Engineering noncentrosymmetry in 2D atomic crystals via chemical vapor deposition

Abstract

In contrast to extensively studied centrosymmetric 2D materials, noncentrosymmetric 2D atomic crystals (2DACs) exhibit unique properties—such as nonlinear optical responses, ferroelectricity, and piezoelectricity—making them promising for next-generation optoelectronics and quantum devices. Despite their potential, the controlled synthesis and scalable fabrication of these materials remain challenging, limiting further exploration of their physics and applications. This Feature Article highlights our group's recent advances in engineering noncentrosymmetry in 2DACs via chemical vapor deposition (CVD). We discuss three key strategies: (1) thinning of intrinsically noncentrosymmetric bulk crystals (e.g., nonlayered materials), (2) precise manipulation of van der Waals (vdW) stacking sequences to break inversion symmetry in 2DACs, and (3) alternative routes including self-intercalation, heterostructure assembly, and etching. By correlating synthesis protocols with emergent properties, we demonstrate how CVD enables tailored asymmetry at the atomic scale. Finally, we provide a forward-looking perspective on unresolved challenges, such as achieving phase purity and large-area homogeneity, and propose future research directions for integrating noncentrosymmetric 2DACs into functional devices. This review aims to serve as a roadmap for the controlled synthesis and property exploration of noncentrosymmetric 2DACs.

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Yongshuai Wang

Yongshuai Wang is currently a Postdoctoral Researcher at the State Key Laboratory of Advanced Materials for Intelligent Sensing, Department of Chemistry, Tianjin University. He received his PhD (2023) and MS (2020) from the Institute of Chemistry, Chinese Academy of Sciences (ICCAS). His research focuses on the controllable synthesis and optoelectronic properties of two-dimensional organic/inorganic van der Waals materials.

Qing Zhang

Qing Zhang received her PhD degree from the National University of Singapore in 2023. Earlier, she received her MS degree from the institute of Chemistry, Chinese Academy of Sciences in 2019 after she received her Bachelor's degree from Xiamen University in 2016. Her research focuses on the controllable preparation and optoelectronic devices of two-dimensional organic–inorganic van der Waals heterojunctions.

Lin Li

Lin Li has been an Associate Professor at Tianjin Normal University. Before that, she conducted postdoctoral studies at the University of Electronic Science and Technology of China. She received her PhD from the Institute of Chemistry, Chinese Academy of Sciences in 2016. Her research interests mainly focus on the controlled synthesis of 2D materials, and their further properties and biological applications.

Fan Wu

Fan Wu has been a professor at Tianjin University since 2024. Earlier, Fan received his PhD from PLA University of Science and Technology in 2017. After one year of postdoctoral experience at Duke University (America), Fan is employed as an associate professor in Mechanical Engineering at Nanjing University of Science and Technology since 2019. His research is mainly focus on inorganic–organic hybrids and electromagnetic properties.

Dechao Geng

Dechao Geng has been a Professor at Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Science, Tianjin University since 2019. Earlier, he had had postdoctoral experience at the National University of Singapore and Singapore University of Technology and Design. He received his PhD from the Institute of Chemistry, Chinese Academy of Sciences in 2015. His research interests mainly focus on the chemical vapor deposition synthesis of 2D materials and their further properties and applications.

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Introduction

Two-dimensional atomic crystals (2DACs), including graphene, transition metal dichalcogenides (TMDs), hexagonal boron nitride (h-BN), black phosphorus, and bismuth oxide, exhibit exceptional optical, magnetic, electrical, and spin properties owing to quantum confinement effects at the atomic scale.¹ The electronic behaviour of 2DACs spans semimetallic, semiconducting, and insulating regimes, and their ultrathin profiles—for example, monolayer graphene with a thickness of merely ∼0.3 nm—surpass the physical scaling limits of conventional silicon-based materials, offering promising pathways toward sub-1 nm transistor technologies.^2,3 Furthermore, the stacking of different 2DACs facilitates heterostructure engineering,⁴ enabling the integration of multiple functionalities within a single device and unlocking unprecedented opportunities for the miniaturization and integration of optoelectronic semiconductor systems.

