Twist engineering induced spin-orbit coupling for photosynthesis of ethane from carbon dioxide and water

Abstract

Harnessing sunlight, carbon dioxide, and water to produce two-carbon products is promising but constrained by sluggish kinetics and high carbon–carbon coupling barriers. Here, we report Ni single-atom anchored twisted SnS₂ (Ni-TSnS₂) for ethane (C₂H₆) photosynthesis. In-situ electron paramagnetic resonance was developed to observe spin-orbit coupling in Ni-TSnS₂. Spontaneous long-range spin-momentum locking originated from spin-orbit coupling enables magnetic-field-free long-range spin pinning. Topological protection inherent to long-range spin-momentum locking enhances its stability and ensures spin-polarized electron supply for charge separation. In-situ electron paramagnetic resonance further revealed single-electron transfer at Ni sites during CO₂ reduction. Single-electron transfer raised from spin-orbit coupling induces surface-adsorbed methyl intermediate to form methyl radicals (·CH₃). ·CH₃-to-C₂H₆ chain reaction pathway enhances C₂H₆ photosynthesis and selectivity. Consequently, Ni-TSnS₂ achieves a C₂H₆ production rate of 139.58 ±  5.14 μmol g^-1 h^-1 with 89.41 ±  4.43% electron selectivity. In this work, we propose a twist engineering strategy to modulate spin states of charge, thereby promoting charge separation and single-electron transfer in photoreduction of CO₂ to C₂H₆.

Introduction

The negative impacts of excessive CO₂ emissions are becoming increasingly apparent, and photocatalytic CO₂ reduction into C₂ hydrocarbons from CO₂ and H₂O is a promising approach that could contribute to a more sustainable and carbon-neutral future^1,2. Among the numerous two-carbon (C₂) products, C₂H₆ are not only essential feedstocks in the chemical industry but also possess substantially higher energy densities than C₁ products, endowing them with significant economic value³. However, CO₂-to-C₂H₆ conversion requires 14e^- transfer processes, which impose sluggish reaction kinetics. In addition, the production of C₂ species typically proceeds via carbon–carbon (C–C) coupling on catalyst surfaces, a process that involves high-energy barriers and demands precise control over the electronic structure and geometric configuration of active sites^4,5. These challenges collectively result in low formation rates and poor selectivity of C₂ products. Therefore, development of photocatalysts that can facilitate efficient electron transfer and lower the energy barrier for C–C coupling is central to overcoming the bottlenecks in C₂ compound synthesis.

Currently, electron spin mediated electron-hole separation mechanism has been widely exploited in photocatalysis^6,7,8. Photogenerated electrons and holes with opposite spin orientations cannot recombine, a mechanism that effectively prolongs charge lifetimes and ensures sufficient electron supply for multi-electron transfer reactions^9,10. For instance, spin photocatalysts such as Mn/Co₃O₄ and Mn-CsPbBr₃ have demonstrated markedly enhanced performance in the eight-electron CO₂ methanation reaction through spin-mediated charge separation^6,11. However, the efficiency of current spin catalysts often relies on spin-pinning effects induced by external magnetic fields, while spin polarization introduced via doping, lattice distortion, or vacancy engineering remains randomly distributed in photocatalysts, thereby limiting the overall charge separation efficiency^7,11,12. However, constructing spontaneous long-range spin pinning in photocatalysts remains a fundamental challenge.

In addition, the highly endothermic C–C coupling process remains a fundamental bottleneck in the formation of C₂ products⁴. Rational design of active sites has been demonstrated as an effective strategy to promote C–C coupling. In recent years, numerous catalysts that promote C–C coupling have been developed. For example, the CeZrZnAgPbO–Cu and RhCo–RhGd nanoalloys designed by Du et al. markedly boost C₂-product yields by two distinct mechanisms, i.e., enhanced *CO adsorption and spin-polarization, leading to reduction of C–C coupling barrier and enhanced catalytic activity^13,14. However, the underlying mechanisms, particularly how active sites interact with CO₂ and its reaction intermediates to drive C–C bond formation, remain to be further elucidated². Gaining such insights is critical for further improving both the rate and selectivity of C₂ product generation.

Here, we design Ni single-atom-anchored twisted SnS₂ nanosheets (Ni-TSnS₂, Fig. 1a) for photosynthesis of C₂H₆ from CO₂ and H₂O. We show that twist engineering induces spontaneous spin–orbit coupling (SOC) in Ni-TSnS₂. By correlating SOC intensity with C₂H₆ photosynthesis performance, we establish a positive relationship between SOC strength and C₂H₆ production. Magnetization curves, photoelectric characterization, and theoretical investigations show that SOC-induced long-range spin-momentum locking (LRSL) promotes charge separation in Ni-TSnS₂. Furthermore, SOC-mediated single-electron transfer (SET) drives the conversion of surface-adsorbed methyl intermediates (*CH₃) into methyl radicals (·CH₃) at Ni sites, and C₂H₆ forms via a · CH₃-to-C₂H₆ radical chain reaction with intrinsically high reaction rate and selectivity. This work offers a LRSL strategy to overcome spatial disorder of spin polarization in photocatalysts, thereby facilitating the kinetics of C₂H₆ photosynthesis. Moreover, we uncover a radical reaction pathway for C₂H₆ formation, in which circumvents the high C–C coupling barriers on the catalyst surface, improving C₂H₆ production rates and selectivity. Overall, the results of this study provide important guidance for the future development of spin-based photocatalysts and the rational design of C₂H₆ synthesis reactions.

Fig. 1: Characterizations of Ni-TSnS₂.

a Crystal pattern of Moiré superlattice and corresponding atom arrangement of the local regions in the Moiré superlattice. The Moiré superlattice exhibits quasi-crystalline periodicity and consists of three distinct domains: Triangular, Square, and Rhombus regions. b AC-STEM images and corresponding strain mapping of untwisted SnS₂, TSnS₂, and Ni-TSnS₂. c SAED of Ni-TSnS₂. d, e Atomic displacement directions and magnitudes of Sn atoms in AC-STEM image of Ni-TSnS₂, respectively. Ni atoms are highlighted by red circle. The positions of the black circles are High-symmetry stacking sites. The dot in (d) are colored based on the displacement direction, as given in the color wheel. Color wheel: mapping between hue and in-plane displacement direction, with the rightward blue sector set to 0° and angles increasing counterclockwise. Colored dot in (e) mark the positions of Sn atomic columns, and their hue encodes the in-plane displacement distance as defined by the color scale. f Intensity profiles of the two sites in AC-STEM image of Ni-TSnS₂. g FT k²-weighted Ni K-edge of the EXAFS spectra and corresponding EXAFS fitting results of Ni-SnS₂ and Ni-TSnS₂. The insets are the schematic illustration of C_3v and C_2v symmetric Ni atoms.

