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

Domain: chemistry
Published: 2026-01-30
Editorial outcome: minor_revision

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 future1,2. 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 sites4,5. 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 photocatalysis6–8. Photo-generated 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 reactions9,10. 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 separation6,11. 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 efficiency7,11,12. 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 activity13,14. 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.

Results
Moiré superlattice and C2v 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 confirm 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 here in 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–S configuration in Ni-TSnS2 can be described by C2v 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 C2v-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 3d 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, C2v symmetric Ni sites exhibit stronger SOC effects.

Furthermore, X-ray absorption spectrometry (XAS) measurements of Sn L2 (p1/2 → d3/2) and L3 (p3/2 → d5/2) 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 L3 and L2 edges (known as the branching ratio, BR) is directly proportional to the expected value of the angular part of the SOC (denoted by hL·Si)23,24:

BR = RL3 / RL2 = (ni + hLi·si) / (ni - hLi·si) (1)

hL·Si = 1/3 (BR - 2) / (BR + 1) (2)

where ni is the number of holes in the d shell; and li and si 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 inferior25,26, whereas the emergence of moiré superlattice and C2v-symmetric Ni coordination elevate the BR value for Ni-TSnS2. The resulting value is comparable to those obtained for 4d transition metal compounds (generally regarded as moderate-strength SOC materials), indicating greatly enhanced SOC strength for Ni-TSnS2 27.

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, C2v-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 SnS2, which has a comparable concentration of sulfur vacancies to TSnS2, indicating that the moiré superlattice is crucial to the improvement in CO2RR performance (Supplementary Fig. 19).

By introducing C2v-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 C2v-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 originates solely from photocatalytic CO2RR (Supplementary Fig. 21b). Based on band gaps 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 intertwined29,30. 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 (Δgxx = 0.024, Δgyy = 0.019, Δgzz = 0.062) than observed for sulfur vacancies (Δg = 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).

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 C3v-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 C2v-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 C2v-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 C2v-symmetric Ni sites32,33. 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 (Sx, Sy, and Sz) show negligible spin splitting (Fig. 4a and Supplementary Fig. 29). By comparison, TSnS2 and Ni-TSnS2 exhibit more pronounced spontaneous in-plane (Sx and Sy) and out-of-plane (Sz) 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 band gaps for TSnS2 (Eg = 1.98 eV) and Ni-TSnS2 (Eg = 1.89 eV) are reduced by 0.21 and 0.30 eV compared with that of SnS2 (Eg = 2.19 eV).

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 M4, 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)35–37. 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 correlations39–41. 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 exhibit 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). *CHO (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), *OCH–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 C2v-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, AN = 15.90 G, AH = 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 selectivity45,46.

·CH3 + ·CH3 → C2H6 (3)

·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 C2H6 47. ·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 CO 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 underscore 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 2pz orbital (Fig. 5c). Therefore, SET from Ni-TSnS2 to 2pz 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 (μeff) by:

2.828 χm T = μeff = sqrt(n(n+2)) (4)

where χm 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 2pz 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 3dz2-2pz bonding orbital. In particular, the DOS and crystal orbital Hamilton population (COHP) results reveal that the 3dz2-2pz 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 3dz2 orbital hybridizes with the C 2pz orbital, resulting in the formation of a fully occupied 3dz2-2pz 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 3dz2-2pz 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 2pz 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).

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 (Vwater:Vethyleneglycol = 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 LSM 980 Airyscan 2). 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 70v, 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 Digital Micrograph (DM 3.1 GatanTM). 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 AM 1.5 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 GC 9790 Plus). 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:

Electron selectivity (%) = (C2H6 production × 14) / (H2 production × 2 + CO production × 2 + CH4 production × 8 + C2H6 production × 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:

AQY = (yield(CO) × 2 + yield(CH4) × 8 + yield(C2H6) × 14) / incident 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:

STC = [yield(CO2RR products) × G(reduction CO2 to products)] / (light intensity × irradiation area × 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 1T 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. Electron-ion interactions are described by means of projector-augmented wave (PAW) pseudopotentials. Total energies are converged to <10-5 eV. 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 = p2 / 2m* + αR (σ × k) · z^ (8)

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

E±(k) = (ℏ2k2 / 2m*) ± αR k = (ℏ2 / 2m*) (k ± kR)2 - ER (9)

ψ±(k) = eikr / sqrt(1) * (1 / sqrt(2)) * (1, ±ie±iθ) (10)

where k = k(cosθ, sinθ, 0) are defined as vector in the kx-ky plane. “+” and “-” distinguish the two conduction-band minima at Γ. Spin texture is calculated as:

s± = hσi = hψ± |σ| ψ±i = ± (sinθ, -cosθ, 0) (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 = EDFT + EZPE - TS (12)

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

Data availability
Data that support the findings of this study are included in the Main text and the SI files. Source data are provided with this paper.

