Main

Electrocatalytic water splitting is well suited for the production of hydrogen, which could act as a clean and renewable energy carrier to help alleviate the current energy crisis1. However, the sluggish kinetics of the anodic oxygen evolution reaction (OER), which involves the generation of triplet oxygen from singlet water on the electrocatalyst surface2,3, results in a low overall energy efficiency and necessitates the use of high voltages to drive the spin transition4. Most attempts at solving this problem have relied on optimizing the binding energy of oxygen intermediates to active sites via dopant, strain, and vacancy introduction and so on5. However, in such approaches, the electron spin state is overlooked; thereby, the conventional catalysts still suffer from large overpotentials, which are restricted by the volcano plot.

Topological semimetals, which exhibit high catalytic activities owing to their topological surface states and high carrier mobilities, have been actively researched as electrocatalysts for the OER and hydrogen evolution reaction6,7,8. When integrated with crystal chirality, the topological chiral semimetals can exhibit Fermi surfaces with monopole-like spin textures in the bulk state9,10. Such topological spin textures induce spin polarization of transmitted carriers, which is proportional to the spin–orbit coupling (SOC)11,12, and can therefore provide spin-polarized carriers for spin-dependent catalysis. Consequently, topological chiral semimetals are promising catalysts for the spin-boosted OER. In addition, chiral molecules have been used to promote the OER based on the chirality-induced spin selectivity (CISS)13,14,15 effect, that is, the induced spin polarization for electrons passing through chiral molecules. CISS-based catalysts are obtained by imparting chirality to initially achiral metal surfaces through the adsorption of chiral molecules16,17,18,19,20,21,22,23,24 or imprinting of chiral cavities25. The insulating chiral molecules in hybrid molecule–metal electrodes block the active sites on the catalytic surface and reduce conductivity26,27, which is detrimental to the overall OER performance23. Consequently, the existing CISS-based catalysts generally exhibit large OER overpotentials, particularly at high current densities (for example, >400 mV at 100 mA cm–2 and specific activity (SA) < 1.2 mA cm–2)23,25. In addition, the mechanism of spin polarization induction in CISS-based catalysts is still debated, that is, the required SOC may originate from the organic molecules or metal electrode28,29. Moreover, hybrid chiral electrocatalysts complicate the rationalization of the role of SOC in CISS and the quantification of spin contributions to OER activity17.

Here we report a family of topological semimetals with intrinsic chirality capable of highly efficient water splitting. The rationally designed Rh-based topological single crystals (RhSi, RhSn and RhBiS) exhibit three key components in one electrode: chirality (geometric chirality and chirality-induced topological Fermi surface), large SOC and good conductivity30,31,32,33,34,35. When applied as OER catalysts in alkaline electrolyte, these Rh-based chiral crystals show significantly enhanced OER activity compared with RuO2. Experimental investigations and quantum transport calculations reveal that the OER activity of the Rh-based chiral crystals is proportional to the SOC and spin polarization. Therefore, the RhBiS with largest SOC exhibits an overpotential of 266 mV even at a current density of 100 mA cm–2, outperforming state-of-the-art nanostructured catalysts with considerable surface areas. The SA of RhBiS (calculated at an overpotential of 300 mV) exceeds that of RuO2 by more than two orders of magnitude. Further enhanced OER catalytic activities can be achieved by increasing the electrochemical surface area (ECSA) of the chiral catalysts, with the polycrystalline RhBiS particle-based electrode exhibiting an overpotential of 135 mV at 10 mA cm–2. This study presents the experimental evidence of the close relationship between the spin-amplified OER and SOC to establish a design principle for high-performance intrinsic chiral OER catalysts.

Homochirality in single crystals

RhSi, RhSn and RhBiS have a structurally chiral cubic lattice belonging to the P213 (no. 198) space group. The chirality of these crystals is caused by the Rh atoms forming a right- or left-handed spiral (Fig. 1a) and leads to an enantiomer-specific monopole-like spin texture at the Fermi surface, which is mainly composed of Rh d orbitals10 (Fig. 1b). A flow of current (that is, Fermi surface shift) induces a net spin polarization around the Rh sites36,37,38.