Results

Moiré superlattice and C _2v symmetric Ni sites of Ni-TSnS₂

Ni-TSnS₂ was fabricated by chemical vapor deposition (CVD) and the photo-deposition method (see “Methods” Section). Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images show that Ni-TSnS₂ exhibits a hierarchical architecture comprising large-area basal SnS₂ nanosheets with numerous smaller secondary nanosheets stacked (Supplementary Figs. 1a–c). The synthesized Ni-TSnS₂ nanosheets have an overall thickness of 0.59–15.93 nm (Supplementary Figs. 1d–f). X-ray energy dispersive spectra (EDS) elemental mapping analysis confirms the co-existence of Sn, S and Ni elements in Ni-TSnS₂ (Supplementary Fig. 2). In the X-ray diffraction (XRD) pattern (Supplementary Fig. 3), the (001) peak of Ni-TSnS₂ at 15.1° splits into two obvious superlattice diffraction peaks at 7.51° and 19.09°^15,16, consistent with the simulated XRD spectrum. The emergence of these superlattice diffraction peaks confirms the long-range ordering property of the superlattice structure.

Aberration-corrected-scanning transmission electron microscopy (AC-STEM) images of SnS₂, twist SnS₂ (TSnS₂), and Ni-TSnS₂ reveal [001]-oriented growth with exposed (001) facets (Fig. 1b). Notably, both nanosheets, TSnS₂ and Ni-TSnS₂, exhibit nearly identical moiré superlattice patterns. AC-STEM further reveals the emergence of moiré superlattices exclusively within twist stacking regions of Ni-TSnS₂ nanosheets (Supplementary Fig. 4), and the selected area electron diffraction (SAED) pattern obtained for Ni-TSnS₂ provides evidence of a twist angle of 30° between adjacent SnS₂ layers (Fig. 1c)¹⁷. Two sets of first- and second-order Bragg peaks with six-fold rotation symmetry are marked by red and blue hexagons, respectively (Fig. 1c). Simulated high-angle annular dark field (HAADF)-STEM images closely match the experimental observations (Supplementary Fig. 5), validating our structural model shown in Fig. 1a. The moiré-periodic relative displacement field obtained by geometric phase analysis (GPA) further confirms interlayer twist stacking structure (Fig. 1b and Supplementary Fig. 6)¹⁸. Atomic displacement analysis reveals that Sn atoms within the moiré superlattice structure uniformly shift toward high-symmetry stacking sites (marked by a black circle), albeit with varying displacement magnitudes. This uniform displacement induces pronounced local compressive strain around the high-symmetry regions¹⁹. Owing to the periodic arrangement of these stacking sites, corresponding peak shifts are also observed in the XRD patterns, providing direct evidence for the presence of long-range ordered compressive strain (−0.85%) in Ni-TSnS₂ (Supplementary Fig. 3). Moiré periodic strain leads to periodic symmetry breaking in TSnS₂ and Ni-TSnS₂, which underpins the emergence of SOC effects¹⁸. Therefore, the long-range periodic symmetry breaking structure observed herein implies long-range SOC effects in both TSnS₂ and Ni-TSnS₂.

The atomic structure of each material was further investigated using synchrotron radiation-based X-ray absorption fine structure (XAFS) spectroscopy. The first shell Sn–S of SnS₂ is located at 2.19 Å, whereas that of TSnS₂ and Ni-TSnS₂ shifts to a smaller value of 2.10 Å, indicating the existence of compressive strain (Supplementary Fig. 7)²⁰. Electron paramagnetic resonance (EPR) results suggest the formation of sulfur vacancies (Sv) in TSnS₂ and Ni-TSnS₂. (Supplementary Fig. 8).

The AC-STEM image shows that single Ni atoms (marked by a red circle) are distributed on TSnS₂ (Fig. 1b, f) Ni K-edge FT-EXAFS spectra for Ni-SnS₂ and Ni-TSnS₂ feature peaks at ~1.93 Å, assigned to Ni-S bonding (Fig. 1g). Compared with Ni foil and NiO, no obvious peaks of Ni-Ni coordination are detected, indicating that Ni species exist in the form of single atoms in Ni-SnS₂ and Ni-TSnS₂. The local coordination number of Ni single atoms anchored on pristine-SnS₂ (Ni-SnS₂) is determined to be 3.11  ±  0.22 via detailed EXAFS fitting (Supplementary Table 1). By comparison, Ni-TSnS₂ has a low coordination number of Ni (2.06  ±  0.13 for Ni–S). According to crystal field theory, the local Ni–S₂ configuration in Ni-TSnS₂ can be described by C_2v symmetry (Fig. 1g)²¹. Simulated XANES of Ni-SnS₂ and Ni-TSnS₂ configurations are in good accordance with the experimental profiles, particularly regarding the characteristic peaks A to E at K-edge (Supplementary Fig. 9)²¹. Synchrotron radiation XPS (SRXPS) results indicate that Ni-SnS₂ exhibits Ni(II) and Ni(III) mixed valence states, whereas an Ni(I) state solely exists in Ni-TSnS₂ (Supplementary Fig. 10). The lower formation energy of an Ni single atom at Sv indicates that Sv serves as the preferred location for Ni deposition (Supplementary Fig. 11). Sv might be the reason for the 2-coordination of Ni atoms. GPA results further demonstrate that extra displacement loading on TSnS₂ after Ni anchoring (Fig. 1b), suggesting that C_2v-symmetric Ni single atoms exacerbate symmetry breaking of Ni-TSnS₂.

Symmetry-breaking induced SOC effect

SRXPS spectra results reveal the enlarged spin-orbit (SO) splitting of Sn 3 d spectra of Ni-TSnS₂ (Fig. 2a) suggesting it has larger SOC effect than SnS₂, Ni-SnS₂ and TSnS₂. Ni L-edge X-ray magnetic circular dichroism (XMCD) spectra also illustrate that Ni-TSnS₂ exhibits a more pronounced response than Ni-SnS₂ (Fig. 2b). It is well-established that XMCD signals originate from Zeeman-type SOC²², and consequently, C_2v symmetric Ni sites exhibit stronger SOC effects.

Fig. 2: Characterization of SOC effect and SOC-mediated photocatalytic CO₂RR performance of various materials.

a SRXPS spectra. b soft XAS spectra of Ni-SnS₂ and Ni-TSnS₂. c XAFS spectra. d Evolution rates of C₂H₆, CH₄, CO and H₂ for various photocatalysts. All measurements were performed at 1 atm CO₂ and room temperature. Data in Fig. 2d are presented as mean values  ±  s.d. (standard deviation). Each error bar indicates the standard deviation calculated from three independent measurements for a given sample. e Blank control experiments for Ni-TSnS₂.

