Chiral Quantum Materials: When Chemistry Meets Physics

Chirality is a fundamental property of nature with relevance in biochemistry and physics, particularly in the field of catalysis. Understanding the mechanisms underlying chirality transfer is crucial for advancing the knowledge of chiral‐related catalysis. Chiral quantum materials with intriguing chirality‐dependent electronic properties, such as spin‐orbital coupling (SOC) and exotic spin/orbital angular momentum (SAM/OAM), open novel avenues for linking solid‐state topologies with chiral catalysis. In this review, the growth of topological homochiral crystals (THCs) is described, and their applications in heterogeneous catalysis, including hydrogen evolution reaction (HER), oxygen electrocatalysis, and asymmetric catalysis are summarized. A possible link between chirality‐dependent electronic properties and heterogeneous catalysis is discussed. Finally, existing challenges in this field are highlighted, and a brief outlook on the impact of THCs on the overarching chemical–physical research is presented.


Introduction
[3][4][5][6] Moreover, it seamlessly interlaces these disciplines, extending well beyond the mere consideration of the structural asymmetry of materials.By combining the topology of solids with the chirality of electrons arising from their spin, orbit, and momentum coupling, exciting possibilities emerge, which manifest when structural chirality intersects with electronic chirality or when chiral molecules encounter topological solids, surfaces, and surface states.Apart from the conventional study of structural chirality, contemporary scientific research has delved into profound depths by examining the intricate interplay between chirality and various quantum-mechanical aspects.These include aspects such as orbitals, spins, wave functions, and phases, such as the enigmatic Berry phase and other geometric phases. [7,8]11][12][13][14][15][16][17][18][19] Chirality is commonly observed in organic molecules containing sp 3 -hybridized carbon atoms with four distinct functional groups.This structural arrangement gives rise to two possible tetrahedral configurations, known as enantiomers.Although enantiomers display comparable physical and chemical properties, the interactions between homochiral molecules and their heterochiral counterparts diverge because of their unique spatial orientations. [20,21]onsequently, this enantioselectivity plays a pivotal role in the emergence of homochirality in nature, wherein a specific enantiomer such as L-amino acids or Dsugars overwhelmingly adopts a single-handed orientation. [19,22]n various biological systems, the enantiomers of compounds often display markedly different biological activities.For example, the enantiomers of limonene exhibit distinct odors, and in the case of thalidomide, one enantiomer offers therapeutic benefits, whereas the other leads to congenital disorders. [23]Hence, producing enantiomerically pure compounds for the pharmaceutical and food industries is important.
Asymmetric catalysis is a promising approach that achieves the selective production of one enantiomer over its mirror-image counterpart, offering exceptional product specificity compared with the separation of racemic mixtures. [24]Because heterogeneous asymmetric catalysis relies on the chirality transfer between catalytic surfaces and reactants, as well as electron transfer during the reaction pathways, homochiral catalysts are imperative for enhancing the enantiomeric excess (ee).Significantly, intrinsically homochiral catalysts are essential to investigate the interplay between chiral quantum properties and catalytic efficiency.However, most chiral surfaces used in heterogeneous asymmetric catalysis have been obtained by introducing chirality on achiral metal surfaces via the adsorption of chiral modifiers. [25,26]n condensed matter physics, chirality is a vital link connecting structural symmetry and exotic quantum physical properties.Chiral structures lack symmetry elements such as mirrors, inversions, or rotation-reflections.Among the 230 space groups, 22 are enantiomeric, and 43 are non-enantiomeric. [27,28]In the case of enantiomeric chiral structures, two enantiomers can crystallize in a pair of space groups; for example, P6 1 and P6 5 represent two opposing chiralities.For non-enantiomeric space groups, compounds with opposing chiralities cannot be differentiated by the space group because they share the same spatial symmetry; for example, this is the case with space groups such as P6 3 and P2 1 3.
When chemistry intersects with the physics of chiral crystals, electronic quantum properties such as strong spin-orbital coupling (SOC) and spin/orbital angular momentum (SAM/OAM) offer fresh insights into the mechanism of chirality transfer in chemical reactions.A compelling phenomenon is chiralityinduced spin selectivity (CISS), which arises from the interplay between chirality and the intrinsic spin/orbit of electrons. [48]This interplay reveals a distinct propensity for the selective manipulation and control of electron spins, depending on the surrounding chirality.[52][53][54] Crystals can be easily studied through experiments and understood via theoretical modeling. [55,56]On the one hand, helical structures are primarily present in crystals, indicating that the CISS effect in chiral crystals yields improved electron spin polarization performance.On the other hand, quantum properties are inherently governed by the electronic band structure, a characteristic that can be accurately computed in crystals.However, the fundamental mechanism of the CISS phenomenon, either in chiral molecules or crystals, has not yet been fully elucidated.The origin of CISS is a subject of intensive investigation, with potential factors such as SOC, topological aspects, and OAM currently under scrutiny. [48]Recently, the CISS effect has been recognized as a novel dimension for manipulating spin control in chemical reactions, establishing a connection between structural chirality and electron spin. [9,57,58]High-quality topologically homochiral crystals (THCs) with specific chiralities are anticipated to bridge chemical processes and underlying physical mechanisms via the CISS effect, providing insights into its origin and the associated interdisciplinary properties in the realms of chemistry and physics.
To date, several outstanding review articles have offered indepth discussions on spin-control of electrocatalysis by the CISS effect, [59] quantum materials and tuning strategies for electronic interaction parameters, [60] and chiral matter, and their applications in quantum science. [61]In contrast to these previous reviews, this article focuses on the interplay between chiral quantum properties and chiral heterogeneous catalysis.First, we showcase several exemplary THCs featuring chiral noble metal active sites synthesized by our group.We delve into the homochiral structures and provide insights into the characterization of these THCs.Subsequently, we offer a comprehensive overview of the advancements achieved in the field of THCs in heterogeneous catalysis, encompassing critical areas such as the hydrogen evolution reaction (HER), oxygen reduction reaction/evolution reaction (ORR/OER), and asymmetric catalysis.We also explore the potential connections between chirality-dependent electronic properties and their impact on heterogeneous catalysis.Last, we address the existing challenges in the growth of homochiral crystals and offer a succinct glimpse into the future, outlining the significance of THCs in shaping and advancing the domain of chemical-physical research.