Fig. 1: Crystal- and electronic-structure chirality of RhSi, RhSn and RhBiS.
figure 1

a, Illustration of the intrinsically chiral structure. Handedness can be distinguished by considering the helix formed by Rh atoms. Large (grey) and small (blue and red) arrows represent the current flow direction and induced spin polarization around Rh, respectively. b, Illustration of the spin texture on the Fermi surfaces around the Γ-point. Lattice chirality leads to a monopole-like spin texture, which gives rise to spin polarization when a current flows through the crystal. c, Single-crystal XRD pattern of the (0kl) planes in the reciprocal lattice of RhBiS. The diffraction spots are consistent with the P213 space group. d, Laue diffraction pattern of RhBiS (black dots) superimposed on a theoretically simulated pattern (red dots) of the (100) surface. e, STEM image of RhBiS. f, Illustration of the RhBiS crystal structure on the (111) surface with a helical arrangement of Rh atoms along the (111) direction. Yellow, pink and grey spheres represent Rh, Bi and S, respectively.

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The single-crystal X-ray diffraction (XRD) patterns of RhSi, RhSn and RhBiS showed well-ordered and symmetric diffraction spots of the (0kl) planes, revealing the high quality of the single crystals and allowing them to be indexed to the B20 chiral group (Fig. 1c and Extended Data Fig. 1). Moreover, the structural chirality of RhBiS was determined by the Flack method, and the Flack parameter of −0.031 indicated 100% homochirality of the crystal (Extended Data Table 1). In addition, the surfaces of single-crystalline RhSi, RhSn and RhBiS were further analysed by Laue diffraction at room temperature. The resulting patterns featured (100) surface and were indexed to the chiral B20 space group (P213, no. 198; Fig. 1d and Extended Data Fig. 2) by simulation. The sharp diffraction spots in the Laue diffraction patterns of RhSi, RhSn and RhBiS indicated the presence of a perfect single-crystal structure devoid of any twinning or domains.

The direct atomic imaging of RhSi, RhSn and RhBiS was accomplished for thin lamellar samples prepared using a focused ion beam using aberration-corrected scanning transmission electron microscopy (STEM). Given that the brightness of the dots in high-angle annular dark-field (HAADF) images is positively correlated to the atomic weight, the clearly distinguishable bright dots in Fig. 1e signify Bi atoms, whose stacking sequence agrees with the crystal structure on the (111) surface of RhBiS. Moreover, the chiral motif is illustrated by the helical arrangement of Rh or Bi atoms along the (111) direction (Fig. 1f). Upon mirroring, these helices reverse their handedness for RhBiS (Supplementary Fig. 1a), RhSi and RhSn (Supplementary Fig. 1b). The HAADF images show spots for all elements constituting RhSi and RhSn, whose atomic stacking sequences match the simulated atomic representation on the (101) and (001) surfaces, respectively (Extended Data Fig. 3).

The above data confirm the synthesis of high-quality homochiral single crystals of RhSi, RhSn and RhBiS, which belong to the P213 chiral space group and exhibit increasing SOC. Owing to the similarities in their lattice geometry and composition, RhSi, RhSn and RhBiS have similar band structures32,39,40, and the Rh sites in all three materials can be considered OER active41. Importantly, Rh-based materials are generally considered as the state-of-the-art OER electrocatalysts from a thermodynamic perspective. Therefore, further improvement of the activity will mainly be attributed to the spin-dependent OER transition states, which offers another degree of freedom to optimize the catalyst. As a result, topological chiral single crystals (RhSi, RhSn and RhBiS) provide an ideal platform for studying the interplay between chirality and spin in catalytic reactions. These crystals also fulfil a key requirement for a well-defined topological chiral structure and can be used to explore the role of SOC and quantify the contributions of spin to OER activity by excluding undesired factors such as defects, grain boundaries and interfaces5,42.

Electrocatalytic OER activity and stability

The OER activities of single-crystalline RhSi, RhSn and RhBiS were examined by directly using the bulk crystals as the working electrodes (Methods and Supplementary Fig. 2). Achiral single crystals of RuO2 and RhTe and bulk crystal of RhTe2 were used as the reference samples (Supplementary Figs. 3–5 and Supplementary Tables 1 and 2). Figure 2a presents iR-corrected linear sweep voltammetry (LSV) curves recorded at a scan rate of 10 mV s–1 in 1 M KOH. The current densities in this figure are normalized with respect to the geometric surface area of the crystals. The overpotential at 10 mA cm–2 (ɳ10) for RuO2, RhTe, RhTe2, RhSi, RhSn and RhBiS equalled 335 mV, 309 mV, 308 mV, 315 mV, 267 mV and 221 mV, respectively (Fig. 2b). In particular, the ɳ10 for RhBiS was lower than those of nanostructured electrocatalysts with substantial surface areas7,25,43,44,45,46,47 (Fig. 2c). Similar to ɳ10, the overpotential at 100 mA cm–2 (ɳ100), which was used to assess the activity at high current density, was lower for the chiral single crystals than for the achiral crystals (RhTe2, RhTe and RuO2). The ɳ10 and ɳ100 values of the chiral single crystals followed the order of RhSi > RhSn > RhBiS, that is, OER activity followed the reverse order (Fig. 2b). Moreover, we examined the OER activities of RhSi, RhSn and RhBiS in other electrolytes with different pH, revealing that the activity follows the same trend in a wide pH range (Fig. 2d and Supplementary Fig. 6). In addition, further enhanced OER catalytic activities were observed for the polycrystalline particle-based electrodes of RhSi, RhSn and RhBiS with ɳ10 of 235 mV, 192 mV and 135 mV, respectively (Supplementary Figs. 7 and 8).