Code availability
The Vienna ab initio Simulation Package (VASP) for the density functional theory calculations is available at https://www.vasp.at. We used the VASPKIT.1.3.0 code and Lobster 5.1.0 code for post-processing of the VASP calculated data. The VASPKIT.1.3.0 code and Lobster 5.1.0 code are available at Overview-VASPKIT 1.5 documentation and COHP - Crystal Orbital Hamilton Population - COHP (rwth-aachen.de), respectively.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study developed a new material of Ni single-atom anchored twisted SnS2 nanosheets (Ni-TSnS2), which was used in\nphotocatalytic reduction of CO2 for ethane (C2H6) synthesis. Through a combination of spectroscopic characterizations and\ntheoretical calculations, the authors systematically demonstrate that the twist angle structure induces spin-orbit coupling in\nSnS2, leading to spin-momentum locking. This spin-momentum locking effect prolongs the lifetime of photogenerated\ncharge carriers during photocatalysis, thereby facilitating the kinetics of CO2 hydrogenation. In addition, in-situ electron\nparamagnetic resonance (EPR) results reveal that the Ni single atoms anchored on the angular substrate also exhibit strong\nspin-orbit coupling, which induces the formation of methyl radicals. Then, these radicals subsequently participate in chain\nreactions to efficiently produce ethane. Generally, this work is of high quality with clear presentation and deep\nmechanism discussion. Therefore, this work can be published in Nature Communications after some revisions, and detailed comments\nare listed below:\n1. In order to comprehensively evaluate the catalytic performance, AQY and STC results should be provided.\n2. The authors need to further explain the statement of “Quadrupole moment splitting serves as a key indicator of symmetry\nbreaking”, so that readers can understand the principle of this representation of data and underlying mechanism of\nquadrupole moment splitting.\n3. The authors claim that “Fig. 3g reveals that τ2 in Ni-TSnS2 and TSnS is extended by factors of more than 43 and 21\nrespectively compared to SnS2”. The author should provide the value of τ2.\n4. In recent years, radical-mediated CO2 reduction mechanisms have attracted increasing attention. For instance, Basak et\nal. (Nat. Catal., 2025, 8, 794-803) reported that CO2 reduction at Ni(I) sites involved single-electron transfer and radical\nprocesses. I suggest that the authors compare their findings with this reference to further refine the discussion of radical\nreaction mechanisms presented in this work.\n5. During ethane (C2H6) photosynthesis, the ∙CH3-to-C2H6 radical chain reaction mentioned in this study raises an\nimportant question: does this reaction pathway exist in natural systems? Please clarify whether such a reaction occurs in\nnature and, if so, describe its natural occurrence and context.\n6. In this study, single-electron transfer (SET) at Ni sites of Ni-SnS2 leads to formation of form methyl radicals (∙CH3), which\nis found as the primary intermediate during CO2 reduction. The authors should provide solid evidences for formation of\n∙CH3.\n7. The authors should illustrate the most important reaction or rate-limiting step for formation of ethane in this system. Why\naren’t other reduction products such as CH4 and CO generated?", "reviewer_2": "This manuscript proposes an intriguing strategy to induce spontaneous long-range spin–orbit coupling (SOC) in SnS2\nthrough moiré engineering, and to achieve highly selective photocatalytic CO2-to-C2H6 conversion using single-atom Ni\nsites with C2v coordination. A comprehensive set of experimental characterizations combined with DFT calculations\nprovides a relatively complete evidence chain. Overall, the manuscript is well-structured, methodologically rich, and\npresents innovative conclusions. Therefore, I believe the manuscript might be published after addressing the following\nissues.\n1. The authors emphasize the effect of spontaneous long-range spin pinning for photocatalysis. How to define long-range? It\nwould also be helpful to discuss how the performance of catalysts with short-range orders compared to those exhibiting\nlong-range orders.\n2. The Ni EXAFS spectra of Ni-TSnS2 should be compared with suitable reference compounds, such as Nickel sulfide or\nNickel oxide, to clarify the coordination environment of Ni.\n3. The EDS mapping images would benefit from showing a larger area to capture an entire nanosheet, ensuring that the\nelemental distribution is representative of the material rather than localized regions. In addition, for comparison, AC-STEM\nimage of the Ni-free TSnS2 sample should be provided to better illustrate the Ni incorporation.\n4. Although the observed g-shift in the EPR spectra can be interpreted as evidence of changes in local spin or orbital\ncontributions, the authors should clarify how alternative factors, such as variations in chemical state, coordination\nenvironment, or local fields induced by surface adsorption, have been excluded.\n5. In Supplementary Fig. 8, the x-axis should be consistent for better comparison.\n6. Why does the distribution of C2H6 fragment peak look different between reactions under 12CO2 and 13CO2, given that\nboth show a main signal at m/z = 30?\n7. According to the experimental details, the photocatalytic experiments were carried out without sacrificial agents, meaning\nthat H2O oxidation occurred. The production rate of oxidation products should also be well investigated to demonstrate the\noccurrence of overall reaction. Besides, GC spectra for standards and reaction samples should be presented.\n8. It is noted that increasing Ni loading appears to decrease catalytic performance. The authors should discuss possible\nreasons for this phenomenon.\n9. The detection of DMPO-∙CH₃ is strong evidence for methyl radicals. However, further verification is recommended, such\nas inhibition or trapping experiments using known ∙CH₃ scavengers or radical inhibitors, and monitoring the effect on C2H6\nyield and selectivity.\n10. It is suggested to measure the AQY to quantitatively evaluate the photochemical efficiency of the system.\n11. The stability of the catalyst should be evaluated. Characterizations of Ni-TSnS2 before and after reaction (e.g., XRD,\nXPS, EPR, ICP-MS) is recommended to evaluate any structural or compositional changes in both the Ni species and the\nsupport.", "reviewer_3": "This work finished by Liu et al. presents a novel twist engineering for synthesis of SnS2 nanosheets (Ni-TSnS2), and strong\nspin-orbit coupling (SOC) was observed after Ni single-atom anchored on Ni-TSnS2. The developed material exhibits\nspontaneous long-range spin-momentum locking (LRSL) due to SOC, and enhances its reactivity and stability for\nphotocatalytic reduction of CO2 for ethane (C2H6) synthesis. The authors deeply explain the SOC effect for enhanced spin-\npolarized electron transfer and specific radical (∙CH3) formation. This work gives new insights into CO2 photocatalytic\nreduction by twist material with consideration of SOC and long-range spin-momentum locking. I recommend its acceptance\nafter further consider the following suggestions:\n(1) Material characterizations including TEM and selected area electron diffraction (SAED) pattern obtained for TSnS2 and\nNi-TSnS2 present twist angle of 30° between adjacent SnS2 layers. Can the twist angle be adjusted through CVD synthesis\ncondition, and why 30° is selected in this study?\n(2) For Ni-TSnS2 with strong SOC effects, the authors claim the anchored C2v symmetric Ni sites are the primary reason for\nthis SOC effect (based on XMCD results), then what is the role of twist engineering in SOC? What is the mechanism for\nimproved SOC after twist engineering and then Ni deposition?\n(3) Based on Mössbauer spectra analysis, the quadrupole splitting of TSnS2 and Ni-TSnS2 is 0.88 and 0.92 mm s-1,\nrespectively, so is it a big improvement for this value after Ni deposition for TSnS2?\n(4) The relationship between SOC and LRSL for Ni-TSnS2 should be more clearly explained, and is the strong SOC a\nprerequisite for long-range spin-momentum locking?