Growth and Characterization of THCs
Rh(DIPAMP) (DIPAMP = 1,2-bis[(2-methoxyphenyl)(phenylphosphino)]ethane), a well-known asymmetric catalyst, shows excellent performance (94% ee) in the asymmetric hydrogenation of prochiral dihydroxyphenylalanine (DOPA) precursors. [16,62,63]he enantiomers of Rh(DiPAMP) exhibit inverse molecular structures, as shown in Figure 2a-d.The noble metal centers in the complexes are important for the high enantioselectivity in the asymmetric synthesis. [24]Accordingly, the THCs grown by our group (such as PdGa, RhSi, EuIr 2 P 2 ) contain different noble metal centers, which can potentially be high performance chiral catalysts.In contrast to homogeneous asymmetric catalysis, heterogeneous asymmetric catalysis offers several advantages, such as simplified regeneration processes and enhanced catalytic properties.These benefits expand the use of catalytic substrates for synthesizing chiral molecules. [15]With such a demand, THCs offer these advantages: a) THCs have naturally chiral structure and surface that can enhance the efficiency of chirality transfer; b) THCs with noble-metal as constituent components possess numerous active sites for chiral charge transfer; c) THCs have good chemical stability and is easy to be separated from reactants or products.These characteristics render THCs promising catalysts for research endeavors and practical applications.Some crystalline materials exhibiting chiral structures are outstanding candidates for promoting heterogeneous asymmetric catalysis. [64]The formation energies of chiral crystals are identical for both enantiomers [65] ; hence, only a few crystals with specific chiralities have been grown.For example, the homochiral crystals of TMSi 2 (TM = V, Nb, or Ta) can be grown at relatively high temperatures (≈2 000 °C) using small crystals with specific chirality as seeds, in a process conducted with a laser floating zone furnace. [66]Our prior research demonstrated that the homochiral PdGa crystals could be successfully grown using a seed-controlled Bridgeman method. [30]Notably, homochiral crystals are anticipated to be explored extensively from both experimental and theoretical perspectives.
Usually, circular dichroism (CD) spectra distinguish molecules with varying chiralities by exhibiting contrasting intensities, as illustrated in Figure 2b,c when exposed to lefthanded-and right-handed circularly polarized (LHCP and RHCP) lights, respectively. [67]However, particular techniques are needed for characterization of THCs.In this review, we considered PdGa crystallized in the B20 structure with space group P2 1 3 (No.198) and EuIr 2 P 2 in the CaIr 2 P 2 -type structure with space group P3 1 21 (No.152) or P3 2 21 (No.154) as potential catalysts. [30,68]Figure 2e-h shows the Laue patterns of the (111) surfaces of the distinct enantiomers of the PdGa single crystals.The Laue diffraction points are well-defined and exhibit threefold symmetry, implying that the polished surface is the (111) surface.The insets show the crystal structures of the two enantiomers.The Pd and Ga atoms crystallized anticlockwise and clockwise along the [111] direction, respectively, reveal distinct structural chiralities of this compound.In enantiomer-A (inset of Figure 2e), Pd occupies the 4a site with atomic coordination of x Pd = y Pd = z Pd = 0.14246(4), and Ga occupies the 4a site with atomic coordination of x Ga = y Ga = z Ga = 0.84301(6). [30]n contrast, the atomic coordination of the Pd and Ga atoms in enantiomer-B (inset of Figure 2h) is x Pd = y Pd = z Pd = 0.85758(3) and x Ga = y Ga = z Ga = 0.15694(5), [30] respectively.Figure 2f,g shows the electron backscattering diffraction (EBSD) patterns of the (111) surfaces of both enantiomers.EBSD is an efficient method for determining the chirality of crystals, as reported in -Mn. [69]Several points on the polished surface of the crystals are measured and assigned similar structural chirality, thus indicating that the entire crystal exhibits homochirality in each enantiomeric form.The insets show images of the PdGa single crystals with distinct chiralities.
In contrast to PdGa, which crystallizes in the nonenantiomeric space group P2 1 3, the two enantiomers of EuIr 2 P 2 with opposite chiralities crystallize in different space groups, that is, P3 1 21 (No.152) or P3 2 21 (No.154).Figure 2i-k shows the single-crystal X-ray diffraction (SXRD) patterns of the two enantiomers of the EuIr 2 P 2 single crystal with opposite chiralities.The scattering planes for both crystals are [H,K,0].The insets show the crystal structures of the two enantiomers.For convenience, we designated EuIr 2 P 2 with space groups P3 2 21 (No.154) and P3 1 21 (No.152) as enantiomer-A and enantiomer-B, respectively.From the crystal structure, evidently, the Eu atoms in enantiomer-A form a clockwise screw along the (001) direction, whereas the Eu atoms in enantiomer-B form an anticlockwise screw along the same (001) direction.By employing the EBSD technique to map the entire crystal surface, it becomes evident that the exposed surface of enantiomer-A maintains the same crystal chirality assignment (Figure 2j).Conversely, the other crystal portion is identified as enantiomer-B, as shown in Figure 2k.The structural chirality assignment was consistent on the naturally grown surfaces of the crystals.The insets of Figure 2j and k show images of EuIr 2 P 2 crystals with opposite chiralities, respectively.The crystalline structures of the two enantiomers are confirmed using SXRD, as shown in Figure 2i,l.The clear diffraction patterns of the [HK0] scattering plane indicate the high quality of the as-grown crystals.