Furthermore, X-ray absorption spectrometry (XAS) measurements of Sn L₂ (p_1/2 → d_3/2) and L₃ (p_3/2 → d_5/2) edges were undertaken to quantify the SOC of all synthesized materials (Fig. 2c). Due to the selection rules that govern electric dipole transitions, the relative integrated intensity of white-line features at the L₂ and L₃ edges (known as the branching ratio, BR) is directly proportional to the expected value of the angular part of the SOC (denoted by$\langle L\cdot S\rangle$)^23,24:

$${{{\mathrm{BR}}}}=\frac{\int {L}_{3}-2\int {L}_{2}}{\int {L}_{3}+\int {L}_{2}}=\frac{{\sum }_{i}{l}_{i}\cdot {s}_{i}}{\underline{{{{\rm{n}}}}}}$$

(1)

$$\langle L\cdot S\rangle=\left\langle {\sum}_{{i}}{{l}}_{{i}}\cdot {{s}}_{{i}}\right\rangle$$

(2)

where n is the number of holes in the d shell; and l_i and s_i are the orbital angular momenta and spin momenta in the shell for each of the i d electrons, respectively. In Fig. 2c, the calculated BR values of SnS₂, Ni-SnS₂, TSnS₂, and Ni-TSnS₂ are 2.11, 2.15, 2.37, and 2.51, respectively, indicating that the SOC intensity increases in the order of SnS₂ < Ni-SnS₂ < TSnS₂ < Ni-TSnS₂. In general, the SOC effects in Sn-based materials are inferior^25,26, whereas the emergence of moiré superlattice and C_2v-symmetric Ni coordination elevates the BR value for Ni-TSnS₂. The resulting value is comparable to those obtained for 4 d transition metal compounds (generally regarded as moderate-strength SOC materials), indicating greatly enhanced SOC strength for Ni-TSnS₂²⁷.

Quadrupole moment splitting serves as a key indicator of symmetry breaking²⁸. In ¹¹⁹Sn Mössbauer spectra (Supplementary Fig. 12), the quadrupole splitting of materials follows the same trend as the SOC strength. Specifically, the quadrupole splitting of SnS₂, Ni-SnS₂, TSnS₂, and Ni-TSnS₂ is 0, 0, 0.88, and 0.92 mm s^-1, respectively, further indicating that the observed SOC effect originates from the symmetry-broken structure.

In general, SOC signatures emerge from symmetry breaking. Twist engineering of SnS₂ produces interlayer lattice incommensurability, which lowers the structural symmetry and thereby induces SOC in SnS₂. In addition, C_2v-symmetric Ni sites on TSnS₂ further amplify symmetry breaking, leading to an additional enhancement of SOC.

SOC-mediated photocatalytic CO₂RR performance

Photocatalytic CO₂RR performance was next investigated. We found that SnS₂ exhibits a CO evolution rate of 11.53 ±  3.15 μmol g^-1 h^-1 but no CH₄ production, and TSnS₂ displays both increased production rates of CO (63.4 ±  4.09 μmol g^-1 h^-1), CH₄ (3.73 ±  2.39 μmol g^-1 h^-1), and C₂H₆ (10.27 ± 1.31 μmol g^-1 h^-1) (Fig. 2d). As the cooling period time increases from 3 to 6 h during the synthesis process for TSnS₂, the photocatalytic CO₂RR performance of TSnS₂ significantly improves compared against SnS₂, with C₂H₆ starting to be produced (Supplementary Fig. 13). Moreover, Ni-TSnS₂ displays an O₂ production rate of 243.19 μmol g^-1 h^-1, close to the theoretical value of 241 μmol g^-1 h^-1, demonstrating that O₂ is exactly the oxidation product (Supplementary Fig. 17). SEM analysis shows that the number of ‘islands’ on the TSnS₂ surface increases as the cooling period time extends from 3 to 5 h, indicating the growth of twist-stacking layers (Supplementary Fig. 18a). When the cooling period time exceeds 5 h (for TSnS₂-6), the ‘islands’ begin to merge, leading to a reduced number of twisted SnS₂ layers and shrunken moiré superlattice regions (Supplementary Fig. 18b). TSnS₂-5 exhibits a 4.56-fold higher CO generation rate than SnS_1.78, which has a comparable concentration of sulfur vacancies to TSnS₂-5, indicating that the moiré superlattice is crucial to the improvement in CO₂RR performance (Supplementary Fig. 19).

By introducing C_2v-symmetric Ni single atoms in Ni-TSnS₂ (1.17 wt% Ni loading), a greatly enhanced C₂H₆ production rate of 139.58 ±  5.14 μmol g^-1 h^-1 is achieved, featuring a C₂H₆ electron selectivity of 89.41 ±  4.43%. Notably, compared to Ni-SnS₂ (0 μmol g^-1 h^-1 of C₂H₆ yield), Ni-TSnS₂ exhibits superior C₂H₆ yield and selectivity, highlighting the critical roles of moiré superlattice structure and C_2v-symmetric Ni single atoms in CO₂-to-C₂H₆ conversion. Noting that C₂H₆ formation involves an 14-electron transfer process whereas CO generation requires only a 2-electron transfer process, the CO₂RR performance of Ni-TSnS₂ is significantly enhanced compared to other SnS₂ materials. The photocatalytic performance of Ni-TSnS₂ is characterized by two key metrics: a significant apparent quantum yield (AQY) of 4.91% at 380 nm and a notable solar-to-chemical (STC) efficiency of 0.67% sustained over 10 h of operation (Supplementary Fig. 20).

Overall, the photocatalytic CO₂RR performance of the four materials follows the order of SnS₂ < Ni-SnS₂ < TSnS₂ < Ni-TSnS₂, which aligns with the SOC quantification results, confirming the critical role of SOC in enhancing photocatalytic CO₂RR rate and selectivity.

Our blank control experiments demonstrate that no CO, CH₄, and C₂H₆ is generated in the dark, in the absence of photocatalysts, or without a supply of CO₂ (Fig. 2e). The ¹³C isotopic labelled test further verifies that ¹³CO, ¹³CH₄, and ¹³C₂H₆ are the products of ¹³CO₂, which originate solely from photocatalytic CO₂RR (Supplementary Fig. 21b). Based on bandgaps from UV-visible diffuse reflectance spectroscopy (UV-DRS, Supplementary Fig. 22) and synchrotron radiation photoemission spectroscopy (SRPES, Supplementary Fig. 23), both SnS₂ and Ni-TSnS₂ have conduction band (CB) potentials suitable for CO, CH₄, and C₂H₆ production through CO₂ reduction (Supplementary Fig. 24).