\n(5) DRIFTS analysis indicates that CO2 reduction to C2H6 on Ni-TSnS2 proceeds through an unconventional reaction\npathway, and the specific transformation pathway or key step should be explained with consideration of SOC effect. Why\ncan ∙CH3 be produced in a large amount but not other radicals or other CORR pathways?\n(6) According to UV-vis DRS results, both SnS2 and Ni-TSnS2 have conduction band (CB) potentials suitable for CO, CH4,\nand C2H6 production through CO2 reduction. Then, what is the key reason for inhibition of other reactions for formation of\nCO and CH4?\n(7) The authors also should explain the key mechanism for the high stability of developed Ni-TSnS2 for CO2 photocatalytic\nreduction.\n(8) Some related works are suggested to discuss, such as Angew. Chem. Int. Ed. 2024, 63, e202412591；Adv. Mater. 2025,\n37, 2503027；"}, "author_response": "Authors’ Responses to Referees’ Comments\nManuscript ID: NCOMMS-25-79418-T\nTitle: Twist engineering induced long-range spin-momentum locking and radical pathway for\nphotosynthesis of ethane from carbon dioxide and water\nWe greatly appreciate the reviewers’ comments and revision suggestions about our manuscript. The\ncorresponding part has been carefully revised (marked in blue in the revised manuscript).\nR1\nResponse to Reviewer #1\nGeneral comment: This study developed a new material of Ni single-atom anchored twisted SnS\n2\nnanosheets (Ni-TSnS ), which was used in photocatalytic reduction of CO for ethane (C H ) synthesis.\n2 2 2 6\nThrough a combination of spectroscopic characterizations and theoretical calculations, the authors\nsystematically demonstrate that the twist angle structure induces spin-orbit coupling in SnS , leading\n2\nto spin-momentum locking. This spin-momentum locking effect prolongs the lifetime of\nphotogenerated charge carriers during photocatalysis, thereby facilitating the kinetics of CO\n2\nhydrogenation. In addition, in-situ electron paramagnetic resonance (EPR) results reveal that the Ni\nsingle atoms anchored on the angular substrate also exhibit strong spin-orbit coupling, which induces\nthe formation of methyl radicals. Then, these radicals subsequently participate in chain reactions to\nefficiently produce ethane. Generally, this work is of high quality with clear presentation and deep\nmechanism discussion. Therefore, this work can be published in Nature Communications after some\nrevisions, and detailed comments are listed below:\nAuthor reply: We appreciate the reviewer’s comments about the quality of our study. The point-by-\npoint responses to your comments are shown as follows:\nSpecific comments:\nComment 1: In order to comprehensively evaluate the catalytic performance, AQY and STC results\nshould be provided.\nAuthor reply: Thank you for your professional comment. The apparent quantum yield (AQY) and\nsolar-to-chemical (STC) efficiency values are now provided in the revised manuscript.\nLine 198-201: The photocatalytic performance of Ni-TSnS is characterized by two key metrics: a\n2\nsignificant apparent quantum yield (AQY) of 4.91% at 380 nm and a notable solar-to-chemical (STC)\nefficiency of 0.67% sustained over 10 hours of operation (Supporting Fig. 20).\nSupporting Fig. 20 AQY and UV-DRS spectra of Ni-TSnS .\nidentified in Ni-TSnS sample at the wavelength of 380 nm, which was 4.91% accounting the total\nconsumption of excited electron (Supporting Fig. 20).\nThe methods used for their calculation are described in the revised Supporting Information as:\nLine 35-47: Apparent quantum yield (AQY) measurement. AQY is calculated as the ratio of\neffective electrons (derived from product yields) to incident photons. Product formation (CO, CH and\n2 6\n(380, 420, 450, 500, and 550 nm, respectively). The photon flux for each wavelength was calculated\nfrom the incident light intensity, which was measured utilizing a calibrated silicon photodiode with a\nUV-enhancement filter. Then, the AQY for CO reduction is given by:\n2\nyield(CO)2yield(CH )8yield(C H )14\nAQY 4 2 6 (1)\nincident photons\nSolar-to-chemical (STC) efficiency measurement. STC efficiency is used to quantify the efficiency\nof energy conversion from solar energy to stored chemical energy, which is calculated as:\n \n yield(CO RR products)G(reduction CO to products)\n 2 2 \n \nSTC (2)\nlight intensityirradiation areatime\nComment 2: The authors need to further explain the statement of “Quadrupole moment splitting serves\nas a key indicator of symmetry breaking”, so that readers can understand the principle of this\nrepresentation of data and underlying mechanism of quadrupole moment splitting.\nAuthor reply: We are grateful to the reviewer for the kind suggestion. We further explain how\nquadrupole splitting in Mössbauer spectroscopy serves as a sensitive probe for local structural\nsymmetry in the revised Supporting Information.\nLine 155-162: A non-zero quadrupole splitting (QS) arises from the interaction between the nucleus\nand an asymmetric electric field gradient (EFG) at the atomic site. In a perfectly symmetric crystal\nlattice (e.g., ideal octahedral or tetrahedral coordination), the EFG is zero9. Thus, the observed\nquadrupole splitting in Ni-TSnS indicates a breakdown of this local symmetry around the Sn atom.\ndistribution of electron density, i.e. the asymmetric EFG. Therefore, the presence of quadrupole\nsplitting is a key indicator confirming successful local symmetry breaking induced by Ni anchoring.\nComment 3: The authors claim that “Fig. 3g reveals that τ in Ni-TSnS and TSnS is extended by\n2 2 2\nfactors of more than 43 and 21 respectively compared to SnS ”. The author should provide the value\n2\nof τ .\nmapping image (Fig. 3f). To complement this spatial information, we present the statistical\ndistributions of the individual lifetime components (τ and τ ) in the revised manuscript (Fig. 3g)\n1 2\nR3\nFig. 3f, Average PL lifetime mapping of SnS , TSnS , Ni-SnS , and Ni-TSnS . g, Radiation lifetime τ\n2 2 2 2 1\nand non-radiation lifetime τ of SnS , TSnS , Ni-SnS , and Ni-TSnS .\n2 2 2 2 2\nComment 4: In recent years, radical-mediated CO reduction mechanisms have attracted increasing\n2\nattention. For instance, Basak et al. (Nat. Catal., 2025, 8, 794-803) reported that CO reduction at Ni(I)\n2\nsites involved single-electron transfer and radical processes. I suggest that the authors compare their\nfindings with this reference to further refine the discussion of radical reaction mechanisms presented\nin this work.\nAuthor reply: We thank the reviewer for this insightful suggestion. In the revised manuscript, we\nhave carefully studied the results from the literature (Nat. Catal., 2025, 8, 794-803), which further\nconfirms the reliability of this study.\nLine 337-342: Radical pathways have been documented in CO RR. For example, Basak et al. reported\npromote radical conversion of CO through SET. Although the catalytic environments and dominant\n2\nproducts are different, both of the studies offer complementary evidences on advancing radical-based\nreaction mechanisms in CO RR.\n2 6 3 2 6\nin this study raises an important question: does this reaction pathway exist in natural systems? Please\nclarify whether such a reaction occurs in nature and, if so, describe its natural occurrence and context.\nAuthor reply: Thanks. Methyl radical coupling for ethane yield is a well-established natural route in\nnatural reducing environments. In the methane-rich atmosphere of Titan, ∙CH -to-C H radical\n3 2 6\npathway operates naturally in low-oxygen, methane-rich settings, aligning mechanistically with the\n∙CH coupling we observe under photocatalytic conditions. The corresponding explanation is provided\n3\nin the revised manuscript.\nLine 332-333: ∙CH -to-C H chain reaction operates in natural environments. For example, in the\n3 2 6\nR4\nmethane-rich atmosphere of Titan, this reaction dominates the formation pathway for C H 47.\n2 6\nComment 6: In this study, single-electron transfer (SET) at Ni sites of Ni-SnS leads to formation of\n2\nform methyl radicals (∙CH ), which is found as the primary intermediate during CO reduction. The\n3 2\nauthors should provide solid evidences for formation of ∙CH .