THCs for Energy Conversion
Gas-involving reactions, including the HER, ORR, OER, and carbon dioxide reduction reaction, represent promising energy conversion technologies with the potential to drive the development of sustainable and clean energy for the future. [70,71]However, the energy conversion efficiency of these electrochemical reactions is hampered by their sluggish kinetics and considerable overpotential. [72]Hence, the quest for catalysts with exceptional activities is paramount in enhancing the rate, efficiency, and selectivity of these pivotal chemical conversions.
Electronic structural engineering strategies (doping, strain, and defects) are effective approaches for designing highperformance catalysts that require precise control over their active sites.However, obtaining nanostructured catalysts is challenging because of the absence of well-defined active sites and the inevitable occurrence of multiple effects. [73]In such gasinvolved reactions, all processes entail the adsorption/desorption of reactants and electron transfer at the catalyst surfaces, which are strongly related to the surface properties of the catalysts.Therefore, THCs are promising electrocatalysts because of the following advantages: (1) TSSs exist at the surface because of band inversion between the bulk conduction and valence bands.They are robust and resistant to surface modifications as long as the bulk band is preserved.This characteristic enables us to investigate the interplay between surface states and electron transfer in these reactions. [74](2) The large density of states of the topological surface electrons at the Fermi level provides an abundant electron bath for catalytic reactions. [75](3) In contrast to the achiral topological materials, THCs exhibit near-ideal topological electronic structures, such as the largest possible Fermi arcs and wide nontrivial energy windows.These characteristics substantially enhance the topological robustness, even if the chemical potential varies (Figure 3a). [30,76,77]