In-situ EPR was employed to investigate the effect of SOC during photocatalytic CO₂RR. Here, the g factor represents the combined contributions of the spin- and orbital-magnetic moments of each electron²⁹. Deviation from the free-electron g value signal indicates presence of the SOC effect, where the orbital- and spin-angular momenta are intertwined^29,30. The absence of a detectable spin resonance signal in SnS₂ suggests that the SOC effect is weak (Supplementary Fig. 8). For Ni-SnS₂, the g factors associated with sulfur vacancies and Ni(III) species remain constant throughout the reaction, indicating that SOC plays a negligible role in photocatalytic CO₂RR (Fig. 3a). In contrast, both TSnS₂ and Ni-TSnS₂ exhibit discernible positive shifts in the g factor of sulfur vacancies, directly implicating SOC-driven spin states transition of photogenerated charge within the SnS₂ moiré superlattice (Fig. 3b, c). Moreover, for Ni-TSnS₂, the g factor shift of Ni(I) is substantially larger (∆g_xx = 0.024, ∆g_yy = 0.019, ∆g_xx = 0.062) than observed for sulfur vacancies (∆g = 0.003), indicating that photogenerated electrons localized at Ni sites experience more pronounced spin states transition than sulfur vacancies. This spin states transition associated with Ni(I) can be attributed to spin and orbit entanglement of Ni during CO₂RR. Decay of Ni(I) signals in Ni-TSnS₂ indicates a depletion of spin density at Ni sites (Fig. 3c).

Fig. 3: Photogenerated charge separation performance of various materials.

a–c In-situ EPR spectra for TSnS₂, Ni-SnS₂, and Ni-TSnS₂ in the presence of CO₂ and H₂O (g) under solar light irradiation. The arrows in (b) and (c) represent the changing trends of the data lines. d KPFM mapping of SnS₂, TSnS₂, Ni-SnS₂, and Ni-TSnS₂. e Contact potential difference and SPV of SnS₂, TSnS₂, Ni-SnS₂, and Ni-TSnS₂. The error bar indicates the fluctuation range of this set of data, representing mean ± standard deviation (SD). f Average PL lifetime mapping of SnS₂, TSnS₂, Ni-SnS₂, and Ni-TSnS₂. g Radiation lifetime τ₁ and non-radiation lifetime τ₂ of SnS₂, TSnS₂, Ni-SnS₂, and Ni-TSnS₂. The error bar in (e) and (g) indicates the fluctuation range of this set of data, representing mean ± standard deviation (SD).

SOC-induced LRSL and charge separation

Kelvin probe force microscopy (KPFM) was employed to analyze electron-hole separation behavior (Fig. 3d). SnS₂ exhibits weak surface photovoltage (SPV = 1.68 mV) under illumination. SPV increases slightly with C_3v-symmetric Ni single atoms for Ni-SnS₂ (2.52 mV), indicating improved charge separation after Ni anchoring. The moiré superlattice in Ni-TSnS₂ greatly boosts SPV to 19.93 mV, suggesting it plays a major role in charge separation (Fig. 3e). Further incorporation of C_2v-symmetric Ni single atoms into TSnS₂ significantly enhances SPV to 53.99 mV. This more than 32-fold improvement (compared to SnS₂) implies a synergistic effect between moiré superlattice and C_2v-symmetric Ni sites on enhanced charge separation efficency³¹.

We used single-particle confocal fluorescence microscopy to map photogenerated charge carrier lifetimes on Ni-TSnS₂ nanosheets (Supplementary Fig. 25). Spatially and temporally resolved photoluminescence (PL) measurements (Fig. 3f, and Supplementary Fig. 26) show that SnS₂ has the shortest average PL lifetime (~1.29 ns), whereas increased lifetimes are experienced by Ni-SnS₂ (~9.91 ns), TSnS₂ (~33.34 ns), and Ni-TSnS₂ (~62.45 ns), indicating enhanced carrier survival due to the moiré superlattice and C_2v-symmetric Ni sites^32,33. The radiative lifetime (τ₁) reflects the rapid recombination of charge carriers, whereas the non-radiative lifetime (τ₂) represents trapped carriers available for surface reactions. Figure 3g reveals that τ₂ in Ni-TSnS₂ and TSnS₂ is extended by factors of more than 43 and 21 respectively compared to SnS₂. The larger τ₂ fraction (A₂) in Ni-TSnS₂ suggests a higher probability and priority of participation in the photocatalytic reactions (Supplementary Fig. 27). Moreover, the trends in photocurrent intensity of the four materials are in close accordance with the trends in CO₂RR performance and SOC strength (Supplementary Fig. 28a). The peak intensity in the PL spectra follows the order of SnS₂ > Ni-SnS₂ > TSnS₂ > Ni-TSnS₂, providing further evidence that Ni-TSnS₂ has the lowest charge recombination rate (Supplementary Fig. 28b). For all four materials, the CO₂RR performance, SPV, non-radiation lifetime, photocurrent, and PL spectra all concurred with the trend in SOC strength. Therefore, we conclude that the SOC effect in Ni-TSnS₂ plays the dominant role in enhancing charge separation.

The underlying mechanism of SOC mediated charge separation was analyzed by electronic structure calculations including SOC-parameters. Bands of SnS₂ along Γ-K-M-Γ direction with projected values of spin operator (S_x, S_y, and S_z) show negligible spin splitting (Fig. 4a and Supplementary Fig. 29). By comparison, TSnS₂ and Ni-TSnS₂ exhibit more pronounced spontaneous in-plane (S_x and S_y) and out-of-plane (S_z) spin splitting, indicating strong SOC in these two twist materials (Fig. 4a and Supplementary Figs. 29–32). This observation aligns well with the characterizations of SOC in Fig. 2a–c. Furthermore, bandgap narrowing induced by spin splitting is also confirmed by UV-DRS (Supplementary Fig. 22), where the measured bandgaps for TSnS₂ (E_g = 1.98 eV) and Ni-TSnS₂ (E_g = 1.89 eV) are reduced by 0.21 and 0.30 eV compared with that of SnS₂ (E_g = 2.19 eV).

Fig. 4: SOC-induced LRSL of Ni-TSnS₂.

a Spin-projected band structure of SnS₂ and Ni-TSnS₂ along the S_z direction. Spin components polarized parallel to the out-of-plane spin component (S_z) lie along the z-axis. b Spin textures for the conduction band minimum inner (CBM1) and outer (CBM2) of Ni-TSnS₂, the valence band maximum inner (VBM1) and outer (VBM2) of Ni-TSnS₂. The black arrows represent projections of the in-plane spin orientation, and the red and blue regions correspond to projections along the out-of-plane spin direction. c Scheme of spin-forbidden recombination mechanism. The arrow direction in (b) and (c) represents the direction of the spin of electron.