\nprovide in-situ EPR measurements and in-situ high-speed confocal imaging of ∙CH , which directly\n3\nconfirm the formation of the ∙CH . We further highlight the evidences as:\nCO RR by Ni-TSnS can efficiently generate free radical species. In Fig. 5a, no significant\n2 2\nRhodamine-6G fluorescence signal is detected in SnS , Ni-SnS , and TSnS , suggesting that 5,5-\n2 2 2\ndimethyl-1-pyrroline N-oxide (DMPO) quenched the fluorescence signal of Rhodamine-6G. However,\nfor Ni-TSnS , the specific binding of DMPO to the free radicals produced via photocatalytic CO RR\n2 2\ndiminishes the quenching effect on the Rhodamine-6G fluorescence signal. In-situ EPR spectra further\nconfirm that DMPO-∙CH radical adduct (hyperfine splitting constants, A = 15.90 G, A = 22.90 G)\nis exclusively generated during the photocatalytic CO RR process by Ni-TSnS (Supporting Fig. 47)44.\n2 2\nFig. 5a High-speed confocal imaging of ∙CH produced by various materials after light irradiation.\nSupporting Fig. 47 In-situ EPR spectra of ∙CH radical produced by various materials under light\n3\nirradiation.\nSupporting Note 27: C–Centered *CH fragment is a weaker bound and can desorb as ∙CH . In\n3 3\ncontrast, O-centered radicals (e.g., HOCO∙, HCO∙, CH O∙, and CH OH∙) bind much more strongly to\n3 2\nNi (via Ni–O coordination), which can promote rapid surface relaxation to closed-shell adsorbates\nrather than desorption as free radicals30. Moreover, ∙CH has a longer solution/gas-phase lifetime than\n3\nthe O-centered radicals31. Therefore, in the Ni-TSnS reaction system, it is more inclined to generate\n2\n∙CH .\nformation of ethane in this system. Why aren’t other reduction products such as CH and CO generated?\n3\nis the key precursor for C H production in our CO RR pathway, and only Ni-TSnS can generate ∙CH\n2 6 2 2 3\nattributed to a strong SOC-enhanced single-electron transfer process, we identify ∙CH formation as\n3\nthe rate-limiting step in this study. To verify this crucial step, we have incorporated ∙CH -quenching\n3\nexperiments in the revised manuscript, which further substantiate that ∙CH generation is the rate-\n3\nlimiting step. We have further expanded the corresponding discussion in revised manuscript as:\nLine 333-336: ∙CH quenching experiments confirm that ∙CH is a key intermediate for the formation\n3 3\nof C H (Supporting Fig. 48). Therefore, the generation of ∙CH serves as a rate-limiting step to\n2 6 3\nenhance both the C H formation rate and selectivity.\n2 6\nLine 477-480: ∙CH quenching experiment. The as-prepared photocatalyst was dispersed in a 10 mM\nsolution of 2,6-di-tert-butyl-4-methylphenol (BHT) to a concentration of 2 mg mL-1. 5 mL aliquot of\nthe suspension was then deposited onto quartz glass and held at 65 °C to evaporate the solvent. The\nsubsequent photocatalytic CO RR operation was conducted following the above-mentioned method.\n2 2\nSupporting Note 28: To confirm ∙CH is the key intermediate governing the C H yield and selectivity,\n3 2 6\nwe introduced 2,6-di-tert-butyl-4-methylphenol (BHT) dropwise onto the Ni-TSnS photocatalyst and\n2\nperformed photocatalytic CO reduction (CO RR)32,33. Upon BHT addition, the C H yield and\n2 2 2 6\nselectivity approached zero, whereas the CH yield and selectivity increased markedly, consistent with\n4\nhydrogen-atom transfer between ∙CH and BHT (∙CH + BHT–OH → CH + BHT–O)34. We also\n3 3 4\nobserved increased CO and H yields, plausibly because BHT scavenges photogenerated holes, thereby\n2\nsuppressing electron-hole recombination.\nIn addition, we further clarify the mechanism of selective generation of C H . The relevant\n2 6\nexplanations have been supplemented in the revised Supporting Information as follow:\nSupporting Fig. 46 Gibbs free energies of CH desorption on different materials. T, R and S\n4\nrepresent Triangular, Square and Rhombus regions, respectively.\nSupporting Note 26: To evaluate the surface-dependent desorption behavior of CH , we\n4\nsystematically compared its desorption energies on various materials. On Ni-TSnS , both CO and CH\n2 4\nexhibit large desorption barriers (Supporting Fig. 46), rendering their release energetically prohibitive;\nconsequently, neither CO nor CH is favored as main products. By contrast, hydrogenation of CO to\n4 2\nthe *CH intermediate is thermodynamically favorable on this surface (Supporting Fig. 39). Moreover,\n3\nat C -symmetric Ni sites, spin-orbit hybridization between the Ni center and *CH promotes SET\n2v 3\nfrom Ni to *CH , generating a surface ∙CH . The resulting ∙CH then undergoes a radical chain\n3 3 3\ncoupling pathway that yields C H with high selectivity:\n2 6\nCH  CH C H\n3 3 2 6\nR8\nResponse to Reviewer #2\nGeneral comment: This manuscript proposes an intriguing strategy to induce spontaneous long-range\nspin-orbit coupling (SOC) in SnS through moiré engineering, and to achieve highly selective\n2\nphotocatalytic CO -to-C H conversion using single-atom Ni sites with C coordination. A\n2 2 6 2v\ncomprehensive set of experimental characterizations combined with DFT calculations provides a\nrelatively complete evidence chain. Overall, the manuscript is well-structured, methodologically rich,\nand presents innovative conclusions. Therefore, I believe the manuscript might be published after\naddressing the following issues.\nAuthor reply: We appreciate the reviewer for the valuable comments. We have carefully revised the\nmanuscript and Supporting Information with consideration all your constructive comments.\nSpecific comments:\nComment 1: The authors emphasize the effect of spontaneous long-range spin pinning for\nphotocatalysis. How to define long-range? It would also be helpful to discuss how the performance of\ncatalysts with short-range orders compared to those exhibiting long-range orders.\nAuthor reply: We greatly appreciate the reviewer’s suggestion. In the revised Supporting\nInformation, we have clarified our use of the term “long-range” and added a dedicated discussion\ncontrasting long-range and short-range spin pinning.\nLine 301-306: AC-STEM image of Ni-TSnS reveals a periodic moiré superlattice spanning the entire\n2\nfield of view (Supporting Fig. 37 and Supporting Note 22), while superlattice diffraction peaks in the\nXRD patterns (Supporting Fig. 3) corroborate its long-range structural order. This extended\nsuperlattice thereby engenders a long-range spin-pinning effect across the whole domain, in contrast\nto the short-range spin pinning induced by randomly distributed local symmetry-breaking defects.\nSupporting Fig. 37 AC-STEM image of Ni-TSnS .\nSupporting Note 22: As shown in Supporting Fig. 37, the periodic moiré superlattice extends across\nthe entire field of view, confirming its long-range structural ordering. In addition, the emergence of\nsuperlattice diffraction peaks in the XRD patterns further demonstrates the long-range periodicity of\nthis superstructure (Supporting Fig. 3). The spin-pinning effect arising from this periodic superlattice\nis therefore distributed over the whole superlattice domain, with an effective range that far exceeds\nthat of spin pinning induced by randomly distributed, which shows purely local symmetry breaking\nstructure.\nComment 2: The Ni EXAFS spectra of Ni-TSnS should be compared with suitable reference\n2\ncompounds, such as nickel sulfide or nickel oxide, to clarify the coordination environment of Ni.\nAuthor reply: We fully agree with the reviewer’s suggestion, and we have added the spectra of nickel\noxide and Ni foil as references in the revised manuscript.\nLine 126-129: Ni K-edge FT-EXAFS spectra for Ni-SnS and Ni-TSnS feature peaks at ~1.93 Å,\n2 2\nassigned to Ni-S bonding (Fig. 1g). Compared with Ni foil and NiO, no obvious peaks of Ni-Ni\ncoordination are detected, indicating that Ni species exist in the form of single atoms in Ni-SnS and\nNi-SnS and Ni-TSnS . The insets are the schematic illustration of C and C symmetric Ni atoms.\n2 2 3v 2v\nComment 3: The EDS mapping images would benefit from showing a larger area to capture an entire\nnanosheet, ensuring that the elemental distribution is representative of the material rather than\nlocalized regions. In addition, for comparison, AC-STEM image of the Ni-free TSnS sample should\n2\nbe provided to better illustrate the Ni incorporation.\nAuthor reply: We appreciate the reviewer’s suggestion. In the revised Supporting Information, we\nprovide new EDS mapping images of the entire Ni-TSnS nanosheet. As shown in Supporting Fig. 2,\n2\nthe Ni signal is distributed across the whole nanosheet.\nR10\nSupporting Fig. 2 TEM-EDS elemental mapping of Ni-TSnS .