HER
Although the application of topological materials for the HER has been extensively studied considering topological insulators  [56] c) Calculated spin polarization around the Fermi level on PdGa A and PdGa B. d) E 1/2 and J k of TH PdGa, Pt/C, and AC PdGa at 0.85 V vs. RHE.e) Schematic of the effect of the chiral crystal structure-induced spin polarization on the enhancement of the ORR activity. [64]i 2 Te 3 [78] and SnTe [79] ) and topological semimetals (NbP, [80] PtSn 4 , [81] PtTe 2, [82] and MoP [83] ), the investigation of THCs for the HER is still in its infancy.To address the relationship between the topological Fermi-arc surface states and HER activity, our research team conducted a proof-of-concept study using chiral single crystals of the B20 group, including PtAl, PtGa, PdGa, and RhSi.[56] In contrast to topological insulators and WSMs, the sources of topological charges in chiral single crystals of the B20 group are located at different high-symmetry time-reversal invariant momenta, ensuring large nontrivial energy windows and long surface Fermi arcs. Theretical modeling and experimental investigations revealed that the Fermi-arc states originating from the d-orbitals function as catalytically active sites leading to remarkably excellent intrinsic HER activities with high turnover frequency (5.6 s −1 and 17.1 s −1 for PtAl and PtGa, respectively) (Figure 3b).In addition, the representative PtAl chiral catalyst exhibited long-term HER stability with no decrease in current density during continuous chronoamperometry testing for up to 100 h, even at a high current density of 200 mA cm −2 . These chil crystals outperformed commercial Pt/C and nanostructured catalysts in terms of activity and stability. This expeiment serves as the first concrete evidence revealing the pivotal role of chiral electronic structures in heterogeneous catalysis.
Tuning the HER performance of the THC-based catalysts relies mainly on manipulating their distinctive topological electronic structures to promote electron donation or acceptance and tailoring the binding strength of the adsorbates.While funda-mental studies on the evolution of TSSs in the HER are currently limited to theoretical simulations, it remains a formidable technological challenge to validate this hypothesis experimentally.

ORR
In contrast to the HER, the ORR process involves the conversion of oxygen molecules in triplet states ( 3 Σ-g) (unpaired electrons in parallel) and water in singlet ground states ( 1 Δ) (no unpaired electrons) (Acidic conditions: O 2 (↑↑) + 4H + + 4e − → 2H 2 O). [84]herefore, the ORR is a spin-dependent electron transfer process, which, however, suffers from sluggish reaction kinetics and large overpotential. [85,86]For example, owing to the limitations of linear scaling relationships, an overpotential of more than 400 mV is needed to achieve a sufficient operating current in the case of the ORR. [87,88]In addition, singlet H 2 O 2 is a significant byproduct of the overall reaction.
The CISS effect demonstrates that chiral molecules (or structures) exhibit a preferred orientation of electron spins in the molecular frame following charge polarization, significantly influencing the manipulation of spin-dependent electron-transfer processes. [49,89]Several excellent review articles have intensively discussed the spin control of electrocatalysts via the CISS effect. [59,61]Consequently, the O 2 conversion is kinetically favored, and the H 2 O 2 formation is suppressed because the radical intermediates (such as OH•) exhibit parallel spins on the electrode surface, leading to the spin-forbidden combination of OH•, thereby reducing H 2 O 2 formation. [17,49]n addition to the aforementioned "hybrid chiral moleculemetal electrodes," the THC-based oxygen electrocatalysts offer distinct advantages, such as well-defined intrinsic homochiral geometric and electronic structures, as well as high electron mobility. [55]Therefore, THCs provide a gateway for delving into deeper levels of orbitals, spins, and the intricate interplay between chirality and various quantum mechanical aspects.Furthermore, the spin-polarized electrons are generated directly at the intrinsic chiral active sites, making the THC-based electrocatalysts an optimal platform for investigating the spin-dependent electron-transfer dynamics during the ORR.
Our recent experiments have established a link between SOC and electron spin polarization in THCs. [64]Specifically, we employed a topologically homochiral PdGa crystal (TH PdGa) with space group P2 1 3 (No.198) for the ORR.On the surface of the crystal, the electron spin manifests as a spin-orbital-momentum locking state, which is attributed to the substantial SOC. [31]Notably, the chiral electronic structure of TH PdGa exhibits chiral fermions and chiral Fermi-arc surface states with reversed velocities. [30,77]Thus, our investigation elucidates the crucial role of electron spin in the ORR, offering insights into the influence of the topologically protected chiral electronic structure on the ORR kinetics and efficiency.Using spin-resolved photoemission experiments, we directly examined the spin polarization within the TH PdGa crystals, revealing opposite spin polarization values for the two enantiomers of TH PdGa.Theoretical modeling further unveiled the combined contribution of the chiral structure and SOC in engendering spin polarization.Notably, when employed as an electrocatalyst for the ORR in acidic solutions, TH PdGa demonstrated significantly enhanced ORR kinetics, surpassing the benchmark Pt/C catalyst by more than 70-and 200-fold in terms of kinetic current density at 0.85 V vs. reversible hydrogen electrode (RHE) and intrinsic catalytic turnover frequency, respectively.These findings highlight the immense potential of THCs in spin-dependent electrocatalysis, thus offering new avenues for next-generation energy conversion technologies.