Noting that the XMCD signal originates from Zeeman splitting, the response of XMCD is used to validate the credibility of our theoretical calculation results³⁴. In Supplementary Fig. 33, XMCD responses of Sn M_{4, 5}-edge demonstrate spin-splitting in TSnS₂ and Ni-TSnS₂. Moreover, spin texture onto the reciprocal 2D plane of Rhombus region, Triangular region and Square region of Ni-TSnS₂ (as displayed in Fig. 1a) is analyzed, and giant spin branching occurs between the valance band maximum outer (VBM2) and conduction band minimum inner (CBM1) in Ni-TSnS₂ (Fig. 4b), inducing almost opposite spin orientation. This could have an enormous impact on the dynamics of charge carriers: the recombination of CBM1 → VBM2 is a spin-forbidden process due to their different spin orientations, which would inhibit recombination (Fig. 4c)^35,36,37. The results of energy level configuration analysis based on SRPES also confirm the splitting of the band edge (Supplementary Fig. 23).

Furthermore, by considering the tangential and radial characteristics of each texture, we identify the spin textures of the Rhombus region, Triangular region and Square region of Ni-TSnS₂ as Zeeman-type, Rashba-type, and Dresselhaus-type SOC (Fig. 4b and Supplementary Fig. 34)³⁸. The Zeeman effect breaks spin-state degeneracy, generating intrinsic spin polarization, while Rashba- and Dresselhaus-type SOC produce concentric and anisotropic spin textures respectively, establishing spin-momentum locking topology through orthogonal spin-momentum correlations^39,40,41. This topological protection ensures strong spin polarization against impurities and disorder⁴². Furthermore, the moiré superlattice architecture establishes long-range ordered SOC patterns, enabling topological protection of long-range spin-momentum locking (LRSL) through synergetic Rashba-Dresselhaus mechanisms⁴³. Such LRSL enables long-range ordered spin-pinning, thereby ensuring temporal stability of spin states. We note that DFT results, limited by standard approximations, are intended to provide qualitative mechanistic insight. Therefore, magnetization curve was performed. In Supplementary Fig. 35a, a magnetization curve similar to ferromagnetism emerges in Ni-TSnS₂ demonstrated the long-range spin pining.

Moreover, the intrinsic long-range order preserves the spatial stability of spin states during electron transfer. Therefore, Ni-TSnS₂ exhibits efficient charge separation, CO₂RR rate, and stability. Therefore, CO₂RR rate and C₂H₆ selectivity of Ni-TSnS₂ remain almost unchanged even after a long-time reaction of 50 h (Supplementary Fig. 35b). Furthermore, after 50 h of photocatalytic CO₂RR, Ni-TSnS₂ exhibits no appreciable changes in either crystal structure or chemical composition, confirming its high stability under operating conditions (Supplementary Fig. 36).

Above all, twist engineering and low-symmetry Ni sites activate three types of SOC, thereby strengthening the SOC strength of the Ni-TSnS₂. Then, the cooperative action of these SOC effects promotes LRSL. AC-STEM image of Ni-TSnS₂ reveals a periodic moiré superlattice spanning the entire field of view (Supplementary Fig. 37 and Supplementary Note 22), while superlattice diffraction peaks in the XRD patterns (Supplementary Fig. 3) corroborate its long-range structural order. This extended superlattice thereby engenders a long-range spin-pinning effect across the whole domain, in contrast to the short-range spin pinning induced by randomly distributed local symmetry-breaking defects.

SOC-mediated radical formation and reaction pathway

To explore the mechanism of SOC-mediated high electron selectivity for C₂H₆ production, we performed in-situ diffuse reflectance infrared Fourier transformation spectroscopy (DRIFTS) analysis to investigate the CO₂RR pathways for Ni-TSnS₂ (Supplementary Fig. 38). *CH₂O (1473.34 cm^-1), *OCH₃ (1077–1162 cm^-1), and *CH₃ (1374–1455 cm^-1) absorption bands can be seen on the surface of Ni-TSnS₂. However, no reaction intermediates associated with C₂H₆ formation, such as *OC–COH (1552 cm^-1), *OCH₂–CH₃ (1325 cm^-1), and *OC–CO (1531/1549 cm^-1), were detected on the Ni-TSnS₂ surface. Supplementary Figs. 39–44 summarize the Gibbs free energy change diagrams of the reaction pathway for the different materials, suggesting that the C_2v-symmetric Ni sites reduce the energy barrier for CO₂ activation leading to the production of *CH₃. Moreover, the Gibbs free energy diagrams for C–C coupling on Ni-TSnS₂ reveal high reaction barriers (Supplementary Figs. 39b, c). These findings suggest that CO₂ reduction to C₂H₆ on Ni-TSnS₂ proceeds through an unconventional reaction pathway.

High-speed laser confocal microscopy analysis further reveals that photocatalytic CO₂RR by Ni-TSnS₂ can efficiently generate free radical species. In Fig. 5a, no significant Rhodamine-6G fluorescence signal is detected in SnS₂, Ni-SnS₂, and TSnS₂, suggesting that 5,5-dimethyl-1-pyrroline N-oxide (DMPO) quenched the fluorescence signal of Rhodamine-6G. However, for Ni-TSnS₂, the specific binding of DMPO to the free radicals produced via photocatalytic CO₂RR diminishes the quenching effect on the Rhodamine-6G fluorescence signal. In-situ EPR spectra further confirm that DMPO- · CH₃ radical adduct (hyperfine splitting constants, A_N = 15.90 G, A_H = 22.90 G) is exclusively generated during the photocatalytic CO₂RR process by Ni-TSnS₂ (Supplementary Fig. 47)⁴⁴. ·CH₃-to-C₂H₆ radical chain reaction is a typical radical process characterized by high reaction rate and selectivity^45,46.

$$\cdot {{{\mathrm{CH}}}}_{3}+\cdot {{{\mathrm{CH}}}}_{3}\to {{{{\rm{C}}}}}_{2}{{{{\rm{H}}}}}_{6}$$

(3)

Fig. 5: SOC mediated radical pathway.

a High-speed confocal imaging of ∙CH₃ produced by various materials after light irradiation. b Schematic of molecular orbital of ∙CH₃. c Schematics of molecular orbital of C atom in ∙CH₃ and spin-charge density of ∙CH₃. d Hybridization energy levels of Ni 3d orbitals of Ni-TSnS₂ and C 2p_z orbitals of *CH₃. The inset illustrates wave functions for the molecular orbital hybridizations. The arrow direction in (b–d) represents the direction of the spin of electron. The blue, yellow, grey, brown and white spheres respectively represent Sn, S, Ni, C and H atoms.