\n2 2\nIn the AC-STEM image of Ni-TSnS , Ni single atoms are marked with red circles. Considering the\n2\natomic number of Ni is much lower than that of Sn, the HAADF-STEM Z-contrast renders Ni as low-\nintensity spots that do not belong to the intrinsic moiré superlattice of TSnS ; we therefore identify Ni\n2\nby these faint, isolated features. One-dimensional intensity line profiles extracted from the red-boxed\nregion in Fig. 1b further demonstrate this assignment, showing a reproducible and low-contrast peak\n(Fig. 1f), which is assigned to a single Ni atom.\nTo validate the identification the criterion of Ni single atoms, we simulated AC-STEM images using\nthe crystallographic model of Ni-TSnS .\n2 2\nFig. 1f, Intensity profiles of the two sites in AC-STEM image of Ni-TSnS .\n2 2\nR11\nintensity feature anchored within the moiré superlattice, which matches well with our experimental\nmicrographs. This agreement between experiment and simulation confirms the robustness of our\nidentification criteria of Ni single-atoms.\nComment 4: Although the observed g-shift in the EPR spectra can be interpreted as evidence of\nchanges in local spin or orbital contributions, the authors should clarify how alternative factors, such\nas variations in chemical state, coordination environment, or local fields induced by surface adsorption,\nhave been excluded.\nAuthor reply: Thank a lot for this professional comment. In the revised Supporting Information,\nwe have expanded the discussion of the in-situ EPR spectra to exclude contributions from changes in\nchemical state, coordination environment, or surface adsorption to the observed EPR signals.\nLine 458-474: EPR measurements collected before and after reaction demonstrate a fully reversible\ng-value shift (Supporting Fig. 36a). Such reversibility is consistent with modulation of spin-orbit\ncoupling by photogenerated electrons, whereas changes in oxidation state, coordination\nrearrangements, or surface adsorption typically exhibit slower kinetics and partial irreversibility26.\nGenerally, alterations in valence state or coordination would be expected to modify the EPR line shape;\nthe invariant profile after CO RR, indicating that the Ni spin electrons and their local coordination\n2\nenvironment are well preserved27. Furthermore, during photocatalysis, electron delocalization at Ni\nsites is expected to attenuate the EPR signal, and dynamic changes in the Ni oxidation state may occur,\nconsistent with previous reports28. However, the pronounced shift in the g-value observed here is, to\nour knowledge, reported for the first time, suggesting that this g-value shift is unlikely to arise from\nvalence changes. In addition, in Ar atmosphere, the g-value of Ni-TSnS shows no discernible change,\n2\nfurther confirming surface adsorption is the origin of the g-value shift (Supporting Fig. 36a).\nFurthermore, we have added XRD, XPS, and ICP-MS data collected before and after photocatalytic\nCO RR, which present the structural, oxidation-state, and compositional stability of Ni-TSnS under\n2 2\nthe reaction conditions (Supporting Fig. 36b-f).\nR12\nSupporting Fig. 36 The stability of the structure and chemical composition of Ni-TSnS before\n2\nand after 50 hours of photocatalytic reaction. a, EPR spectra of Ni-TSnS under Ar, under CO , and\n2 2\nafter photocatalytic CO RR. b, XRD patterns of Ni-TSnS before and after CO RR. c, Elemental\n2 2 2\ncomposition of Ni-TSnS before and after CO RR. d-f, Ni 2p, S 2p, and Sn 3d XPS spectra of Ni-\n2 2\nTSnS before and after CO RR.\n2 2\nSupporting Note 22: To evaluate the stability of Ni-TSnS under working conditions, we compared\n2\nits structural and compositional features before and after 50 h of photocatalytic CO reduction. EPR\n2\nspectra display nearly overlapping line shapes and g-factor positions (Supporting Fig. 36a), indicating\nthat the Ni spin electrons and their local coordination environment are well preserved25. The powder\nXRD patterns before and after reaction can be fully indexed to Ni-TSnS with no additional diffraction\n2\npeaks and negligible changes in peak positions or widths (Supporting Fig. 36b), confirming that the\ntwisted lattice remains intact without phase transformation. ICP-MS analysis reveals almost identical\nmass fractions of Ni, Sn and S (Supporting Fig. 36c), suggesting negligible leaching of Ni and a\nconserved overall stoichiometry. Furthermore, the high-resolution Ni 2p, S 2p and Sn 3d XPS spectra\nexhibit coincident binding energies before and after catalysis (Supporting Fig. 36d-f), demonstrating\nthat the oxidation states and chemical environments of Ni, S and Sn are essentially unchanged. In total,\nthese results verify the high structural and compositional stability of Ni-TSnS during prolonged\n2\nphotocatalytic operation.\nComment 5: In Supporting Fig. 8, the x-axis should be consistent for better comparison.\nAuthor reply: Thanks. To ensure clarity and direct comparability, we have provided EPR spectra with\nuniform x-axis in the revised Supporting Information.\nR13\nSupporting Fig. 8 EPR spectra for different materials. a, SnS , b, TSnS , c, Ni-TSnS .\n2 2 2\nComment 6: Why does the distribution of C H fragment peak look different between reactions under\n2 6\n12CO and 13CO , given that both show a main signal at m/z = 30?\n2 2\nAuthor reply: Thank you for this comment. The earlier gas-phase mass spectrometry (GC-MS) data\nwere biased by the relatively low isotopic purity of the 13CO source used initially. To resolve this, we\n2\nrepeated the isotopic labeling experiments with a certified 99 atom% 13CO gas. As shown in the new\n2 2\nfollow consistent patterns, conclusively demonstrating that the carbon in the detected products\noriginates from CO . The peaks assigned to C H , C H , C H , and C H originate from\n2 2 5 2 4 2 3 2 2\nphotoionization-induced fragmentation of C H in the GC-MS. Such fragmentation pathways are\n2 6\nintrinsic to GC-MS measurements and have been widely documented in previous literatures (Chem\n2025, 11, 102295; Nano Lett. 2023, 23, 10914−10921).\nSupporting Fig. 21 Carbon sources determination tests. b, Mass spectra of C H , CH and CO\n2 6 4\nproduced in photocatalytic 13CO and 12CO conversion by Ni-TSnS .\n2 2 2\nComment 7: According to the experimental details, the photocatalytic experiments were carried out\nwithout sacrificial agents, meaning that H O oxidation occurred. The production rate of oxidation\n2\nproducts should also be well investigated to demonstrate the occurrence of overall reaction. Besides,\nGC spectra for standards and reaction samples should be presented.\nAuthor reply: Thanks for your valuable comment. In a CO\nR14\nagent, oxygen (O ) is usually used as the oxidation product (Nat. Catal. 2025, 8, 728-739; Chem 2025,\n2\n11, 102295). In this study, the formation of oxidation products was also monitored using gas\nchromatography (GC). The O evolution rate is presented in the revised Supporting Information. In\n2\naddition, following the reviewers’ suggestion, we present the gas chromatograms of both the reduction\nand oxidation reaction products.\nLine 182-184: Moreover, Ni-TSnS displays an O production rate of 243.19 μmol g-1 h-1, close to the\n2 2\ntheoretical value of 241 μmol g-1 h-1, demonstrating that O is exactly the oxidation product\n2\n(Supporting Fig. 17).\nSupporting Fig. 17 O production rate obtained using SnS , Ni-SnS , TSnS , and Ni-TSnS .\n2 2 2 2 2\nSupporting Note 9: Under photocatalytic CO RR conditions, Ni-TSnS delivers an O evolution rate\n2 2 2\nof 243.19 μmol g-1 h-1, in excellent agreement with the theoretical value of 241 μmol g-1 h-1 expected\nfor the four-electron water oxidation half-reaction. This near-stoichiometric match confirms that\nmolecular O is the exclusive oxidation product and rules out significant parasitic or sacrificial\n2\noxidation pathways (Supporting Fig. 17).\nR15\nSupporting Fig. 17 Gas chromatography (GC) spectra of (a) flame ionization detector-C channel, (b)\n1\nflame ionization detector-C channel, and (c) thermal conductivity detector channel for standards and\n2\nreaction gas samples.\nComment 8: It is noted that increasing Ni loading appears to decrease catalytic performance. The\nauthors should discuss possible reasons for this phenomenon.