar 2025). Switching to fused silica yields 25 area free of wrinkles in Janus MoSeS (Zhang et al., 28 Mar 2025).
Carrier transport adds another optimization axis. A Born effective charge (BEC) method proposed for Janus TMDs includes both acoustic and polar-optical phonon scattering, correcting the well-known overestimation of mobilities by deformation-potential theory in polar Janus structures (Hu et al., 2022). The reported trend is 26 with 27, and the lower the absolute BEC, the higher the electron or hole mobility (Hu et al., 2022). Among pristine systems listed, H-WSSe has 28, 29, and 30, higher than H-MoSSe with 31, 32, and 33 (Hu et al., 2022). The paper therefore recommends W–S–Se Janus monolayers for high-mobility 2D electronics (Hu et al., 2022).
7. Functional responses and application space
The combination of intrinsic asymmetry, strong SOC, tunable band edges, and chemically distinct surfaces gives Janus monolayer TMDs a broad application space that spans optoelectronics, spintronics, electromechanics, and catalysis. In band-engineered Janus WSSe, the elevation of 34-derived valence-band states and the Rashba splitting are expected to open new direct and spin-forbidden optical channels, potentially observable in helicity-resolved PL or pump–probe studies, while the coexistence of out-of-plane 35-valley spin locking and in-plane Rashba spins at 36 suggests richer spin textures for spintronic devices, including electric-field control of spin orientations (Sakano et al., 5 Oct 2025). In Janus WSeTe, optical irradiation can generate pure spin Hall currents; at hole doping 37, 38 peaks near 39 at 40, 41 peaks near 42 at 43, and the spin Hall angle reaches values of order 44 in the visible range (Kameda et al., 10 May 2025).
Current-induced orbital and spin polarizations constitute a related direction. For Janus TMDs of the form 45, a DC in-plane electric field produces both orbital and spin Edelstein effects, with the orbital response one order of magnitude larger (Sahu et al., 13 Nov 2025). For MoSSe hole doped by 46 below the valence-band maximum, 47 and 48 (Sahu et al., 13 Nov 2025). Across the family, Te-based compounds such as MoSTe and WSTe show the largest 49, up to 50 (Sahu et al., 13 Nov 2025). This suggests that Janus asymmetry can act not only through spin textures but also through current-induced orbital accumulation, an increasingly important theme in orbitronics.
Electromechanical functionality is likewise enhanced by asymmetry. In a charge-dipole model combined with molecular dynamics, the bending flexoelectric constant 51 of Janus TMDCs is positively correlated with the initial bond-length asymmetry 52 (Javvaji et al., 2022). Reported values are 53 for MoSSe, 54 for MoSeTe, 55 for MoSTe, 56 for WSSe, 57 for WSeTe, and 58 for WSTe, compared with 59 for MoS60 (Javvaji et al., 2022). The enhancement is linked to stronger 61 and 62 interactions as asymmetry increases (Javvaji et al., 2022).
Catalysis was one of the earliest experimentally demonstrated functional gains. For the hydrogen evolution reaction, basal-plane overpotentials at 63 were reported as 64 for MoS65, 66 for MoSe67, 68 for SMoSe, and 69 for SeMoS, with Tafel slopes of 70, 71, 72, and 73, respectively (Zhang et al., 2017). DFT 74 calculations on vacancy sites gave 75 for MoS76 S vacancies, 77 for SMoSe S vacancies, 78 for MoSe79 Se vacancies, and 80 for SeMoS Se vacancies, indicating that vacancies together with intrinsic strain and dipole modulate local electronic states toward 81 (Zhang et al., 2017).
Finally, work-function and band-edge engineering expand the heterostructure design space. In anisotropic Janus rhenium dichalcogenides, the work function can be tuned across 82; for example, in the selenization series 83 it varies from 84 in ReS85 to 86 in ReSSe (Zibouche et al., 2021). In high-throughput studies of Ti- and Zr-based Janus systems, negative 87 at 88, 89 up to 90, and continuously tunable band edges were identified as a favorable combination for device design (Linderälv et al., 2022). Across the literature, the recurring device themes are photovoltaic and photodetector architectures, piezoelectric and flexoelectric energy conversion, nonlinear Hall and spin-Hall transport, orbitronic and spin-orbit-torque platforms, valley-selective optics, and catalysis (Gan et al., 2022, Joseph et al., 2022, Javvaji et al., 2022, Smaili et al., 2020).
Taken together, these results define Janus monolayer TMDs not as a single material class with one canonical behavior, but as a symmetry-engineered family in which the consequences of chalcogen asymmetry depend sensitively on polytype, orbital composition, defect landscape, and dielectric environment. The most robustly established principles are the lowering of symmetry from symmetric 91 parents, the emergence of a built-in out-of-plane dipole, orbital-selective band reconstruction, and the resulting access to functionalities that are weak or absent in centrosymmetric or mirror-symmetric monolayer TMDs.