Beyond dimensionality control, the intrinsic crystal structure and symmetry—particularly the presence or absence of inversion symmetry—also play a decisive role in dictating the fundamental physical properties of 2DACs.⁵ Based on inversion symmetry, 2DACs can be classified into centrosymmetric and noncentrosymmetric crystals (Fig. 1a and b).⁶ These two types exhibit pronounced differences in their band structures, optical responses, and charge transport behaviours. Centrosymmetric 2DACs, such as monolayer graphene (Fig. 1a) and h-BN, remain invariant under spatial inversion (r → −r). Their high structural symmetry endows them with broadband optical absorption and high carrier mobility, making them suitable for applications in broadband photodetectors and ultrafast optoelectronic devices. In contrast, noncentrosymmetric 2DACs—such as monolayer MoS₂ (Fig. 1b) and WSe₂—lack spatial inversion symmetry, giving rise to distinct properties such as strong second-order nonlinear optical responses (e.g., second harmonic generation, SHG), valleytronic phenomena, and anisotropic photoresponse.^7,8 These characteristics make noncentrosymmetric 2DACs uniquely advantageous for applications in polarization control, nonlinear optics, and ferroelectric, and quantum devices.⁹ By effectively engineering symmetry breaking, noncentrosymmetric 2DACs are poised to drive the development of next-generation semiconductor technologies toward greater efficiency and intelligence.

Fig. 1 Schematic illustration of the (a) centrosymmetric atomic configuration of graphene, (b) noncentrosymmetric atomic configuration of monolayer MoS₂. (c) Three distinct synthesis strategies for achieving noncentrosymmetric 2DACs.

Despite their attractive physical properties and theoretical prevalence, noncentrosymmetric 2DACs have remained considerably less explored than centrosymmetric 2DACs.¹⁰ This research gap is particularly striking given that, from a crystallographic standpoint, noncentrosymmetric crystals are theoretically more abundant. According to crystallographic theory, only 11 of the 32 crystal point groups possess a centre of inversion, categorizing them as centrosymmetric; the remaining 21 are noncentrosymmetric, as summarized in Table 1. Thus, from a symmetry classification perspective, noncentrosymmetric crystals are theoretically more abundant. However, achieving controllable synthesis of noncentrosymmetric 2DACs at the atomic scale remains highly challenging within current mainstream chemical vapor deposition (CVD) methods. Tailoring atomic configurations and achieving large-area, high-quality growth of noncentrosymmetric 2DACs are still significant hurdles. This difficulty primarily stems from the fact that commonly used growth substrates are typically centrosymmetric.¹¹ During the growth of noncentrosymmetric 2DACs, antiparallel domains inevitably form because their formation energies are equivalent on centrosymmetric substrates. Consequently, in contrast to the relatively facile synthesis of centrosymmetric 2DACs like graphene, growing noncentrosymmetric 2DACs continues to be a formidable challenge. Overcoming these obstacles requires a comprehensive understanding of the growth mechanisms, precise control over experimental parameters, and the development of novel synthetic strategies. Our research group is actively exploring innovative approaches, aiming to balance thermodynamic and kinetic factors to realize the controlled CVD growth of noncentrosymmetric 2DACs.

Table 1 Classification of the 32 crystallographic point groups into centrosymmetric (with inversion centre) and noncentrosymmetric (without inversion centre) categories

Crystal system	Centrosymmetric point groups	Noncentrosymmetric point groups
Triclinic	1̄	1
Monoclinic	2/m	2, m
Orthorhombic	mmm	222, mm2
Tetragonal	4/m, 4/mmm	4, 4̄, 422, 4mm, 4̄2m
Hexagonal	6/m, 6/mmm	6, 6̄, 622, 6mm, 6̄m
Trigonal	3̄, 3̄m	3, 32, 3m
Cubic	m3̄, m3̄m	23, 432, 4̄3m

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In this Feature Article, we summarize our recent advances in the controlled synthesis of noncentrosymmetric 2DACs via CVD, with particular emphasis on symmetry engineering. Specifically, we highlight three key approaches: (1) direct thinning of noncentrosymmetric bulk crystals into 2D layers; (2) symmetry manipulation through controlled stacking of vdW 2DACs; and (3) alternative pathways including self-intercalation, heterostructure formation, and selective etching. These approaches offer versatile pathways for tailoring inversion asymmetry and unlocking emerging functionalities. Fig. 1c provides an integrated summary of our methodology. Taken together, our efforts not only deepen the mechanistic understanding of symmetry control in 2DAC growth, but also pave the way for the integration of noncentrosymmetric 2DACs into next-generation optoelectronic and semiconductor devices. Looking ahead, we highlight critical challenges such as the precise control of phase purity and the scalable synthesis of uniform large-area noncentrosymmetric 2DACs, and outline future directions for their seamless integration into functional device applications. This work aims to serve as a roadmap for the controlled synthesis and property exploration of noncentrosymmetric 2DACs.