\nAuthor reply: Thank you for your kind comment. We address this phenomenon in the revised\nSupporting Information. To further elucidate the relationship between Ni loading amount and\nphotocatalytic performance, we further increased the Ni single-atom loading to 1.74 wt% and\nevaluated its photocatalytic CO RR activity. The result indicates that, with increasing Ni loading, the\n2\nselectivity toward C H progressively declines, whereas the selectivity toward H and CO increases.\n2 6 2\nIn addition, Ni K-edge XAFS fits reveal a concomitant increase in the Ni–S coordination number,\nindicating that a fraction of Ni single atoms adopts higher local symmetry upon anchoring on TSnS .\n2v\nsymmetry Ni single atoms (e.g., C -symmetric Ni sites in Ni-SnS ) are inactive for C H formation.\n3v 2 2 6\nConsequently, increasing the Ni loading diminishes the CO -to-C H conversion efficiency.\n2 2 6\nWe explain the reason in the revised Supporting Information as:\nR16\nSupporting Fig. 13 Photocatalytic CO RR performance of various materials. a, CO RR\n2 2\nproduction rate obtained using SnS , Ni-SnS , TSnS , and Ni-TSnS .\n2 2 2 2\nTSnS . b, Products selectivity of Ni-\n2\nof 1.36 wt% Ni-TSnS . d, FT k2-weighted Ni K-edge of the EXAFS spectra and corresponding EXAFS\n2\nfitting results of 1.74 wt% Ni-TSnS . e, Coordination number of 1.17/1.36/1.74 wt% Ni-TSnS and\n2 2\nNi-SnS .\natoms exceeds 1.17 wt%, the product selectivity of C H progressively decreases, whereas the product\n2 6\nselectivity of H and CO increases. To further explore the loading-selectivity relationship, we collected\n2 2\nFig. 13c and 13d, the both samples exhibit a Ni–S first-shell distance of 1.94 Å and no discernible Ni–\nNi scattering, confirming atomically dispersed Ni on TSnS . EXAFS fitting yields Ni–S coordination\n2\nnumbers of 2.12 ± 0.17 and 2.29 ± 0.15 respectively, which are higher than that of the 1.17 wt% sample\n(2.06 ± 0.13) (Supporting Fig. 13e; Supporting Table 1). The increased coordination number\nindicates that a fraction of Ni single atoms shows higher local symmetry (e.g., C ), which disfavors\n3v\nthe formation of ∙CH intermediates; consequently, C H selectivity declines while H and CO\n3 2 6 2\nselectivity rise.\nR17\nSupporting Table 1. EXAFS fitting parameters for Ni-TSnS and Ni-SnS (N: coordination number;\n2 2\nR: distance; σ2: mean-square disorder; E Energy correction; R factor is used to value the goodness of\n0:\nthe fitting).\nR-\nSample Path N R(Å) σ2/Å2 E\n0 factor\n1.17 wt% Ni-\nNi-S 2.06 ± 0.13 1.94 0.013 1.49 0.037\nTSnS\n2\n1.36 wt% Ni-\nNi-S 2.12± 0.17 1.94 0.014 1.42 0.026\nTSnS\n2\n1.74 wt% Ni-\nNi-S 2.29± 0.15 1.94 0.010 1.37 0.024\nTSnS\nComment 9: The detection of DMPO-∙CH is strong evidence for methyl radicals. However, further\n3\nverification is recommended, such as inhibition or trapping experiments using known ∙CH scavengers\n3\nor radical inhibitors, and monitoring the effect on C H yield and selectivity.\n2 6\nAuthor reply: Thank you for your constructive suggestion that is quite useful for improving the quality\nof this work. In the revised Manuscript, we have further provided solid evidences on the conclusions\nand experimental details of the ∙CH quenching experiment.\n3 3\nof C H (Supporting Fig. 48).\n2 6\nLine 477-480: ∙CH quenching experiment. The as-prepared photocatalyst was dispersed in a 10 mM\n3\nsolution of 2,6-di-tert-butyl-4-methylphenol (BHT) to a concentration of 2 mg mL-1. 5 mL aliquot of\nthe suspension was then deposited onto quartz glass and held at 65 °C to evaporate the solvent. The\nsubsequent photocatalytic CO RR operation was conducted following the above-mentioned method.\n2 6\nupon addition of the ∙CH quencher, 2,6-di-tert-butyl-4-methylphenol (BHT), and results are added as\n3\nfollows:\nSupporting Fig 48. CO RR production rate obtained using Ni-TSnS and BHT.\n2 2\nR18\nSupporting Note 28: To confirm ∙CH is the key intermediate governing the C H yield and selectivity,\n3 2 6\nwe introduced 2,6-di-tert-butyl-4-methylphenol (BHT) dropwise onto the Ni-TSnS photocatalyst and\n2\nperformed photocatalytic CO reduction (CO RR)32,33. Upon BHT addition, the C H yield and\n2 2 2 6\nselectivity approached zero, whereas the CH yield and selectivity increased markedly, consistent with\n4\nhydrogen-atom transfer between ∙CH and BHT (∙CH + BHT–OH → CH + BHT–O)34. We also\n3 3 4\nobserved increased CO and H yields, plausibly because BHT scavenges photogenerated holes, thereby\n2\nsuppressing electron-hole recombination.\nComment 10: It is suggested to measure the AQY to quantitatively evaluate the photochemical\nefficiency of the system.\nAuthor reply: Thank you for this comment. The apparent quantum yield (AQY) values are now\nprovided in the revised Supporting Information.\nLine 198-201: The photocatalytic performance of Ni-TSnS is characterized by two key metrics: a\n2\nsignificant apparent quantum yield (AQY) of 4.91% at 380 nm and a notable solar-to-chemical (STC)\nefficiency of 0.67% sustained over 10 hours of operation (Supporting Fig. 20).\nSupporting Fig. 20 AQY and UV-DRS spectra of Ni-TSnS .\nidentified in Ni-TSnS sample at the wavelength of 380 nm, which was 4.91% accounting the total\n2\nconsumption of excited electron (Supporting Fig. 20).\nThe methods used for their calculation are described in the revised Supporting Information as:\nLine 35-42: Apparent quantum yield (AQY) measurement. AQY is calculated as the ratio of\neffective electrons (derived from product yields) to incident photons. Product formation (CO, CH and\n2 6\n(380, 420, 450, 500, and 550 nm, respectively). The photon flux for each wavelength was calculated\nfrom the incident light intensity, which was measured utilizing a calibrated silicon photodiode with a\nUV-enhancement filter. Then, the AQY for CO reduction is given by:\nyield(CO)2yield(CH )8yield(C H )14\nAQY 4 2 6 (1)\nincident photons\nComment 11: The stability of the catalyst should be evaluated. Characterizations of Ni-TSnS before\n2\nand after reaction (e.g., XRD, XPS, EPR, ICP-MS) is recommended to evaluate any structural or\ncompositional changes in both the Ni species and the support.\nAuthor reply: Thank you for the professional comment. In the revised manuscript and revised\nSupporting Information, we have added new data on the stability of Ni-TSnS under photocatalytic\n2 2\nafter reaction, which further confirm the structural and compositional robustness of Ni-TSnS .\nduring electron transfer. Therefore, Ni-TSnS exhibits superior charge separation, CO RR rate, and\n2 2\nstability. Therefore, CO RR rate and C H selectivity of Ni-TSnS remain almost unchanged even for\n2 2 6 2\na long-time reaction of 50 h (Supporting Fig. 35). Furthermore, after 50 h of photocatalytic CO RR,\n2\nconfirming its excellent stability under operating conditions (Supporting Fig. 36).\nSupporting Fig. 35 Photocatalytic CO RR stability of Ni-TSnS over 50 h.\n2 2\nR20\nSupporting Fig. 36 The stability of the structure and chemical composition of Ni-TSnS before\n2\nand after 50 hours of photocatalytic reaction. a, EPR spectra of Ni-TSnS under Ar, under CO , and\n2 2\nafter photocatalytic CO RR. b, XRD patterns of Ni-TSnS before and after CO RR. c, Elemental\n2 2 2\ncomposition of Ni-TSnS before and after CO RR. d-f, Ni 2p, S 2p, and Sn 3d XPS spectra of Ni-\n2 2\nTSnS before and after CO RR.\n2 2\nSupporting Note 21: To evaluate the stability of Ni-TSnS under working conditions, we compared\n2\nits structural and compositional features before and after 50 h of photocatalytic CO reduction. EPR\n2\nspectra display nearly overlapping line shapes and g-factor positions (Supporting Fig. 36a), indicating\nthat the Ni spin electrons and their local coordination environment are well preserved25. The powder\nXRD patterns before and after reaction can be fully indexed to Ni-TSnS with no additional diffraction\n2\npeaks and negligible changes in peak positions or widths (Supporting Fig. 36b), confirming that the\ntwisted lattice remains intact without phase transformation. ICP-MS analysis reveals almost identical\nmass fractions of Ni, Sn and S (Supporting Fig. 36c), suggesting negligible leaching of Ni and a\nconserved overall stoichiometry. Furthermore, the high-resolution Ni 2p, S 2p and Sn 3d XPS spectra\nexhibit coincident binding energies before and after catalysis (Supporting Fig. 36d-f), demonstrating\nthat the oxidation states and chemical environments of Ni, S and Sn are essentially unchanged. In total,\nthese results verify the high structural and compositional stability of Ni-TSnS during prolonged\n2\nphotocatalytic operation.