Fig. 2: Electrocatalytic OER activities.
figure 2

a, LSV polarization curves in 1 M KOH. b, Corresponding ɳ10 (red) and ɳ100 (blue) derived from a. c, Comparison of the ɳ10 values for selected state-of-the-art OER electrocatalysts and chiral RhBiS in alkaline electrolytes. d, ɳ10 values measured across a wide pH range: 1× phosphate-buffered saline (PBS, red), 0.1 M KOH (blue) and 0.5 M H2SO4 (yellow). The current density is normalized with respect to the geometric area of the electrodes. All data were collected with iR correction.

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The intrinsic OER activities were further examined by normalizing the LSV curves with respect to the ECSA to confirm that the overpotential changes were not related to the geometric surface area (Fig. 3a and Supplementary Figs. 9 and 10). The results revealed that the ɳ10 values of the chiral catalysts were substantially lower than those of the achiral samples (RhTe2, RhTe and RuO2; Extended Data Fig. 4) in 1 M KOH. The SA was further calculated to estimate OER activities and exclude the influence of other electrode parameters (Fig. 3b and Methods). The SAs of the chiral catalysts exceeded those of achiral electrodes in 1 M KOH. In particular, the SA of RhBiS at an overpotential of 300 mV exceeded achiral electrodes of RuO2, RhTe and RhTe2 by about 200-fold, 25-fold and 40-fold, respectively. The SA of RhSn was 1.76 times that of the achiral RhTe despite the stronger SOC in the latter. The Gibbs free energies further indicated that the activities of all Rh-based chiral catalysts were dependent on the SOC strength rather than following the free energy from a thermodynamic perspective (Supplementary Fig. 11 and Supplementary Table 3). These findings indicate the importance of structural chirality for the spin-related electron transfer in the OER.

Fig. 3: Normalized OER activities and selectivity.
figure 3

a, LSV polarization curves. b, SAs in 1 M KOH. The current density is normalized with respect to the ECSA. c, Tafel plots and slopes. d, UV–vis spectra revealing H2O2 formation after 1 h chronoamperometry testing (see more details in Supplementary Fig. 21).

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Other than the catalytic activity, the robustness and durability are also important for OER catalysis48. As shown in Supplementary Fig. 12a–c, the LSV polarization curves of the chiral electrodes remained almost unchanged after the accelerated durability test-cyclic voltammetry (ADT-CV) for 1,000 cycles, indicating an excellent stability of the single crystals for OER in alkaline conditions. Moreover, the stability was further confirmed by a 20 h chronoamperometry operation in 1 M KOH at potentials of 1.597 V, 1.544 V and 1.489 V for RhSi, RhSn and RhBiS, respectively, with no appreciable decrease in current density observed for the three electrodes (Supplementary Fig. 12d–f). By contrast, the current density of Rh foil was dramatically decreased by about 30% within 4 h of chronoamperometry test, revealing that doping or alloying Rh-based intermetallic compounds can improve their OER durability compared with pure Rh49,50,51 (Supplementary Fig. 13). In addition, the morphology and electronic states of Rh sites on the chiral crystal surface were completely maintained after the OER test (Supplementary Figs. 14–18), substantiating their excellent stability. To confirm the fixation of Rh in chiral electrodes, inductively coupled plasma optical emission spectroscopy (ICP-OES) was performed to analyse the concentration of the dissolved elements in the solution during the 20 h stability test. The results of ICP-OES revealed that the Rh element in the electrolytes was under 0.02 ppm (approximately 4 µg cm−2) after 20 h (Supplementary Table 4), further evidencing the robustness of the Rh sites in the chiral catalysts. Therefore, the chiral crystals of RhSi, RhSn and RhBiS are stable for the electrocatalytic OER in alkaline electrolyte.