Characterization techniques for noncentrosymmetric 2D atomic crystals

Noncentrosymmetric 2D atomic crystals exhibit unique physical properties such as piezoelectricity, ferroelectricity, second-harmonic generation (SHG), and chiral optical responses. The characterization of noncentrosymmetry is essential for understanding their symmetry-dependent functionalities in applications ranging from nonlinear optics to quantum materials. Since centrosymmetric and noncentrosymmetric phases can have similar average structures, specialized techniques are required to distinguish them. These methods can be broadly categorized into diffraction-based, microscopy-based, and optical spectroscopy based approaches. Below, we discuss key experimental techniques and their specific capabilities in probing noncentrosymmetry.

Diffraction-based techniques

X-ray diffraction (XRD). Identifies crystal structures based on scattering patterns. In centrosymmetric crystals, diffraction intensities follow Friedel's law, but this symmetry breaks in noncentrosymmetric crystals due to anomalous scattering, requiring complementary methods like resonant XRD, SHG, or transmission electron microscopy (TEM) for confirmation.

Convergent beam electron diffraction (CBED). Sensitive to atomic displacements breaking symmetry, CBED provides atomic-scale resolution and can directly be used to visualize noncentrosymmetry at defects or domain walls. It is superior to XRD and TEM in symmetry analysis due to its combination of real-space imaging and reciprocal-space analysis.

Microscopy-based techniques

Scanning transmission electron microscopy (STEM). Allows atomic-scale imaging of symmetry-breaking displacements and provides chemical specificity through electron energy-loss spectroscopy (EELS)/energy-dispersive X-ray spectroscopy (EDS). It is ideal for nanoscale systems where bulk-averaging techniques fail, offering sub-Ångström resolution, polarity mapping, and correlative analysis of structural, chemical, and symmetry data.

Piezoresponse force microscopy (PFM). Critical for materials exhibiting piezoelectricity or ferroelectricity, PFM maps the electromechanical response with high spatial resolution, observing domain dynamics and polarization reversal. Its ability to link topographical and electromechanical properties distinguishes it from bulk techniques like XRD or SHG.

Optical spectroscopy techniques

Second harmonic generation (SHG). This probes broken inversion symmetry through nonlinear light–matter interactions. SHG microscopy offers non-invasive, label-free imaging with sub-micron resolution, making it suitable for both real-time monitoring and structural analysis.

Raman spectroscopy. Sensitive to symmetry-forbidden vibrational modes in noncentrosymmetric materials, Raman spectroscopy provides structural and chemical insights with non-destructive, sub-micron spatial resolution.

Circular dichroism (CD) and optical rotation. These techniques measure differential interactions with circularly polarized light, detecting asymmetry in chiral systems.

Sum frequency generation (SFG) spectroscopy. This is surface-sensitive and ideal for probing symmetry-breaking at interfaces or monolayers in 2D materials. SFG offers high resolution, chemical identification, and operando compatibility, making it valuable for investigating edge states and interfacial polarization.

Noncentrosymmetry engineering

The deliberate design and manipulation of noncentrosymmetry in 2D atomic crystals have emerged as a powerful paradigm for unlocking unconventional electronic, optical, and quantum properties. CVD, as a scalable and tuneable synthesis method,¹² offers unique opportunities to precisely manipulate symmetry-breaking effects in 2D atomic crystals. In recent years, our group has made significant advancements in systematically engineering the symmetry of 2D atomic crystals through CVD, which can be primarily classified into three main strategies: (i) intrinsic noncentrosymmetric 2D crystals, where controlled thinning techniques enable the realization of atomically thin layers with inherent polarity or chirality; (ii) noncentrosymmetric stacking of 2D layers, achieved through thermal gradients, interlayer symmetry control, heterostructuring, or twist-angle modulation to artificially break inversion symmetry; and (iii) centrosymmetry breaking in 2D atomic crystals, induced via doping, intercalation, or selective etching to disrupt native symmetric configurations. Each approach offers distinct routes to tailor symmetry-dependent functionalities—such as piezoelectricity, valley polarization, or nonlinear optical responses—while addressing fundamental challenges in scalability, stability, and interfacial control. The following sections delve into our group's recent breakthroughs in CVD-based symmetry engineering, while systematically contrasting these advances with seminal works from other groups. By bridging critical knowledge gaps between synthesis control and symmetry–property relationships, it is expected to provide a fresh insight into the symmetry breaking of 2D atomic crystals.