·CH₃-to-C₂H₆ chain reaction operates in natural environments. For example, in the methane-rich atmosphere of Titan, this reaction dominates the formation pathway for C₂H₆⁴⁷. ·CH₃ quenching experiments confirm that ·CH₃ is a key intermediate for the formation of C₂H₆ (Supplementary Fig. 48). Therefore, the generation of ·CH₃ serves as a rate-limiting step to enhance both the C₂H₆ formation rate and selectivity. This chain reaction pathway effectively circumvents the high-energy C–C coupling step on the catalyst surface. Radical pathways have been documented in CO₂RR. For example, Basak et al. reported CO₂ activation and CO formation via SET at an enzymatic Ni(I) center⁴⁸. This result aligns with the SET-induced radical formation proposed in this study and further underscores the potential of Ni(I) to promote radical conversion of CO₂ through SET. Although the catalytic environments and dominant products are different, both of the studies offer complementary evidences on advancing radical-based reaction mechanisms in CO₂RR.

To investigate the source of ·CH₃, we analyzed the electron arrangement and molecular orbital of ·CH₃. As shown in Fig. 5b, three sp² hybrid orbitals of the C atom hybridize with the 1s orbitals of three H atoms, forming σ bonds between the C and H atoms. In particular, the radical character originates from the spin electron in the 2p_z orbital (Fig. 5c). Therefore, SET from Ni-TSnS₂ to 2p_z orbital of *CH₃ contributes to the formation of the ·CH₃ radical.

To further investigate the physical origin of the SET process, we analyzed the electronic structure features of Ni single atoms on SnS₂ and TSnS₂. According to the SRPES spectra (Supplementary Fig. 49), the higher secondary electron cutoff (SEC) of Ni-TSnS₂ than Ni-SnS₂ verifies that Ni-TSnS₂ possesses more frontier molecular orbitals (FMOs)⁴⁹, which display increased Ni 3d electron aggregation⁵⁰; similar electron aggregation is observed for Bader charge and differential charge density calculation results (Supplementary Fig. 50). The magnetization-temperature (M-T) curve for Ni-SnS₂ indicates negative magnetization (M < 0) (Supplementary Fig. 51a), suggesting that the number of spin electrons of Ni-SnS₂ is nearly zero. By plotting the inverse magnetic susceptibility against temperature for Ni-TSnS₂, we find that the curve has a steep positive gradient for temperatures from 200 to 300 K; this indicates Ni-TSnS₂ exhibits a stronger paramagnetism than Ni-SnS₂ (Supplementary Fig. 51b)⁴⁹. The number of spin electrons (n) at the center of Ni center is related to the effective magnetic moment (μ_eff) by:

$$2.828\sqrt{{\chi }_{{{{\rm{m}}}}}T}={\mu }_{eff}=\sqrt{n(n+2)}$$

(4)

where χ_m is magnetic susceptibility. Using formula (4), n for Ni-TSnS₂ is calculated to be 5. In short, Ni-TSnS₂ possesses more spin-polarized electrons than the other materials considered here, and thus exhibits stronger spin splitting.

A working hypothesis for the SOC between Ni sites and *CH₃ intermediate is presented in Fig. 5d, providing insight into the formation of ·CH₃ radical. Specifically, when *CH₃ intermediate adsorbs on Ni-SnS₂, the density of states (DOS) of the C 2p_z orbitals displays an obvious overlap with the Ni 3d orbitals (Supplementary Fig. 52a). This hybridization process lowers the energy level of the *CH₃ intermediate and leads to formation of 3d_z²-2p_z bonding orbital. In particular, the DOS and crystal orbital Hamilton population (COHP) results reveal that the 3d_z²-2p_z bonding orbital exhibits identical bonding energy levels (spin-up = −3.23 eV, spin-down = −3.19 eV) and bonding strengths (ICOHP of spin-up and spin-down = −0.138 and −0.14) in different spin channels, indicating a weak SOC phenomenon between the *CH₃ intermediate and the Ni atom (Supplementary Fig. 52b). As shown in Fig. 5d, the 3d_z² orbital hybridizes with the C 2p_z orbital, resulting in the formation of a fully occupied 3d_z²-2p_z bonding orbital.

Bonding orbitals between the *CH₃ intermediate and the Ni atom exhibited pronounced SOC effects for the configurations of *CH₃ intermediate adsorbed on Ni-TSnS₂. This is confirmed by both DOS and COHP results, which show distinct differences in both bonding energy levels and bonding strengths for different spin channels. Specifically, in the Ni-TSnS₂ (Square region) configuration, the fully occupied 3d_z²-2p_z bonding orbital that formed between the Ni and C atoms lies at a significantly lower energy level (spin-up: −2.73 eV, spin-down: −2.94 eV) than the Ni 3d orbital, facilitating electron transfer from the Ni 3d to C 2p orbital (Fig. 5d and Supplementary Fig. 52c). Partially occupied antibonding states emerge below the Fermi level, demonstrating the SET process between Ni and C atom, which is verified by spin charge density calculations (Supplementary Fig. 53). Moreover, the antibonding state below the Fermi level weakens the Ni-C chemical bond, thereby facilitating the desorption of *CH₃ and the formation of ·CH₃ (Supplementary Fig. 54d). A similar SOC-induced SET mechanism is also observed in the Ni-TSnS₂-CH₃ (Rhombus and Triangular region) configurations (Fig. 5d and Supplementary Fig. 54).

Discussion

We present a twisting stacking strategy to regulate photosynthesis of C₂H₆ from CO₂ and H₂O. The developed Ni-TSnS₂ achieves a C₂H₆ production rate of 139.58 ±  5.14 μmol g^-1 h^-1 with 89.41 ±  4.43% electron selectivity, representing a state-of-the-art photocatalyst for CO₂-to-C₂H₆ conversion. Moiré superlattices, combined with C_2v-symmetric Ni, collectively generate Zeeman, Rashba, and Dresselhaus-type SOC in Ni-TSnS₂. Rashba and Dresselhaus SOC in Ni-TSnS₂ provide LRSL with topological protection, preventing spin degeneration. This effect leads to a 32-fold enhancement of SPV and a 43-fold increase in charge lifetime, greatly improving charge separation and accelerating C₂H₆ photosynthesis kinetics. Moreover, C_2v symmetry strengthens SOC effect of Ni sites, while in-situ EPR and molecular orbital analysis reveal strong SOC and SET interactions between Ni sites and *CH₃ intermediates, driving the formation of ·CH₃. Thereby, Ni-TSnS₂ exhibits high reactivity and selectivity for C₂H₆ photosynthesis. This study provides a reference for improving the catalytic rate, selectivity and stability of C₂H₆ photosynthesis.