As discussed above, chirality improved the OER activity. Moreover, the OER activity and SOC followed the same trend, namely RhSi < RhSn < RhBiS, which inspired us to explore the relationship among SOC, spin polarization and OER performance.

Effect of spin polarization on OER kinetics and selectivity

The Tafel slope is inversely correlated with the OER kinetics52. As shown in Fig. 3c, the resulting Tafel slope of RhBiS (52.4 mV dec−1) is smaller than achiral electrodes of RuO2 (74.9 mV dec−1), RhTe (63.5 mV dec−1) and bulk RhTe2 (65.4 mV dec−1), signifying superior reaction kinetics53. Among the chiral electrodes, the Tafel slopes followed an order of RhSi > RhSn > RhBiS, indicating the reverse order of OER kinetics, which was consistent with the trend of SOC strength.

Previously reported CISS-based catalysts were expected to hinder the formation of singlet H2O2 because of the CISS effect, that is, the reduced formation of H2O2 was correlated with the extent of spin polarization17. Thus, we measured the amount of H2O2 produced after a 1 h chronoamperometric test using ultraviolet–visible (UV–vis) spectrophotometry (Methods, Extended Data Fig. 5 and Supplementary Figs. 20 and 21a). As expected, the chiral catalysts effectively inhibited H2O2 production compared with the achiral electrodes (Fig. 3d). In addition, chiral RhBiS generated less H2O2 compared with chiral RhSn and RhSi, indicating a negative correlation with SOC strength. The rotating ring-disk electrode (RRDE) was further used to indicate the side reaction on the working electrode. As shown in Supplementary Fig. 21b, much lower current densities were detected on the ring electrodes of the chiral catalysts compared with the achiral catalysts, demonstrating a superior ability to prevent H2O2 formation on chiral materials. The ring current densities of the RRDE among the chiral electrodes are in agreement with the ex situ UV–vis measurement. The above experimental data and analysis results show that spin polarization can be varied by controlling the SOC of chiral materials. Thus, our results help to correlate the spin-amplified OER with SOC and quantify the contribution of spin polarization to the OER.

Mechanism study of spin polarization in topological chiral crystals

According to the mechanism of the spin-amplified OER in Rh-based topological chiral crystals (Fig. 4a), the charge carriers in these crystals are spin-polarized, which further induces the formation of spin-aligned oxygen intermediates. In detail, when electrons transfer from the adsorbates to the chiral electrode, spin-polarized holes are emitted from the catalyst surface, impacting the OER activity. Importantly, the large electron mean free path (ℓmfp), which exceeds 100 nm in the topological chiral single crystals (Supplementary Table 6), indicates the robustness of the spin-polarized carriers against surface modifications. In addition, when electrons pass through the bulk chiral crystal and reach the electrode surface, the spin polarization is always along the current direction, regardless of which crystalline axis the current flows along (Extended Data Fig. 6). Thus, transition states at the electrode–water interface feel the same spin polarization, even though chiral crystals may orient along different axes. This agrees with the experimental results that polycrystalline particle-based chiral electrodes show a similar OER activity trend as the single-crystal-based electrodes (Figs. 2 and 3 and Supplementary Fig. 8). Given the homochirality of the single crystals, only spin-down carriers (red arrow) are generated, which leads to the formation of spin-aligned oxyl radicals (O·, blue arrow). Subsequently, the spin-down carriers are transferred from the hydroxide anions (OH−) to the chiral electrode, which results in the high spin multiplicity of the oxygen intermediates generated at the catalytic surface. Finally, triplet oxygen (3Σ–g) is formed at the chiral anode. Conversely, both spin-up and spin-down electrons are injected into the achiral electrode, leading to the formation of oxygen intermediates with mixed spin states; the need for an additional spin flip to form the final triplet oxygen decelerates the reaction. Therefore, the concept of utilizing spin-polarized carriers (in this case, holes) generated by topological chiral materials remains a promising strategy to enhance OER kinetics. Given that the magnitude of spin polarization rather than its sign is considered, both enantiomers can contribute to the OER. The bottom line is that opposite enantiomers should be separated in space, which is obviously the case for homochiral single crystals.

Fig. 4: Mechanisms of spin polarization in chiral crystals.
figure 4

a, Illustration of the spin polarization mechanism of the OER on the chiral catalytic surface. b, Calculated spin polarizations (left axis) and corresponding SA (right axis) in the chiral crystals.