Thinning of intrinsically noncentrosymmetric bulk crystals

The fabrication of 2D derivatives from nonlayered, intrinsically noncentrosymmetric bulk crystals poses distinct synthetic challenges that fundamentally differ from conventional vdW material exfoliation, primarily due to their three-dimensional covalent/ionic network structures characterized by omnidirectional strong bonding (e.g., Si–O tetrahedra in quartz or Zn–S sp³ bonds in ZnS). The absence of natural cleavage planes renders mechanical exfoliation ineffective, while even advanced techniques like ion intercalation frequently fail to achieve layer separation without inducing phase degradation, owing to the substantial energy barriers inherent in these materials. Furthermore, conventional CVD synthesis often results in nonuniform, island-like growth morphologies with stochastic defect formation (e.g., anti-site vacancies in GaN), as the anisotropic growth kinetics of noncentrosymmetric units compete with substrate interactions, ultimately limiting the production of continuous, thickness-controlled monolayers. These combined factors underscore the significant hurdles in realizing atomically thin versions of such materials while preserving their structural integrity and noncentrosymmetric properties.

To solve the problems, our group has demonstrated various strategies during CVD, such as substrate engineering and surface passivation, to obtain large-area 2D nonlayered atomic crystals with unprecedented thickness control, ranging from a few-nanometers to sub-nanometer dimensions, while maintaining excellent crystallinity and intrinsic noncentrosymmetric properties.

Transition metal carbides (TMCs) such as molybdenum carbide (Mo₂C) and tungsten carbide (WC) are a unique class of materials that combine exceptional mechanical hardness, metallic conductivity, and catalytic activity, making them indispensable for applications ranging from electrocatalysts, mainly for hydrogen evolution (HER) and CO₂ reduction reactions, to next-generation electronics.¹³ However, realizing their ultrathin 2D counterparts, which could unlock novel quantum phenomena and enhanced catalytic performance, faces additional obstacles including thickness nonuniformity and environmental instability, as these ultrathin carbides are highly susceptible to surface oxidation and structural degradation.

Building upon the pioneering work of Xu et al. who first synthesized large-area (>100 μm) 2D α-Mo₂C crystals (Fig. 2a and b) via liquid Mo–Cu alloy-catalyzed CVD in 2015,¹⁴ revealing thickness-dependent superconducting transitions characteristic of 2D systems (Fig. 2c and d), our group has also developed advanced CVD strategies to overcome these fundamental limitations. We have achieved unprecedented control over crystal morphology and thickness while maintaining excellent crystallinity and intrinsic noncentrosymmetric properties. It is worth mentioning that liquid metals possess unique properties that make them particularly valuable for synthesizing 2D ultrathin atomic crystals, with their exceptional fluidity playing a pivotal role in enabling precise thickness control and large-area uniformity. For decades, liquid metal catalysis has been extensively investigated for 2D material synthesis,^15–18 and has proven equally transformative for fabricating ultrathin nonlayered materials.¹⁹ Specifically, our liquid Cu-catalyzed CVD technique enables precise modulation of catalyst layer thickness, yielding ultrathin Mo₂C crystals with tuneable size.²⁰ Furthermore, we extended this methodology to create novel heterostructures, including the tailored growth of Mo₂C/graphene²¹ and WC/graphene heterostructures.²²

Fig. 2 Noncentrosymmetry engineering in 2DACs through thinning the nonlayered crystals. (a) and (b) The microscopic images of ultrathin Mo₂C. (c) Perpendicular magnetic field strength-dependent superconducting curves of the ultrathin Mo₂C. (d) Magnetic field-dependent superconducting curve of the ultrathin Mo₂C. Reproduced with permission.¹⁴ Copyright 2015, Springer Nature. (e) The atomic structure of WC crystals. (f) Wavelength-dependent SHG responses of WC crystals. (g) Illumination intensity-dependent SHG responses of WC crystals. (h) SHG intensity as a function of laser power with linear fit. (i) Polarization-dependent SHG intensity reveals WC crystal anisotropy. (j) SHG mapping result of the produced ultrathin WC crystal. Reproduced with permission.²² Copyright 2024, Wiley-VCH.