OER
The OER is the main obstacle in electrocatalytic water splitting because of its sluggish kinetics.Similar to the ORR, the OER involves a spin-dependent multielectron transfer process (Alkaline conditions: 4OH − → O 2 (↑↑) + 2H 2 O + 4e − ) and produces H 2 O 2 as the undesired byproduct.Naaman et al. first applied the CISS effect to (photo)electrocatalytic water splitting, demonstrating enhanced kinetics and selectivity. [90]Subsequently, various chiral catalysts have been developed for the OER, such as chiral organic molecules, [57,91,90] chiral inorganic oxides (e.g., CuO, ZnO, and CoO x ), [92][93][94] and imprinted chiral cavities. [9]he experimental studies have confirmed that CISS improves the activity and selectivity of the OER.However, it is still necessary to quantify the contribution of spin polarization to the enhancement of the OER activity.Therefore, THCs with welldefined structures and intrinsic chiral active sites are important bridges to address the inherent driving force of spin polarization in chiral catalysts and establish the quantum property-activity relationship for a strong collaboration between experimentalists and theoreticians.

THCs for Asymmetric Catalysis
Biological homochirality is essential for life; However, the origin of chirality in organic compounds remains unclear.One proposed mechanism for the enantiomeric enrichment of organic compounds involves asymmetric synthesis and/or their subsequent asymmetric adsorption on the surface of inorganic chiral crystals. [95]HCs are attractive compared with other inorganic chiral solids because of the unique combination of their intrinsic structural and electronic chirality.This distinctive characteristic is a platform for advancing our fundamental understanding of enantiospecific interactions between reactants and catalysts. [55]Furthermore, THCs open a pathway for delving into structural chirality, enabling an in-depth exploration of the intricate interplay between chirality and several quantum properties.Such investigations have the potential to shed light on the origins of life. [22]