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Quantum transport calculations were performed to directly estimate the spin polarization of conduction electrons propagating through the chiral crystals. We considered first-principles band structures with intrinsic SOC, calculated the number of electrons transmitted between the two electrodes through the chiral crystal, and estimated the induced spin polarization after non-polarized electrons pass through the chiral material (Extended Data Figs. 7 and 8). RhSi and RhSn exhibited spin polarizations of 0.62% and 0.78%, respectively, for conductance at the Fermi energy. Semiconducting RhBiS exhibited the largest spin polarization of 5% at the bottom of the conduction band corresponding to the experimental carrier density and type (Supplementary Figs. 22 and 23). Although these spin polarizations were smaller than those of the chiral molecules measured using magnetoresistance54,55,56,57, the high carrier density in these chiral semimetals eventually generated a significant number of spin-polarized electrons (Supplementary Fig. 23). The SA followed the same trend as spin polarization (Fig. 4b), which suggested that SOC is the driving force for spin polarization and the enhancement of OER activity in the same family of chiral crystals. Importantly, the mechanism remains robust against surface modifications because spin polarization and SOC are governed by the bulk properties of the crystal rather than its surface states.

Conclusion

We have uncovered a design principle for chiral catalysts that promote the spin-dependent OER, quantified the effects of topological spin texture on OER activity and presented the experimental evidence of a close relationship between the spin-amplified OER and SOC. Our results suggest that a strong SOC is crucial for generating high spin polarization in chiral crystals. The SA of RhBiS, which exhibited the strongest SOC among the tested chiral catalysts, was about 200 times that of the RuO2. Our work facilitates the design of highly efficient chiral catalysts for spin-dependent chemical reactions. Therefore, in future endeavours, the development of top-performing catalysts could encompass spin polarization as a fundamental property for chiral materials with SOC serving as a valuable descriptor.

Methods

Crystal growth and structure refinement

RhSi

Single crystals of RhSi with an off-stoichiometric composition (slight excess of Si) were synthesized using the vertical Bridgman crystal-growth technique. A polycrystalline ingot obtained from a 1:1 (mol/mol) mixture of Rh and Si (each with a purity of 99.99%) by arc melting was crushed, and the powder was filled into a custom-made sharp-edged alumina tube that was sealed into a Ta tube under Ar. The Ta tube was heated to 1,500 °C and then cooled to the cold zone at a rate of 0.8 mm h−1 to obtain single crystals with an average length and diameter of ~15 mm and ~6 mm, respectively.

RhSn

Single crystals of RhSn were grown by the flux growth method using Sn as a flux. Highly purified Rh (99.999%) and Sn (99.99%) were cut into small pieces and weighed in a 9:11 molar ratio. The mixture (5 g) was placed in an alumina crucible that was then sealed in a quartz tube at an Ar pressure of 20 kPa. The quartz ampoule was placed in a box furnace, heated to 1,100 °C at a rate of 100 °C h−1 and held at this temperature for 12 h to ensure homogeneity. Subsequently, the furnace was cooled to 1,000 °C at a rate of 2 °C h−1 for crystal growth. At 1,100 °C, the excess flux was removed by centrifugation. Several of the resulting silvery single crystals (1–3 mm in size) were separated for further characterization.

RhBiS

Single crystals of RhBiS were grown by the solid-state method. Highly purified Rh (99.999%), Bi (99.999%) and S (99.99%) were cut into small pieces and weighed in a 1:1:1 molar ratio. The mixture (8 g) was placed in an alumina crucible that was then sealed in a quartz tube at an Ar pressure of 0.2 bar. The quartz ampoule was placed in a box furnace, heated to 1,050 °C at a rate of 100 °C h−1 and kept at this temperature for 12 h to ensure homogeneity. Subsequently, the furnace was cooled to 950 °C at a rate of 10 °C h−1, held for 12 h, further cooled to 700 °C at a rate of 4 °C h−1 for 5 h and finally cooled to room temperature at a rate of 20 °C h−1. Several of the resulting silvery single crystals (0.5–1 mm in size, embedded in polycrystals) were separated for further characterization. The composition of RhBiS crystals was determined through scanning electron microscopy and energy-dispersive X-ray spectroscopy.