In terms of the preparation of WC/graphene, we selected a liquid Cu–Zn alloy as the growth substrate and realized a selective growth of WC/graphene heterostructures or ultrathin WC crystals through tuning the concentration of Zn in the alloy. To be specific, the existence of Zn would suppress the growth of graphene, thus WC/graphene heterostructures occur when the concentration of Zn in the liquid Cu–Zn alloy is relatively low (3.16–12.67%). In contrast, >25.33% Zn concentration would enable the fabrication of solely WC. Fig. 2e shows the atomic structure of 2D WC atomic crystal. Noted that SHG microscopy directly confirmed the preserved noncentrosymmetric character in ultrathin (<3 nm) WC domains (Fig. 2f and j), posing a critical validation of their structural integrity and potential for nonlinear optical applications.

In addition to TMCs, transition metal oxides (TMOs) represent another important class of nonlayered materials with strong three-dimensional bonding networks (e.g., ionic/covalent or mixed-valence interactions).²³ Their unique electronic structures and surface chemistries enable extraordinary functionalities, including catalysis, electronics, spintronics, optoelectronics, energy storage, and quantum materials. However, unlike vdW materials, these oxides—such as TiO₂, ZnO, and WO₃—typically exhibit omnidirectional chemical bonds, making their exfoliation or synthesis in ultrathin forms particularly challenging.

In order to prepare ultrathin TMOs, researchers have taken a lot of efforts on the strategies such as flux assisted growth,^24,25 surface oxide (also known as liquid metal printing),²⁶ additive-assisted growth,²⁷ and others, and have gained significant achievements on the successful growth of 2D ultrathin SiO₂,¹⁸ MoO₂,²⁵ Ga₂O₃,²⁸ In₂O₃,²⁹ SnO₂,³⁰ Bi-doped/Cu-doped/ZnO-doped Ga₂O₃,^31,32etc.

Building upon these achievements, our group reports the controlled synthesis of ultrathin 2D Ga₂O₃ single crystals via liquid Ga-catalyzed CVD method.³³ The dynamic liquid Ga surface enables: (i) large-area growth of hexagonal α-Ga₂O₃ through oxygen-regulated reactions, and (ii) thickness control via oxygen dosage modulation. Phase engineering to β-Ga₂O₃ is further achieved by temperature tuning.

In another work, our group has developed an innovative surface-assisted passivation growth strategy to overcome the long-standing challenge in synthesizing ultrathin TMOs (Fig. 3a).³⁴ Through precise Se-mediated surface passivation, we have successfully achieved the growth of remarkably thin β-Bi₂O₃ crystals with unprecedented thickness control down to 0.77 nm and large lateral dimensions up to 163 μm, as shown in Fig. 3b, representing a major breakthrough in 2D nonlayered material synthesis. The key to our success lies in the engineered bonding between Se atoms and unsaturated Bi atoms on the β-Bi₂O₃ surface, which not only passivates the surface but also dramatically suppresses vertical growth. More importantly, the intrinsic noncentrosymmetric nature of these ultrathin β-Bi₂O₃ crystals has been unambiguously confirmed by strong SHG response, as shown in Fig. 3c. Moreover, the noncentrosymmetric nature of thus-produced β-Bi₂O₃ crystals enables polarization-sensitive photodetection with the merits of record-high photoresponsivity of 71.91 A W⁻¹, outstanding detectivity reaching 6.09 × 10¹³ Jones, and high-resolution UV imaging performance at 365 nm (Fig. 3d). The schematic diagram of the polarization-sensitive photodetection based on β-Bi₂O₃ is shown in Fig. 3e and f exhibits the typical polarization-dependent photocurrent.

Fig. 3 Noncentrosymmetry engineering in 2DACs through thinning the nonlayered materials. (a) The atomic structure of β-Bi₂O₃ and the schematic diagram of the surface passivation strategy. (b) A comparison of the thickness of the product produced respectively from Route 1 and Route 2 (surface passivation). (c) Wavelength-dependent SHG responses of the ultrathin β-Bi₂O₃. (d) The polarization imaging ability of the ultrathin β-Bi₂O₃. (e) The device configuration of the polarization-sensitive photodetector based on the produced ultrathin β-Bi₂O₃. (f) Typical polarization-sensitive I–t curve of the device, demonstrating a high anisotropy. Reproduced with permission.³⁴ Copyright 2025, Wiley-VCH.