Asymmetric Adsorption
Our research group has proposed a potential explanation for the emergence of chirality in nature through an enantioselective pathway using pure inorganic PdGa crystals. [55]In this study, the electrochemical oxidation currents for L-DOPA (I L ) and D-DOPA (I D ) exhibited an inversion when the enantiomers interacted with the surface of chiral PdGa-A and PdGa-B crystals.Specifically, the I L /I D ratios were 1.24 and 0.81 for PdGa-A and PdGa-B, respectively, indicating that the oxidation of L-DOPA was more favorable than that of D-DOPA on the PdGa-A surface, whereas PdGa-B showed a high activity for the oxidation of D-DOPA (Figure 4a,b).These findings indicate that the interaction between L-and D-DOPA was strongly dependent on the bulk chirality of the PdGa crystals.This difference in oxidation behavior was elucidated using classical thermodynamic adsorption theories.The binding energy between the L-DOPA/PdGa-B pair is 63 meV, which is higher than that for the D-DOPA/PdGa-B pair (112 meV).A difference of 48 mV between the adsorption energies of L-and D-DOPA on the PdGa-B was observed owing to chiral interactions.Furthermore, the momentum-space texture of the OAM around the Fermi level was examined.The spin-split branches indicated a parallel OAM between the orbital polarization and momentum, with (Lz) always bearing opposite signs at the +k y and -k y points (Figure 4c,d).Positive or negative magnetization in the [111] direction is expected, depending on the chiral crystal structure of PdGa.This study highlights the significance of OAM polarization as a promising driving force for enantiomeric recognition.
The selectivity of the enantiomeric synthesis can be enhanced by controlling environmental parameters such as temperature, solvents, and external fields.For example, enantioselective on-surface synthesis using an initial racemic mixture of 9-ethynylphenanthrene (9-EP) was achieved on a chiral PdGa surface. [96]The R and S configurations of 9-EP were determined When the SOC effects are considered, Lz exhibits opposite signs at +ky and -ky, and the OAM polarization depends on the chirality of PdGa. [55]e) Molecular structure of prochiral 9-ethynylphenanthrene (9-EP) appears in two distinguishable surface enantiomers, R and S, when restricted to a planar configuration.f) Gaussian-Laplace filtered nc-AFM images of R and S enantiomers.g) Schematic of temperature-controlled near-enantiopure trimerization of an initial racemic mixture of 9-EP molecules occurring on the intrinsically chiral intermetallic PdGa (111) surface. [96]Enantioselectivity of BMA debromination.Br-C intensity for the h) Au(111), i) PdGa: A Pd 3 , and j) PdGa: A Pd 1 surfaces.The contribution of each BMA surface enantiomer, with the enantiomeric form as determined from STM, is shown in a different color.The temperatures at which half of each surface enantiomer is debrominated are specified in the legends. [97]ing scanning tunneling microscopy (STM) and CO-sensitized noncontact atomic force microscopy (nc-AFM) (Figure 4e,f).The STM image of S-9-EP showed an elongated protrusion (green arrows in Figure 4f) attributed to the alkyne group pointing to the right of the phenanthrene backbone.Conversely, the adsorption configuration of R-9-EP resulted in a dot-like image of the alkyne group (blue arrows in Figure 4f).Owing to the ensemble effect of the prochiral 9-EP molecules on the chiral PdGa surface, they formed a racemic mixture at 300 K. Subsequent annealing at 500 K led to near-enantiopure trimerization (ee: 96%) of homochiral 9-EP propellers on the chiral Pd 3 -terminated PdGa surface, in contrast to dimerization without ee on the chiral Pd 1terminated PdGa (111) surface (Figure 4g).The high ee enabled by the trimerization of 9-EP was further explained by the lower energy barrier for the conversion between the R and S monomers and enantiospecific van der Waals interactions with the secondlayer Ga trimer of the substrate. [98]This study highlights the sig-nificant potential of THCs for enantioselective synthesis, emphasizing the crucial role of atomic-level control over catalytically active sites.

Asymmetric Synthesis
To date, a high ee in the asymmetric synthesis of organic molecules using inorganic chiral catalysts has primarily been achieved via Soai reactions employing chiral quartz or sodium chlorate. [99,100]By manipulating external parameters such as temperature, asymmetric reactions such as halogen elimination can be accomplished with THCs. [96]o illustrate this, the thermally triggered asymmetric debromination of prochiral 5-bromo-7-methylbenz(a)anthracene (BMA) on two enantiomers of chiral intermetallic PdGa (111) surfaces is reviewed. [97]This study employs techniques such as STM, temperature-programmed desorption (TPD), and temperatureprogrammed X-ray photoelectron spectroscopy (TP-XPS) under ultrahigh vacuum conditions to investigate molecules deposited on precisely defined chiral PdGa surfaces.Notably, the dehalogenation temperature of the two prochiral BMA enantiomers on the PdGa (111) surfaces reaches an unprecedented increase of 46 K, while no enantioselective debromination was observed on the achiral Au (111) surface (Figure 4h-j).The substantial dependence of the dehalogenation temperature of the BMA enantiomers on the atomic termination of the PdGa (111) surfaces indicates a pronounced influence of the ensemble effect on this reaction step.These findings provide evidence of enantiospecific control, thereby advancing the application of intrinsically chiral crystals in on-surface asymmetric synthesis.

Homochiral Crystal Growth
One of the key challenges in homochiral crystal growth is understanding the fundamental processes governing molecular or atomic self-assembly.Achieving homochirality necessitates precise control over the interactions between chiral building blocks during crystal nucleation and growth.Breaking the symmetry further complicates the search for homochirality.In many cases, a small initial imbalance in the population of the opposite enantiomers can amplify this imbalance during crystal growth.This nonlinear behavior can result in the dominance of a single chiral form, effectively leading to the formation of homochiral crystals; However, the underlying mechanisms governing symmetry breaking and strengthening are complex and often not fully understood.The role of external factors in the homochiral crystal growth adds another layer of complexity.Parameters such as temperature, solvent, and chiral additives can influence the outcome of the crystallization processes.The interplay between thermodynamics and kinetics further complicates this picture because competing crystal structures may form based on the energy profile of the system.Specifically, the introduction of homochiral seeds enable the growth of homochiral crystals using certain methods such as the Bridgeman or Czochralski pulling methods. [52,66]Another approach for controlling chirality during crystal growth involves the application of an external light field or magnetic field via the chemical vapor transport method; However, this method is only applicable to certain materials with low synthesis temperatures.