Methods

Synthesis of Ni-TSnS₂

TSnS₂ was synthesized by a chemical vapor deposition method in vacuum tube furnace. Typically, 1 g of Sn powder (99.90 at.% purity, size ≤100 μm) was placed in a ceramic boat at the center of the heating zone, and 0.5 g of sulfur powder (99.00 at.% purity, size ≤200 μm) was put in another ceramic boat at an upstream distance of about 5 cm. A quartz tube (50 mm in diameter and 50 mm in length) was selected as a substrate for TSnS₂ growth, and placed about 10 cm downstream of the center of the heating zone. Using a pump, the furnace chamber was depressurized to vacuum conditions before heating commenced. Afterwards, the center of the heating zone was programmed to heat to 800 °C within 80 min. When the furnace reached 800 °C, the temperature of the sulfur powder at the upstream was about 360 °C. The furnace was kept at 800 °C for 5 h before cooling. Then, the quartz tube was cooled down to room temperature in 3–6 h as prescribed by a temperature control program. During this cooling period, twisted islands formed on the SnS₂ nanosheets.

For synthesis of Ni-TSnS₂, 100 mg of prepared TSnS₂ was fully dispersed in a mixed solution (V_water: V_{ethylene glycol} = 9: 1) via sonication, followed by the addition of 0.2 mg nickel(II) acetate tetrahydrate (Ni(CH₃COO)₂·4H₂O). After stirring for 2 h under a 300 W Xe lamp (Merry Change, MC-PF300C, spectrum range: 300–2500 nm) with irradiation light intensity of 100 mW cm^-2, the mixture was centrifuged and dried to obtain Ni-TSnS₂.

Synthesis of Ni-SnS₂

SnS₂ was synthesized following the same method as TSnS₂ except for the cooling process. In this case, the quartz tube was cooled to room temperature within 2 h. The Ni single atom photo-deposition process was synthesized in the same way as for Ni-TSnS₂.

Characterizations and instruments

Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (AC-HAADF-STEM) images were obtained using Titan Cubed Themis G2 200. Sn K-edge X-ray absorption tests were performed at the BL11B station in SSRF (Shanghai Synchrotron Radiation Facility, China). Sn L-edge X-ray absorption tests were performed at the XAFCA station in Singapore Synchrotron Light Source. Sn M-edge and Ni L-edge X-ray absorption measurements were carried out using the Beamlines MCD-B (Soochow Beamline for Energy Materials). X-ray magnetic circular dichroism (XMCD) measurements were performed using Beamlines 4.0.2 and 6.3.1 of the Advanced Light Source by switching the magnetization parallel and antiparallel to the propagation direction of circularly polarized X-rays at normal incidence. Synchrotron radiation X-ray photoelectron spectroscopy (SRXPS) and photoemission spectroscopy (SRPES) were performed using the BL11U beamline of the National Synchrotron Radiation Laboratory (NSRL).

An EMXplus-6/1 electron paramagnetic resonance (EPR) spectrometer (Bruker, Germany) was used to detect signals of Ni-TSnS₂ under 300 W Xenon Arc light. The EPR spectra were recorded at 20 °C with a circulating water system used to maintain the temperature; the EPR spectrometer was operated at an X-band frequency of 9.84 GHz. AFM and KPFM were performed using a conductive AFM Enviroscope system (Bruker) in tapping mode at room temperature, equipped with a 300 W Xenon light. Objective-scanning confocal microscopy (MicroTime 200, PicoQuant) coupled to an Olympus IX71 inverted fluorescence microscope was used to collect single-particle photoluminescence images (set-up shown in Supplementary Fig. 25). High-speed confocal imaging of radicals was performed using a fast super-resolution laser confocal microscope (Zeiss LSM980 Airyscan2). X-ray diffraction (XRD) patterns were recorded on a Bruker AXS D8 Advance diffractometer equipped with Cu Kα radiation source (λ = 1.54060 Å). Morphological and microstructural analyses were conducted using a scanning electron microscope SEM (JSM-7600F) at an accelerating voltage of 10 kV. Transmission electron microscopy TEM and high-resolution HR-TEM images were recorded using a JEOL-2100F apparatus for an accelerating voltage of 200 kV. X-ray photoelectron spectroscopy (XPS) was performed by a scanning X-ray microprobe (PHI 5000 Verasa, ULAC-PHI, Inc.) with Al Kα radiation and C 1s peak at 284.8 eV used as the internal standard.

In-situ DRIFTS spectra were carried out on Fourier-transform infrared spectrometer (VERTEX 70 v, Bruker). Quantification of Ni was performed via inductively coupled plasma–mass spectrometry (Agilent 7900). A Shimadzu UV-3200i spectrophotometer was used to record UV-vis diffuse reflection spectra (UV-DRS). Photoluminescence (PL) spectroscopy was carried out by an FLS1000, Edinburgh. ¹¹⁹Sn Mössbauer spectroscopy measurements (MFD-500AV-03, Topologic Systems) were acquired in transmission mode at room temperature, and the spectra fitted with a suitable combination of Lorentzian profiles using the least-square method.

Geometric phase analysis (GPA) was applied to the microscopy data using DigitalMicrograph (DM3.1 Gatan^TM). Photocurrent responses were recorded using an electrochemical workstation (CHI 760E, CH Instruments, Shanghai, China).

Measurements of photocatalytic CO₂ reduction

CO₂ reduction experiments were performed in a flow quartz reactor. Typically, the as-synthesized photocatalyst was dispersed in water until a concentration of 2 mg mL^-1 was achieved, then 5 mL of the mixture (10 mg photocatalyst) was coated on the quartz glass and heated at 65 °C to volatilize the solvent. Before light irradiation, the system (MC-SCO2II-AG, Beijing Merry Change Technology Co., Ltd) was initially vacuum-treated three times and then filled with pure CO₂ (purity > 99.999%) to a gas pressure of 1 atm, after which the system was stored in the dark for 30 min in order to attain the dynamic adsorption-desorption equilibrium of CO₂. Next, 2 mL of deionized (DI) water was injected into the reactor for photocatalysis. The reactor was then irradiated at a controlled light intensity of 100 mW cm^-2 by a 300 W Xe lamp (Merry Change, MC-PF300C, spectrum range: 300–2500 nm) at AM1.5 mode. The incident irradiance was measured at the sample plane using a calibrated optical power meter. Specifically, the optical power was recorded at the position where the catalyst-coated substrate/reactor window was placed during the reaction, and the irradiance (mW cm^-2) was obtained by dividing the measured power (mW) by the effective illuminated area. The distance of the light source to the top of the reactor was 3 cm. The temperature was kept at 20 °C using a water bath. During irradiation, 0.1 mL of gas was collected from the reaction headspace every hour, and the gaseous products were immediately analyzed using gas chromatography (GC, Fuli GC9790Plus). The isotope experiment was conducted using ¹³CO₂ as feedstock, and the products were analyzed using gas chromatography-mass spectrometry (GC-MS, Agilent 8890-5977B, USA). The reductions of H₂O to H₂, CO₂ to CO, CO₂ to CH₄ and CO₂ to C₂H₆ involved two-, two-, eight-, and fourteen-electron transfer processes, respectively. Product selectivity was evaluated based on total electron utilization. Overall selectivity toward C₂H₆ was calculated using the following equation:

$$ {\mathrm{Electron}}\,{\mathrm{selectivity}}(\%) \\ =\frac{{{{\rm{C}}}}_{2}{{{\rm{H}}}}_{6}\,{\mathrm{production}}\times 14}{{{{\rm{H}}}}_{2}\,{\mathrm{production}}\times 2+{\mathrm{CO}}\,{\mathrm{production}}\times 2+{{\mathrm{CH}}}_{4}\,{\mathrm{production}}\times 8+{{{\rm{C}}}}_{2}{{{\rm{H}}}}_{6}\,{\mathrm{production}}\times 14}$$