Building upon this work, researchers recently demonstrated a vapor–liquid–solid–solid (VLSS) growth strategy to achieve sub-1 nm nonlayered 2D β-Bi₂O₃ crystals via topological transformation of BiOCl precursors.³⁵ The resulting p-type transistors exhibit superior hole mobility (136.6 cm² V⁻¹ s⁻¹) and on/off ratio (1.2 × 10⁸), enabled by strong Bi 6s²6p³–O 2p⁴ hybridization at the valence band maximum – a distinct mechanism from our earlier surface-passivation approach. While both methods achieve atomic thickness control, this work shifts focus from noncentrosymmetric photodetection to high-performance p-channel electronics, collectively expanding the 2D oxide toolkit for complementary applications.

Noncentrosymmetric stacking of 2D layers

Noncentrosymmetric stacking refers to the artificial assembly or self-assembly of 2D layers in a manner that breaks inversion symmetry, creating heterostructures with novel properties such as piezoelectricity, valley polarization, or nonlinear optical responses. Unlike naturally occurring centrosymmetric stacking (e.g., AB stacking in bilayer graphene), this approach requires precise control over interlayer rotation, lattice mismatch, or compositional asymmetry to stabilize noncentrosymmetric configurations.

The practical realization of such designed stacks faces fundamental challenges rooted in both thermodynamics and kinetics. From an energetic perspective, nature favours centrosymmetric configurations (e.g., AB-stacked graphene or AA′-stacked MoS₂) due to their optimal interlayer registry and minimized vdW interaction energy, typically making noncentrosymmetric arrangements metastable by several meV atom⁻¹ – a thermodynamic hurdle that often leads to spontaneous relaxation during growth or device operation. On the synthesis front, achieving and maintaining precise noncentrosymmetric alignment demands extraordinary control at sub-Ångström precision (e.g., <0.1° twist angle accuracy or <5% lattice mismatch tolerance), while simultaneously addressing interfacial challenges like charge transfer-induced reconstruction, thermal expansion mismatch, and chemical incompatibility between dissimilar layers. These combined factors currently limit the reproducible fabrication of high-quality, large-area noncentrosymmetric stacks.

To solve the problems, our group reports a substrate-guided CVD strategy to precisely engineer crystal symmetry in SnSe₂ superlattices,³⁶ overcoming the inherent challenge of symmetry control in 2D materials caused by interlayer gliding. By leveraging charge transfer from mica substrates, we successfully stabilized unconventional AB′-stacked SnSe₂ with alternating mirror and glide symmetries, as well as higher-order phases (6R, 12R, 18R, and 18C) that exhibit stacking-dependent nonlinear optical responses as predicted by first-principles calculations. Furthermore, PFM characterization results also demonstrated good ferroelectric properties of the AB′-stacked SnSe₂ crystals, directly pointing out its intrinsic noncentrosymmetric characteristic. The captured atomic structures of these phases and corresponding FFT are shown in Fig. 4a and b.

Fig. 4 Engineering noncentrosymmetry in 2DACs through noncentrosymmetric stackings. (a) Side views of the atomic configurations of 6R, 18R, 12R, and 18C phases. (b) Experimental and simulated fast Fourier transform results of different phases. Reproduced with permission.³⁶ Copyright 2024, Springer Nature. (c) The schematic illustration of the TGACVD method for producing multilayer MoS₂ domains. (d) Layer-number- and stacking-dependent polarized Raman spectrums. Reproduced with permission.³⁷ Copyright 2024, American Chemical Society.

In another work, we have achieved a successful preparation of noncentrosymmetric-stacked MoS₂ multilayers through a customized thermal gradient assembly CVD (TGACVD) method.³⁷ The schematic illustration of TGACVD method is shown in Fig. 4c. The theoretical simulation results demonstrate that the formation energy differences between various stacking configurations with identical layer numbers are substantially smaller than those between structures with different layer counts. Therefore, our strategy enables a precise construction of diverse noncentrosymmetric stacking arrangements such as AA-stacked bilayers, AAB/ABB-stacked trilayers, and AAAA/AAAB/ABBA-stacked quadralayers. We observe distinct layer-number- and stacking-dependent oscillatory SHG responses in multilayer MoS₂, consistent with prior reports of interlayer-interference-mediated SHG modulation.^38–40 Besides, these stackings also show angle-dependent polarization Raman intensities in both parallel and cross modes, as shown in Fig. 4d. This work directly provides a route for tuning the degree of noncentrosymmetry by engineering stacked structures. On this basis, we have also fully investigated the sliding ferroelectric properties of AAA/ABB/AAB/ABA-stacked trilayer MoS₂, achieving both record-high endurance more than 10¹¹ and an interesting ferroelectricity order as AAA > AAB > ABB, with their polarization strengths up to 0.11 μC cm⁻².⁷⁴

A recent work reported by Liu et al. mentions a homoepitaxial growth of rhombohedral-stacked MoS₂, providing a feasible approach toward the large-scale synthesis of noncentrosymmetric materials.⁴¹ The authors identify Mo-substituted sulfur vacancies as key defects promoting rhombohedral-stacked nucleation and achieve wafer-scale (2-inch) growth. They further fabricate ferroelectric semiconductor field-effect transistors with rhombohedral-stacked-MoS₂ channels, showcasing non-volatile memory functionality.