Increasing Chiral Surface Area
As discussed, intrinsically homochiral surfaces can be used for various enantiospecific chemical and physical processes, including crystallization, electron spin polarization, and heterogeneous asymmetric catalysis, often requiring a large surface area.The challenge lies in achieving a large active surface area while maintaining chiral properties and striking a delicate balance between surface area, catalytic activity, and chiral specificity.One promising method to address this challenge is the homochiral heteroepitaxial growth of intrinsically chiral films such as metals, alloys, and metal oxides. [101]This technique relies on using intrinsically chiral substrates such as Si or quartz crystals.However, a distinct advantage of homochiral epitaxial growth is its flexibility in substrate orientation.Film growth strictly adheres to epitaxial principles, enabling the production of films with precise surface orientations.This feature highlights the fact that once the optimal chiral metal surface orientation for a specific enantioselective process is determined, creating chiral metal films with the desired orientation becomes easy.

Selectivity and EE
Homochiral crystals present significant potential for exploring novel reaction mechanisms and catalytic pathways.They offer the means to precisely regulate reaction pathways, enhance enantioselectivity, and gain insights into the factors influencing these processes.However, realizing highly selective and homochiral crystal surfaces encounters two fundamental challenges.The first challenge involves identifying the crystallographic surface orientation that maximizes the enantiospecificity of the desired property for a given crystal.The second challenge is to expose large chiral surfaces while retaining control over surface orientation and composition.Furthermore, developing techniques and methodologies for investigating catalytic reactions at the atomic and electron scales will open doors to innovative realms in catalysis, including applications such as separating topological chiral fermions for enantiomeric recognition and asymmetric catalysis. [48,55]

Stability
The stability and robustness of electrocatalysts are critical for their use in devices that are typically subjected to fluctuations in power supply, voltage, and temperature.Chiral surface modification with chiral molecules requires careful selection of enantiopure modifier molecules to achieve high thermal and/or electrochemical stability.Inorganic metal films lose their chirality within 30 min under operating conditions, [94] whereas THCs with intrinsically chiral geometries and electronic structures have the advantage of high thermal stability.The chiral TSSs at the surface are the result of band inversion between the bulk conduction and valence bands.In other words, they are robust and protected from modifications as long as the bulk band is preserved, which significantly increases the topological robustness to changes in chemical potential. [102]Although theoretical calculations have shown that the topological character does not change by simulating the modification of different atoms on the topological surface, [56,103] challenges still exist in the experimental observation of TSSs during and/or after catalytic reactions.Therefore, advanced characterization techniques are needed to track the TSSs in the catalytic process.

Chirality Characterization
The current experimental techniques for characterizing and determining the chirality of crystals and thin films have certain limitations.Although EBSD can effectively map and assign chirality, it is limited to the crystal surface.Conversely, SXRD provides a precise distinction between the chirality of crystals but typically requires small sample sizes (≈100 μm).Consequently, there is an urgent need for a new technique to characterize and assign chirality to crystals without breaking the samples.Furthermore, in situ monitoring and the quantification of the chirality-related phenomena on crystal surfaces introduce an additional layer of complexity.Addressing this challenge necessitates interdisciplinary collaboration and the integration of advanced spectroscopic and analytical tools such as the spatial resolution in nano-angle-resolved photoemission spectroscopy, electrochemical STM, and interfacial-sensitive electrochemical surface-enhanced Raman spectroscopy.