(5)

Apparent quantum yield (AQY) measurement

AQY is calculated as the ratio of effective electrons (derived from product yields) to incident photons. Product formation (CO, CH₄ and C₂H₆) was measured during 12-h reactions under monochromatic light at a specific wavelength (380, 420, 450, 500, and 550 nm, respectively). The photon flux for each wavelength was calculated from the incident light intensity, which was measured utilizing a calibrated silicon photodiode with a UV-enhancement filter. Then, the AQY for CO₂ reduction is given by:

$${{\mathrm{AQY}}}=\frac{{{\mathrm{yield}}}({{\mathrm{CO}}})\times 2+{{\mathrm{yield}}}({{{\mathrm{CH}}}}_{4})\times 8+{{\mathrm{yield}}}({{{{\rm{C}}}}}_{2}{{{{\rm{H}}}}}_{6})\times 14}{{{\mathrm{incident}}}\,{{\mathrm{photons}}}}$$

(6)

Solar-to-chemical (STC) efficiency measurement

STC efficiency is used to quantify the efficiency of energy conversion from solar energy to stored chemical energy, which is calculated as:

$${{\mathrm{STC}}}=\frac{\sum [{{\mathrm{yield}}}({{{\mathrm{CO}}}}_{2}{{\mathrm{RR}}}\,{{\mathrm{products}}})\times {{\mathrm{\varDelta G}}}({{\mathrm{reduction}}}\,{{{\mathrm{CO}}}}_{2}\,{{\mathrm{to}}}\,{{\mathrm{products}}})]}{{{\mathrm{light}}}\,{{\mathrm{int}}}\,{{\mathrm{ensity}}}\times {{\mathrm{irradiation}}}\,{{\mathrm{area}}}\times {{\mathrm{time}}}}$$

(7)

During the STC measurement, the incident light intensity was set to 175 mW cm^-2 and the reaction was conducted for 10 h. The standard Gibbs free energy changes (ΔG°) for CO₂ reduction to CO, CH₄, and C₂H₆ are 514.2 kJ mol^-1, 800 kJ mol^-1, and 1467.3 kJ mol^-1, respectively.

·CH₃ quenching experiment

The as-prepared photocatalyst was dispersed in a 10 mM solution (10 mL) of 2,6-di-tert-butyl-4-methylphenol (BHT) to a concentration of 2 mg mL^-1. 5 mL aliquot of the suspension was then deposited onto quartz glass and held at 65 °C to evaporate the solvent. The subsequent photocatalytic CO₂RR operation was conducted following the above-mentioned method.

Computational calculation methods

All DFT calculations were carried out using the Vienna ab initio Simulation Package (VASP 6.5.0). In this study, the SnS₂ crystal structure model adopts the 1 T phase, in which Sn is octahedrally coordinated by surrounding S atoms to form an S-Sn-S sandwich layer. The detailed structural information is provided in Supplementary Table 13. Electro-ion interactions are described by means of projector-augmented wave (PAW) pseudopotentials. Total energies are converged to <10^-5eV. Brillouin-zone integrations proceed using 3 × 3 × 3 and 4 × 4 × 4 k-point meshes for structural relaxation and electronic calculations, respectively. SOC Hamiltonian is given by:

$$H=\frac{{p}^{2}}{2m\ast }+{\alpha }_{R}({{{\boldsymbol{\sigma }}}}\times {{{\boldsymbol{k}}}})\cdot \hat{{{{\boldsymbol{z}}}}}$$

(8)

where m*, α_R, σ, k and ẑ denote electron effective mass, Rashba constant, Pauli matrix, electron wave vector, and surface normal, respectively. Rashba eigenvalues and eigenstates can be written as:

$${{E}}_{{\pm }}({{{\boldsymbol{k}}}})=\frac{{\hslash }^{2}{{k}}^{2}}{2{m}{\ast }}\pm {{\alpha }}_{{R}}{{{\boldsymbol{k}}}}=\frac{{\hslash }^{2}}{2{m}{\ast }}{({k}\pm {{k}}_{R})}^{2}-{{E}}_{{R}}$$

(9)

$${{\psi }}_{\pm }({{{\rm{k}}}})=\frac{{e}^{{i}{{{\boldsymbol{kr}}}}}}{2\pi \hslash }\frac{1}{\sqrt{2}}\left(\begin{array}{c}\pm \frac{i{{k}}_{{x}}+{{k}}_{{y}}}{{k}}\\ 1\end{array}\right)=\frac{{e}^{{i}{{{\boldsymbol{kr}}}}}}{2\pi \hslash }\frac{1}{\sqrt{2}}\left(\begin{array}{c}\pm {i}{e}^{-{i}\theta }\\ 1\end{array}\right)$$

(10)

where k = k (cos θ, sin θ, 0) are defined as vector in the k_x-k_y plane. “+” and “-” distinguish the two conduction-band minima at Γ. Spin texture is calculated as:

$${{{{\boldsymbol{s}}}}}_{\pm }=\frac{\hslash }{2}{\langle {\sigma }\rangle }_{\pm }=\frac{\hslash }{2}\langle {{\psi }}_{\pm }|{\sigma }|{{\psi }}_{\pm }\rangle=\pm \frac{\hslash }{2}\left(\begin{array}{c}\sin {\theta }\\ -\,\cos {\theta }\\ 0\end{array}\right)$$

(11)

Projected density of states (PDOS) was computed with VASPKIT, and Crystal Orbital Hamilton Populations (COHP) was evaluated using LOBSTER. Gibbes free energies (G) are calculated as:

$${G}={{E}}_{{DFT}}+{{E}}_{{ZPE}}-TS$$

(12)

E_DFT is the electronic energy obtained from VASP; E_ZPE and TS are calculated under the ideal-gas approximation using vibrational frequencies.