\nR21\nResponse to Reviewer #3\nGeneral comment: This work finished by Liu et al. presents a novel twist engineering for synthesis\nof SnS nanosheets (Ni-TSnS ), and strong spin-orbit coupling (SOC) was observed after Ni single-\n2 2\natom anchored on Ni-TSnS . The developed material exhibits spontaneous long-range spin-momentum\n2\nlocking (LRSL) due to SOC, and enhances its reactivity and stability for photocatalytic reduction of\nCO for ethane (C H ) synthesis. The authors deeply explain the SOC effect for enhanced spin-\n2 2 6\npolarized electron transfer and specific radical (∙CH ) formation. This work gives new insights into\n2\nmomentum locking. I recommend its acceptance after further consider the following suggestions:\nAuthor reply: We greatly appreciate the reviewer’s positive comments and constructive suggestions\non our manuscript. We have made a point-by-point response to your comments and carefully revised\nthe manuscript as you suggested.\nSpecific comments:\nComment 1: Material characterizations including TEM and selected area electron diffraction (SAED)\npattern obtained for TSnS and Ni-TSnS present twist angle of 30° between adjacent SnS layers. Can\n2 2 2\nthe twist angle be adjusted through CVD synthesis condition, and why 30° is selected in this study?\nAuthor reply: Thank you for your kind suggestion. In the twist material synthesis process, we\nsystematically varied the heating temperatures and cooling rates; however, all synthesized TSnS\n2\nsamples consistently exhibited a 30° twist angle between adjacent layers. The corresponding\nexplanation is provided in the revised Supporting Information.\nLine 95-107: Even upon varying the CVD growth conditions during material synthesis, the twist\ndomains observed by AC-STEM are almost exclusively characterized by a 30° rotation.\nMechanistically, 30° represents a discrete, low-energy registry between adjacent SnS layers under our\n2\ngrowth chemistry3. The hexagonal chalcogen sublattices favor a quasi-commensurate √3×√3 R30°-\nlike stacking that minimizes interlayer vdW/electrostatic penalties and is further stabilized by post-\nnucleation relaxation (interlayer super-lubric/low-shear sliding). As a result, even when nucleation\nmay occur with a range of initial orientations, thermal ripening drives the stack toward the 30° local\nminimum rather than a continuum of angles4. This explains why altering CVD parameters within\npractical limits does not yield deterministic angle control in our platform. Deterministic twist\nengineering in vdW materials typically requires ex-situ transfer/rotation or templated epitaxy, however,\nthese routes are outside the scope of our current CVD-only study but are valuable directions for future\nwork.\nComment 2: For Ni-TSnS with strong SOC effects, the authors claim the anchored C symmetric Ni\n2 2v\nsites are the primary reason for this SOC effect (based on XMCD results), then what is the role of twist\nengineering in SOC? What is the mechanism for improved SOC after twist engineering and then Ni\ndeposition?\nAuthor reply: We fully appreciate the reviewer’s professional and constructive comments. We wish\nto clarify the origin of spin-orbit coupling (SOC) in our system. In the revised manuscript,\nwe\nemphasize these points as follows:\nR22\nLine 114-117: Moiré periodic strain leads to periodic symmetry breaking in TSnS and Ni-TSnS ,\n2 2\nwhich underpins the emergence of SOC effects17. Therefore, the long-range periodic symmetry\nbreaking structure observed herein implies long-range SOC effects in both TSnS and Ni-TSnS .\n2 2\nLine 138-140: GPA results further demonstrate that extra displacement loading on TSnS after Ni\n2\nanchoring (Fig. 1b), suggesting that C -symmetric Ni single atoms exacerbate symmetry breaking of\n2v\nNi-TSnS .\n2\nproduces interlayer lattice incommensurability, which lowers the structural symmetry and thereby\ninduces SOC in SnS . In addition, C -symmetric Ni sites on TSnS further amplify symmetry breaking,\n2 2v 2\nleading to an additional enhancement of SOC.\nComment 3: Based on Mössbauer spectra analysis, the quadrupole splitting of TSnS and Ni-TSnS\n2 2\nis 0.88 and 0.92 mm s-1, respectively, so is it a big improvement for this value after Ni deposition for\nTSnS ?\n0.92 mm s-1 is modest. However, in Mössbauer spectroscopy the quadrupole splitting is a direct\nreporter of the electric field gradient (EFG) at the Mössbauer nucleus, and therefore of local symmetry\nbreaking. In this study, twisting SnS already produces a large quadrupole splitting (QS = 0.88 mm s-\n2\n1) relative to the ~0 mm s-1 baseline of high-symmetry Sn sites, establishing that interlayer\nincommensurability breaks symmetry substantially. Moreover, Ni deposition on the TSnS further\n2\nincreases QS to 0.92 mm s-1, which seems a small increase but the diagnostic shift indicates an\nadditional increment in EFG. Because QS depends on both the principal EFG component and the\nasymmetry parameter, even a few-percent increase can arise from subtle, localized distortions around\nSn that are not expected to scale linearly with macroscopic descriptors. Consistently, XAFS assigns\nthe Ni site on TSnS to C (lower symmetry) whereas Ni on pristine SnS is C (higher symmetry),\n2 2v 2 3v\nand we observe weak QS for Ni-SnS but a larger QS for Ni-TSnS . Thus, while the magnitude change\n2 2\nis not “large”, it is mechanistically meaningful: Ni on the twisted lattice amplifies symmetry breaking\nthat twisting already introduced. In the revised Supporting Information, we provide a detailed\nexplanation of this phenomenon.\nLine 155-170: A non-zero quadrupole splitting (QS) arises from the interaction between the nucleus\nand an asymmetric electric field gradient (EFG) at the atomic site. In a perfectly symmetric crystal\nlattice (e.g., ideal octahedral or tetrahedral coordination), the EFG is zero9. Thus, the observed\nquadrupole splitting in Ni-TSnS indicates a breakdown of this local symmetry around the Sn atom.\ndistribution of electron density, i.e. the asymmetric EFG. Therefore, the presence of quadrupole\nsplitting is a key indicator confirming successful local symmetry breaking induced by Ni anchoring.\nQS is governed by both the principal EFG component and the asymmetry parameter; accordingly, a\nfew-percent rise can stem from fine, site-specific distortions around Sn that need not track macroscopic\ndescriptors in a linear fashion10. Consistent with this result, XAFS analysis shows the Ni center on\nTSnS in C (lower symmetry) and on pristine SnS in C (higher symmetry), paralleling the\n2 2v 2 3v\nobservation of a weak QS for Ni-SnS but a larger QS for Ni-TSnS . Thus, although the numerical\n2 2\nchange is modest, it is mechanistically significant: Ni anchored on the twisted lattice further intensifies\nR23\nthe symmetry breaking initiated by twisting.\nComment 4: The relationship between SOC and LRSL for Ni-TSnS should be more clearly explained,\n2\nand is the strong SOC a prerequisite for long-range spin-momentum locking?\nAuthor reply: We greatly appreciate the reviewer’s suggestion. We further clarify the relationship\nbetween SOC and LRSL in revised manuscript.\nLine 282-291: Furthermore, by considering the tangential and radial characteristics of each texture,\nwe identify the spin textures of the Rhombus region, Triangular region and Square region of Ni-TSnS\n2\nas Zeeman-type, Rashba-type, and Dresselhaus-type SOC (Fig. 4b and Supporting Fig. 34)40. The\nZeeman effect breaks spin-state degeneracy, generating intrinsic spin polarization, while Rashba- and\nDresselhaus-type SOC produce concentric and anisotropic spin textures respectively, establishing spin-\nmomentum locking topology through orthogonal spin-momentum correlations41-43. This topological\nprotection ensures strong spin polarization against impurities and disorder44. Furthermore, the moiré\nsuperlattice architecture establishes long-range ordered SOC patterns, enabling topological protection\nof long-range spin-momentum locking (LRSL) through synergetic Rashba-Dresselhaus mechanisms45.