Beyond Structural Chirality
In addition to naturally occurring chiral molecules or crystals, it is possible to create artificial atomic or electronic structures with chiral characteristics using various methods.One important approach involves building artificial twisted moiré structures to generate chiral layered materials.][106][107] This advantage makes it an ideal platform for modulating structural and electronic properties.Some quantum properties such as chiral anomalies can even be induced at room temperature.The chirality of electronic structures can be induced by artificially manipulating the chiral electronic states in crystals, such as chiral CDW and chiral spin structures, often in the presence of magnetic or optical field modulation.Thus, in materials lacking structural chirality, the ordered chiral states of electrons can dominate the electron transport process in the reaction and serve as chiral carriers; However, materials with chiral CDW have only been discovered recently, and research on their interaction with chiral molecules is still in its infancy.
Notably, the CISS effect, a significant phenomenon in chiral molecules and crystals, is closely related to the electronic structure and quantum properties of the material (e.g., SOC). [48]Recent studies indicate that in crystals, the spin polarization of electrons is likely controlled by the OAM of the electrons in the material. [108]In chiral crystals, these quantum properties exert a profound influence, potentially dominating the CISS effect.The unique symmetry of chiral materials results in topologically nontrivial electronic energy band structures.Consequently, the CISS effect in crystals is closely linked to the electronic charge and spin properties ensured by the topological electronic energy band structure.Thus, studying the CISS effect in crystals can reveal the close relationship between the chemical reaction processes and the physical mechanisms that determine the electronic properties.
In conclusion, chiral quantum materials serve as a bridge between chemistry and physics, transcending the boundaries of structural asymmetry of materials.Notably, THCs offer valuable insights into the integration of physical mechanisms and chemical processes in catalysis.This connection opens up a host of exciting opportunities for linking solid-state topology with chiral catalysis.

Figure 1 .
Figure 1.Chiral objects in chemistry and physics, including (clockwise order) chiral molecules and crystals, chiral catalysis, chiral charge transfer in chiral structures, chiral phonon (magnon), chiral topological surface states, and chiral charge density wave.The central figure depicts methods to regulate and detect chiral objects, including (from left to right) circularly polarized light, temperature, electric field, magnetic field, and pH.

Figure 2 .
Figure 2. Chiral objects and characterization.a,d) Structures of chiral enantiomer-A and enantiomer-B of Rh(DiPAMP).b,c) Schematic of circular dichroism (CD) spectra for enantiomers with opposite chiralities.CD is an efficient and common method to identify the chirality of chiral molecules.Insets depict the CD experiment using left-handed circularly polarized (LHCP) light (red) and right-handed circularly polarized (RHCP) light (blue).e,h) Laue backscattering diffraction patterns on the (111) surface of enantiomer-A and enantiomer-B of the PdGa single crystals, respectively.f,g) Electron backscattering diffraction (EBSD) patterns of enantiomer-A and enantiomer-B of the PdGa single crystals, respectively.The left-and right halves exhibit the observed and simulated patterns, respectively.i,l) Single-crystal X-ray diffraction (SXRD) patterns of enantiomer-A and enantiomer-B of the EuIr 2 P 2 single crystals observed in the [H,K,0] plane.j) and k) EBSD mapping images of enantiomer-A and enantiomer-B of EuIr 2 P 2 , which illustrate the homochiral nature of the as-grown crystals.The top-right corners show the photographs of the measured crystals.

Figure 3 .
Figure 3. TCHs for energy conversion.a) Schematic of the band inversion mechanism and topologically nontrivial energy window in the nonchiral topological semimetals and chiral B20 compounds.b) HER volcano plot of PtAl, PtGa, RhSi, PdGa, and related metal catalysts.[56]c) Calculated spin polarization around the Fermi level on PdGa A and PdGa B. d) E 1/2 and J k of TH PdGa, Pt/C, and AC PdGa at 0.85 V vs. RHE.e) Schematic of the effect of the chiral crystal structure-induced spin polarization on the enhancement of the ORR activity.[64]

Figure 4 .
Figure 4. Asymmetric catalysis on chiral crystals.Enantioselective oxidation of DOPA on the surfaces of a) PdGa-A and b) PdGa-B crystals.The calculated orbital textures of c) PdGa-A and d) PdGa-B are projected on the orbital polarization (Lz) component.When the SOC effects are considered, Lz exhibits opposite signs at +ky and -ky, and the OAM polarization depends on the chirality of PdGa.[55] e) Molecular structure of prochiral 9-ethynylphenanthrene (9-EP) appears in two distinguishable surface enantiomers, R and S, when restricted to a planar configuration.f) Gaussian-Laplace filtered nc-AFM images of R and S enantiomers.g) Schematic of temperature-controlled near-enantiopure trimerization of an initial racemic mixture of 9-EP molecules occurring on the intrinsically chiral intermetallic PdGa (111) surface.[96]Enantioselectivity of BMA debromination.Br-C intensity for the h) Au(111), i) PdGa: A Pd 3 , and j) PdGa: A Pd 1 surfaces.The contribution of each BMA surface enantiomer, with the enantiomeric form as determined from STM, is shown in a different color.The temperatures at which half of each surface enantiomer is debrominated are specified in the legends.[97]