RuO2

Single crystals of RuO2 were grown by the chemical vapour transport method. RuO2 powder and the transport agent TeCl4 (5 mg cm−3) were sealed in an evacuated quartz tube. The quartz tube was placed into a two-zone tube furnace with 1,100 °C at the hot side and 1,000 °C at the cold side for 1 week. Millimetre-sized crystals were obtained at the cold side.

RhTe2

Bulk crystals of RhTe2 were grown from a homogeneous powder mixture of Rh (99.9%) and Te (99.999%) with an Rh/Te molar ratio of 1:2.06. The reaction was carried out in a closed silica crucible sealed in a fused silica ampoule filled with Ar (800 mbar). The ampoule was kept at 800 °C for 3 days to obtain polycrystalline RhTe2, heated to 1,250 °C at a rate of 15 °C min−1 and kept for 1 h for homogenization. The crystallization of RhTe2 from the melt was achieved by slow cooling (3 °C min−1) from 1,250 °C to 1,075 °C followed by rapid cooling to room temperature. The RhTe2 regulus was characterized by metallographic analysis, energy-dispersive X-ray spectroscopy and powder XRD, which shows a cubic lattice belonging to the achiral Pa-3 space group (no. 205).

RhTe

The single crystals of RhTe were grown via chemical vapour transport, starting from RhTe2. Polycrystalline RhTe2 powder was synthesized using rhodium (Sigma-Aldrich, 99.95%) and tellurium (Merck, 99%), which were sealed in an evacuated fused silica ampoule and heated at 700 °C for 3 days. Single crystals were then grown by transporting the polycrystalline RhTe2 with Cl2 (2 mg cm−3) as a transport additive. The evacuated silica ampoule was heated in a two-zone furnace with a temperature gradient from 900 °C (T2) to 800 °C (T1) for several days. After the reaction, the ampoule was removed from the furnace and quenched in water.

Material characterization

White-beam backscattering Laue diffraction was conducted to confirm the single-crystalline nature of the crystals at room temperature. The single-crystal XRD patterns were collected using a Rigaku AFC7 four-circle diffractometer with a Saturn 724+ CCD detector and a source of graphite-monochromatized Mo Kα radiation. A summary of the crystallographic information can be found in Extended Data Table 1. STEM (FEI Tecnai G2 F30) was performed at an acceleration voltage of 300 kV. UV–vis absorption spectra were recorded on an Agilent Cary 5000 UV–vis–NIR spectrophotometer equipped with an integration sphere. The hard X-ray high-energy photoelectron spectroscopy (HAXPES) measurements were performed at beamline P22 of PETRA III. The photon energy was set to  6 keV at emission angles of 60° and 5°, respectively, and the overall energy resolution was approximately 65 meV (resolving power ≈ 9 × 104), as determined at the Au Fermi energy. The HAXPES measurement at 5° (with a probing depth of approximately 13 unit cells) is more bulk sensitive, whereas the measurement at 60° (probing depth of 7 cells) is more surface sensitive.

Electrochemical measurements

Electrochemical measurements were carried out using a VMP3 electrochemical workstation in the standard three-electrode configuration (counter electrode, Pt; reference electrode, Hg/HgO in alkaline solution or Ag/AgCl in acidic and neutral electrolytes; working electrode, bulk crystal). The as-grown crystals were orientated by Laue XRD and the plate-like single crystals were obtained by cutting along the (100) direction. Substantially, the working electrode was prepared by attaching the bulk crystal to the Ti wire with silver paste. To ensure precise testing conditions, all surfaces of the electrode, except the designated test surface, were covered with insulating coating. The geometric surface area of the electrode was measured directly using a high-magnification stereomicroscope (Olympus SZX16). This procedure was repeated 3–5 times for each electrode to ensure consistency and accuracy of the effective surface area. OER LSV polarization measurements were performed in Ar-saturated electrolytes, including 1 M KOH, 0.1 M KOH, 1× PBS solution and 0.5 M H2SO4, using a scan rate of 10 mV s−1. Chronoamperometry measurements were conducted in 0.1 M KOH solution for 1 h and the electrolyte after the reaction was used for the H2O2 detection.