In addition, twist angle control has emerged as a powerful strategy for creating noncentrosymmetric stacked structures in 2D atomic crystals.⁴² While early studies primarily relied on mechanical exfoliation followed by artificial stacking to achieve twisted configurations,⁴³ recent advances have demonstrated the direct synthesis of twist-controlled materials through CVD approaches.^44–49 These emerging CVD techniques enable more scalable and precise fabrication of twisted heterostructures with well-defined angular alignment, opening new possibilities for systematic investigation and practical applications of twist-angle-dependent phenomena in noncentrosymmetric systems. Correspondingly, our group has successfully achieved precise twist angle control in graphene/Mo₂C vertical heterostructures, enabled by the unique fluidity of liquid copper catalysts during high-temperature growth.⁵⁰

Beyond twist engineering, the formation of commensurate heterostructures itself can break inversion symmetry, as demonstrated in a recent work on epitaxial MoS₂/WS₂ bilayers raise by Lau's group.⁵¹ Through scalable one-step CVD, they achieved untwisted heterostructures exhibiting unexpected out-of-plane ferroelectricity and piezoelectricity (approximately sixfold stronger than monolayer In₂Se₃), enabled by interlayer charge transfer and symmetry breaking without requiring Moiré patterns.

Our group has extensively explored such symmetry-breaking heterostructures, including MoSe₂/MOFs heterostructure,⁵² graphene/hBN lateral heterostructure,^53–55 graphene/SiO₂ heterostructure,¹⁸ MXene/DPA heterostructure,⁵⁶ MXene/MoSe₂ heterostructure,⁵⁷ and others,^58–60 establishing forming heterostructures as a universal platform for designing noncentrosymmetric 2D systems through both twisted and commensurate stackings.

Centrosymmetry breaking in 2D atomic crystals

In addition to the above two strategies, the deliberate breaking of centrosymmetry in 2D atomic crystals has also emerged as a powerful strategy to unlock novel quantum phenomena and functionalities, such as piezoelectricity, nonlinear optical responses, and valley polarization. Unlike intrinsic noncentrosymmetric materials, where asymmetry is inherent to their crystal structure, centrosymmetric 2D materials require external interventions to disrupt their inversion symmetry. Traditional approaches, including strain engineering and electric field gating, often face limitations in scalability and stability.

Our group demonstrated robust centrosymmetry breaking through self-intercalation and controlled etching strategies during CVD process, which enabled precise modification of atomic arrangements while preserving material integrity. The self-intercalation approach introduces foreign atoms into the vdW gaps, locally distorting the crystal lattice and inducing long-range symmetry lowering. Meanwhile, selective etching creates patterned vacancies that break global inversion symmetry.⁶¹ These methods offer scalable and tuneable routes to engineering symmetry-dependent properties, surpassing the constraints of conventional techniques.

For example, we have demonstrated a temperature-driven CVD approach to precisely synthesize self-intercalated Ta_1+xS₂ (x = 10–58%) with controllable H/T phases, where nonperiodic Ta intercalation at vdW gaps breaks the intrinsic centrosymmetry of Ta_1+xS₂.⁶²Fig. 5a shows the growth mechanism of the self-intercalated Ta_1+xS₂. Atomic-resolution STEM confirms octahedral-site Ta occupancy, which disrupts both the crystal symmetry and Fermi surface. Crucially, this symmetry breaking activates a robust thickness-independent nonlinear optical (NLO) response in otherwise centrosymmetric T-phase Ta_1+xS₂, as verified by consistent SHG (Fig. 5b). Our work establishes self-intercalation as a general strategy to engineer noncentrosymmetry and NLO properties in 2D materials.