\nSuch LRSL enables long-range ordered spin-pinning, thereby ensuring temporal stability of spin states.\nLine 299-301: Above all, twist engineering and low-symmetry Ni sites activate three types of SOC,\nthereby strengthening the SOC strength of the Ni-TSnS . Then, the cooperative action of these SOC\n2\neffects promotes LRSL.\nComment 5: DRIFTS analysis indicates that CO reduction to C H on Ni-TSnS proceeds through\n2 2 6 2\nan unconventional reaction pathway, and the specific transformation pathway or key step should be\nexplained with consideration of SOC effect. Why can ∙CH be produced in a large amount but not other\n3\nradicals or other CO RR pathways?\n3\nis the key precursor for C H production in our CO RR pathway, and only Ni-TSnS can generate ∙CH\n2 6 2 2 3\nattributed to a strong SOC-enhanced single-electron transfer process, we identify ∙CH formation as\n3\nthe rate-limiting step in this study. To verify this crucial step, we have incorporated ∙CH -quenching\n3\nexperiments in the revised manuscript, which further substantiate that ∙CH generation is the rate-\n3\nlimiting step. We have further expanded the corresponding discussion in revised manuscript as:\nLine 333-336: ∙CH quenching experiments confirm that ∙CH is a key intermediate for the formation\n3 3\nof C H (Supporting Fig. 48). Therefore, the generation of ∙CH serves as a rate-limiting step to\n2 6 3\nenhance both the C H formation rate and selectivity.\n2 6\nLine 477-480: ∙CH quenching experiment. The as-prepared photocatalyst was dispersed in a 10 mM\n3\nsolution of 2,6-di-tert-butyl-4-methylphenol (BHT) to a concentration of 2 mg mL-1. 5 mL aliquot of\nthe suspension was then deposited onto quartz glass and held at 65 °C to evaporate the solvent. The\nsubsequent photocatalytic CO RR operation was conducted following the above-mentioned method.\nSupporting Fig 48. CO RR production rate obtained using Ni-TSnS and BHT.\n2 2\nSupporting Note 28: To confirm ∙CH is the key intermediate governing the C H yield and selectivity,\n3 2 6\nwe introduced 2,6-di-tert-butyl-4-methylphenol (BHT) dropwise onto the Ni-TSnS photocatalyst and\n2\nperformed photocatalytic CO reduction (CO RR)32,33. Upon BHT addition, the C H yield and\n2 2 2 6\nselectivity approached zero, whereas the CH yield and selectivity increased markedly, consistent with\n4\nhydrogen-atom transfer between ∙CH and BHT (∙CH + BHT–OH → CH + BHT–O)34. We also\n3 3 4\nobserved increased CO and H yields, plausibly because BHT scavenges photogenerated holes, thereby\n2\nsuppressing electron-hole recombination.\nIn addition, no other CO RR intermediate radicals (e.g., HOCO∙, HCO∙, CH O∙, CH OH∙) were\n2 3 2\ndetected in the Ni-TSnS reaction system. The relevant explanations have been supplemented in the\n2\nrevised Supporting Information.\nLine 572-577: Supporting Note 27: C centered *CH fragment is a weaker bound and can desorb as\n3\n∙CH . In contrast, O-centered radicals (e.g., HOCO∙, HCO∙, CH O∙, CH OH∙) bind much more\n3 3 2\nstrongly to Ni (via Ni–O coordination), which can promote rapid surface relaxation to closed-shell\nadsorbates rather than desorption as free radicals30. Moreover, ∙CH has a longer solution/gas-phase\n3\nlifetime than the O-centered radicals31. Therefore, in the Ni-TSnS reaction system, it is more inclined\n2\nto generate ∙CH .\n2 2\npotentials suitable for CO, CH , and C H production through CO reduction. Then, what is the key\n4 2 6 2\nreason for inhibition of other reactions for formation of CO and CH ?\ngeneration of C H in revised Supporting Information.\n2 6\nR25\nSupporting Fig. 46 Gibbs free energies of CH desorption on different materials. T, R and S\n4\nrepresent Triangular, Square and Rhombus regions, respectively.\nSupporting Note 26: To evaluate the surface-dependent desorption behavior of CH , we\n4\nsystematically compared its desorption energies on various materials. On Ni-TSnS , both CO and CH\n2 4\nexhibit large desorption barriers (Supporting Fig. 46), rendering their release energetically prohibitive;\nconsequently, neither CO nor CH is favored as main products. By contrast, hydrogenation of CO to\n4 2\nthe *CH intermediate is thermodynamically favorable on this surface (Supporting Fig. 39). Moreover,\n3\nat C -symmetric Ni sites, spin-orbit hybridization between the Ni center and *CH promotes SET\n2v 3\nfrom Ni to *CH , generating a surface ∙CH . The resulting ∙CH then undergoes a radical chain\n3 3 3\ncoupling pathway that yields C H with high selectivity:\n2 6\nCH  CH C H\n3 3 2 6\nComment 7: The authors also should explain the key mechanism for the high stability of developed\nNi-TSnS for CO photocatalytic reduction.\n2 2\nAuthor reply: We are grateful to the reviewer for the kind suggestion. High stability of Ni-TSnS for\n2\nbeen supplemented in the revised manuscript as follow:\nLine 284-293: The Zeeman effect breaks spin-state degeneracy, generating intrinsic spin polarization,\nwhile Rashba- and Dresselhaus-type SOC produce concentric and anisotropic spin textures\nrespectively, establishing spin-momentum locking topology through orthogonal spin-momentum\ncorrelations39-41. This topological protection ensures strong spin polarization against impurities and\ndisorder42. Furthermore, the moiré superlattice architecture establishes long-range ordered SOC\npatterns, enabling topological protection of long-range spin-momentum locking (LRSL) through\nsynergetic Rashba-Dresselhaus mechanisms43. Such LRSL enables long-range ordered spin-pinning,\nthereby ensuring temporal stability of spin states. Moreover, the intrinsic long-range order preserves\nthe spatial stability of spin states during electron transfer. Therefore, Ni-TSnS exhibits superior charge\n2\nseparation, CO RR rate, and stability.\ne202412591; Adv. Mater. 2025, 37, 2503027\nAuthor reply: We are grateful to the reviewer for the kind suggestion. In the Introduction, we discuss\nR26\nthe two references to strengthen our overview of strategies for promoting C–C coupling.\nLine 63-66: In recent years, numerous catalysts that promote C–C coupling have been developed. For\nexample, the CeZrZnAgPbO–Cu and RhCo–RhGd nanoalloys designed by Du et al. markedly boost\nC -product yields by two distinct mechanisms, i.e. enhanced *CO adsorption and spin-polarization,\n2\nleading to reduction of C–C coupling barrier and enhanced catalytic activity13,14.\nR27"}, {"round": 2, "reviewer_comments": {"reviewer_1": "This version is nice, please accept it.", "reviewer_2": "The authors present a revised version of their manuscript. They carefully answered all reviews comments and questions.\nThe main issue raised during the first round were checked and solved. Taking all these aspects into account I recommend\nnow this article for publication in Nature Communication.", "reviewer_3": "The authors have addressed the concerns and this paper can be published as it is."}, "author_response": "Authors’ Responses to Referees’ Comments\nManuscript ID: NCOMMS-25-79418A\nTitle: Twist-engineering-induced spin-orbit coupling for photosynthesis of ethane from carbon dioxide\nand water\nAuthors: We greatly appreciate the comments from editorial office and reviewers about our\nmanuscript. The corresponding part has been further revised (marked in blue in the revised manuscript)\nbased on suggestions from the author checklist.\nResponse to Reviewer #1\nComment: This version is nice, please accept it.\nAuthor reply: We appreciate the reviewer again for your kind comments before, which greatly help\nus to improve the quality of our work.\nResponse to Reviewer #2\nComment: The authors present a revised version of their manuscript. They carefully answered all\nreviews comments and questions. The main issue raised during the first round were checked and solved.\nTaking all these aspects into account I recommend now this article for publication in Nature\nCommunication.\nAuthor reply: We appreciate the reviewer again for your kind comments before, which greatly help\nus to improve the quality of our work.\nResponse to Reviewer #3\nComment: The authors have addressed the concerns and this paper can be published as it is.\nAuthor reply: We appreciate the reviewer again for your kind comments before, which greatly help\nus to improve the quality of our work.\nR1"}]

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