The Nernst equation was used to convert potentials (E) versus Hg/HgO or Ag/AgCl scale to those versus the reversible hydrogen electrode (RHE):

$${E}_{{\rm{RHE}}}({\rm{V}})={E}_{{\rm{Hg}}/{\rm{HgO}}}({\rm{V}})+0.059{\rm{pH}}+0.098.$$
(1)
$${E}_{{\rm{RHE}}}({\rm{V}})={E}_{{\rm{Ag}}/{\rm{AgCl}}}({\rm{V}})+0.059{\rm{pH}}+0.197.$$
(2)

CVs for the ECSA were measured in a non-Faradaic region based on the open circuit potentials of the voltammogram at the scan rate of 10 mV s−1, 20 mV s−1, 30 mV s−1, 40 mV s−1, 50 mV s−1 and 60 mV s−1. The working electrode was held at each potential vertex for 10 s before beginning the next sweep. All current was assumed to be due to capacitive charging. The ECSA was calculated from the double-layer capacitance (Cdl) as

$${\rm{ECSA}}={C}_{{\rm{dl}}}/{C}_{{\rm{s}}},$$
(3)

where Cs is the specific capacitance of the sample or the capacitance of an atomically smooth planar surface of the material per unit area under identical electrolyte conditions. Here Cs was assumed to equal 0.040 mF cm–2.

The SA was calculated as SA = j/ECSA, where j is the current density at an overpotential of 300 mV.

H2O2 determination

H2O2 was quantified by the colorimetric titration of the spent electrolyte using o-tolidine as a redox indicator. A solution of o-tolidine prepared according to the Ellms–Hauser method58 (0.8 ml) was added to the spent electrolyte (4 ml) and left to react for 1 h. In the presence of H2O2, the solution turned yellow, and an absorption peak emerged at ~435 nm. H2O2 was quantified using a calibration curve constructed using commercial H2O2 (Supplementary Fig. 20).

Calculations of \({{\boldsymbol{\ell }}}_{{\bf{m}}{\bf{f}}{\bf{p}}}\) in chiral crystals

The \({\ell }_{{\rm{mfp}}}\) for RhSi, RhSn and RhBiS are calculated using the following equation:

$${\ell }_{{\rm{mfp}}}={v}_{f}\cdot \tau =\frac{\hslash }{{m}_{e}}{(3n{\uppi }^{2})}^{-\frac{1}{3}}\cdot \frac{\mu {m}_{e}}{q},$$
(4)

where \(\hslash =h/2\pi\) is the reduced Planck constant, \({m}_{e}\) is the mass of electron, \(q\) is the electron charge, and \(n\) and \(\mu\) are the charge density and mobility, respectively, calculated from the transport data.

Calculations of spin polarization in chiral crystals

We constructed a two-terminal device for quantum transport calculations, as schematically shown in Extended Data Fig. 7a. The central region, composed of chiral crystals, was sandwiched between two semi-infinite leads at the top and bottom. In both leads, we completely exclude the SOC, so that the spin (\({\mathrm{S}}_{\mathrm{z}}=\uparrow \downarrow\)) is a conserved quantity and the spin polarization can be well defined. The intrinsic SOC in the chiral crystals will promise the transmitted electron with a preferential spin polarization that depends on the current direction and the handedness of the chiral crystal. The calculated spin polarization ratio (\({P}_{\mathrm{{S}_{z}}}\)) for RhSi, RhSn and RhBiS is shown in Extended Data Fig. 7b. Among them, RhSi and RhSn are representative topological chiral semimetals characterized by multiple band crossings with large Chern numbers in the bulk state and unique Fermi arcs at the surface31,59. The calculated \({P}_{\mathrm{{S}_{z}}}\) values at the Fermi energy (\({\varepsilon }_{\mathrm{F}}\)) are 0.62% and 0.78% for RhSi and RhSn, respectively. This corresponds to a relatively small enhancement of the OER activity of RhSn compared with RhSi by our electrochemical measurement. Notably, RhBiS is identified as a topological trivial semiconductor with an indirect bandgap of about 0.459 eV according to mBJ calculation32. To estimate the position of the Fermi energy in the band structure, the carrier density of the RhBiS single crystal was measured by Hall measurements. The obtained electron density was \(n=0.754\times {10}^{20}{\mathrm{cm}}^{-3}\) at a gate voltage (VG) = 0 V. Our calculations on this charge carrier density show that the extracted \(n\) corresponds to a \({\varepsilon }_{\mathrm{F}}\) of about 22 meV above the conduction band edge, and correspondingly \({P}_{\mathrm{{S}_{z}}}\) is calculated to be 5%, which is 6–8 times larger than that obtained in RhSi and RhSn. This explains the greatly improved OER performance in RhBiS compared with RhSi and RhSn. The distinctive peaks detected at energy levels of −0.98 eV in RhSi, −0.875 eV in RhSn and −0.52 eV in RhBiS, each associated with \({P}_{\mathrm{{S}_{z}}}\) values of 4.91%, 9.84% and 25%, respectively, primarily arise from the low total conductance near the band edge and the occupation of a single band, since the occupancy of the alternate band with opposite spin angular momentum (Extended Data Fig. 8) would provide partial compensation for the induced spin density. We highlight that the spin polarization has predominantly been studied in the chiral organic molecule with a \({P}_{\mathrm{{S}_{z}}}\) of more than 60% (refs. 28,60,61). It remains poorly explored in chiral crystals. We reveal a small magnitude of \({P}_{\mathrm{{S}_{z}}}\) of only few percent in chiral crystals. However, the exceptionally high carrier density in these chiral metals, compared with the chiral organic molecule, gives chiral crystals promising applications in spin-dependent chemical reactions.

Calculations of electronic structure

Electronic structure calculations were performed on the basis of density functional theory using the Vienna Ab initio Simulation Package62,63. The exchange and correlation energies were described using the modified Becke–Johnson functional64. Bloch wavefunctions were projected into Wannier functions65, and the latter were used to construct the corresponding tight-binding model Hamiltonian of RhSi, RhSn and RhBiS. The k-point grid was set to 12 × 12 × 12, and the total energy convergence criterion was set to 10−6 eV. The obtained Hamiltonian was used to calculate the quantum transport quantity of conductance (G) based on the Landauer–Büttiker approach66:

$${{G}}_{{\rm{L}}\to {\rm{R}}}=\frac{{{e}}^{2}}{{h}}{\sum }_{{\rm{n}}\in {\rm{R}},{\rm{m}}\in {\rm{L}}}{|{{\rm{S}}}_{{\rm{nm}}}|}^{2},$$
(5)

where Snm is the scattering matrix element from the mth eigenstate in the left lead (L) to the nth eigenstate in the right lead (R). With the spin-conserved leads, the spin-polarized conductance in each \({{\rm{S}}}_{{\rm{z}}}\) channel was obtained as

$${{G}}_{{{\rm{S}}}_{{\rm{z}}}}={{G}}_{{\rm{L}}\to {\rm{R}}\uparrow }-{{G}}_{{\rm{L}}\to {\rm{R}}\downarrow },$$
(6)

where \({{G}}_{{\rm{L}}\to {\rm{R}}\uparrow (\downarrow )}\) is the conductance from the left lead to the spin-up (down) channel of the right lead. The corresponding spin polarization ratio was calculated as \({{P}}_{{{\rm{S}}}_{{\rm{z}}}}=\frac{{{G}}_{{{\rm{S}}}_{{\rm{z}}}}}{G}\times 100 \%\).

Calculations of free energy diagram of the OER

To study the free energy diagram of the OER reaction intermediate on the surface of chiral crystals. The revised Perdew–Burke–Ernzerhof67 functional was used to describe the exchange and correlation effects. A slab model with 5-unit cell thickness was constructed and a 20 Å vacuum layer was applied in the z-direction of the slab models, preventing the vertical interactions between slabs. In alkaline conditions, OER could occur in the following four elementary steps:

$${{\rm{OH}}}^{-}+\ast \to {{\rm{OH}}}^{\ast }+{{\rm{e}}}^{-}$$
$${{\rm{OH}}}^{\ast }+{{\rm{OH}}}^{-}\to {{\rm{O}}}^{\ast }+{{\rm{H}}}_{2}{\rm{O}}(l)+{{\rm{e}}}^{-}$$
$${{\rm{O}}}^{\ast }+{{\rm{OH}}}^{-}\to {{\rm{OOH}}}^{\ast }+{{\rm{e}}}^{-}$$
$${{\rm{OOH}}}^{\ast }+{{\rm{OH}}}^{-}\to {{\rm{O}}}_{2}(g)+\ast +{{\rm{H}}}_{2}{\rm{O}}+{{\rm{e}}}^{-}$$

where the asterisk indicates the surface-active site. The free energies of three intermediate states, OH*, O* and OOH*, were calculated based on the computational hydrogen electrode model. The free energy (ΔG) of each elementary step was calculated as68

$$\Delta {G}={\Delta {E}+\Delta {E}}_{{\rm{ZPE}}}-{T}\Delta {S}+{\Delta {G}}_{{\rm{u}}}$$

where ∆E, ∆EZPE and T∆S are the electronic adsorption energy, the zero point energy and the corresponding entropy of the reaction, respectively. ΔGu = \(-e\)URHE, in which URHE is the potential of the electrode relative to the RHE.