Fig. 5 Engineering noncentrosymmetry in 2DACs through breaking the centrosymmetry in 2DACs. (a) The scheme of the growth mechanism for the self-intercalation. (b) Wavelength-dependent SHG responses of the self-intercalated TaS₂. Reproduced with permission.⁶² Copyright 2024, American Chemical Society. (c) Zoom-out SEM image of the etched MoSe₂ domains. (d) Zoom-in SEM image of an individual etched MoSe₂ domain. (e) The Raman spectrum of the etched domain, demonstrating the characteristic peaks of MoSe₂. (f) Raman mapping result of the domain. Reproduced with permission.⁶⁴ Copyright 2022, American Chemical Society. (g) SHG mapping results of the kirigami bilayer MoS₂. (h) Wavelength-dependent SHG responses of the kirigami MoS₂ domain. (i) Log–log plot showing linear fitting of SHG intensity versus laser power. (j) Angle-resolved SHG measurements demonstrate kirigami MoS₂'s anisotropic response. Reproduced with permission.⁶⁵ Copyright 2025, Royal Society of Chemistry.

The nonperiodic Ta intercalation in our work represents a general nonstoichiometric strategy to disrupt centrosymmetry, complementing recent advances in engineering piezo/ferroelectricity through native metal intercalation in 2D chalcogenides. As demonstrated in related studies, such intrinsic nonstoichiometry (e.g., intercalated Mn_1+xSe₂ or Fe_1+xTe₂) induces vdW layer sliding and metal-atom displacement, creating unconventional piezo/ferroelectricity in otherwise centrosymmetric systems.⁶³ These intercalation-driven effects enable functional devices like 2D nanogenerators and ferroelectric memristors, collectively establishing native metal intercalation as a universal route to break inversion symmetry and activate emergent properties in nonstoichiometric 2D materials.

In terms of controllable etching, we have developed an oxygen-assisted anisotropic CVD etching method to create patterned MoSe₂ structures with controlled edge geometries.⁶⁴Fig. 5c–f show the SEM images of etched MoSe₂ flakes, the Raman spectrum and Raman mapping results of a MoSe₂ flake, demonstrating the uniform feature of the product. Atomic-scale characterization reveals preferential formation of zigzag-terminated edges, as confirmed by density functional theory calculations showing their energetic favourability. Importantly, this edge-selective etching locally breaks centrosymmetry in the otherwise symmetric MoSe₂ flakes, introducing noncentrosymmetric configurations at patterned interfaces. The etched structures exhibit enhanced optoelectronic performance, demonstrated by ambipolar photoresponse in MoSe₂/P3HT heterojunction transistors. This approach provides a top-down route to engineering local symmetry breaking in 2D materials through controlled anisotropic etching.

In another work, we developed a precision etching strategy to convert specific bilayer MoS₂ regions into monolayer structures through selective layer removal, thereby creating designed kirigami patterns with controlled Mo- and S-zigzag edge configurations.⁶⁵ This local thickness reduction from bilayer to monolayer effectively breaks the original centrosymmetry of AB-stacked bilayer MoS₂, as unambiguously confirmed by the emergence of strong SHG signals from the etched monolayer regions, as demonstrated in Fig. 5g–j. The resulting heterostructures – combining intact bilayer and etched monolayer domains – exhibit enhanced nonlinear optical responses, demonstrating how spatially controlled etching can serve as an effective approach to engineer noncentrosymmetry and activate nonlinear optical functionalities in 2D materials.

Our findings not only establish new pathways for centrosymmetry manipulation but also provide insights into the design of functional 2D materials for optoelectronics, quantum devices, and energy harvesting applications.

Challenges and perspectives

The pursuit of noncentrosymmetric 2D atomic crystals has evolved along three primary strategies in our group: (i) thinning intrinsically noncentrosymmetric bulk crystals, (ii) precise manipulation of vdW stackings, and (iii) alternative centrosymmetry breaking routes including self-intercalation and etching. While these approaches have significantly expanded the library of symmetry-broken 2D systems, critical challenges remain in their development and implementation.

For thinning of nonlayered materials, the primary obstacle lies in overcoming the strong isotropic bonding that renders conventional exfoliation ineffective. Although our advanced techniques like liquid–metal-assisted thinning (e.g., for Mo₂C) have shown promise, achieving atomic-level precision in thickness control, the scalability of these methods is challenging, as most demonstrations are limited to micrometer-scale flakes.

In the realm of vdW stacking manipulation, while twist engineering has emerged as a powerful tool (e.g., graphene/Mo₂C heterostructures), several limitations persist. First, the thermodynamic instability of twisted configurations often leads to relaxation at room temperature, necessitating new stabilization strategies such as interfacial strain engineering or defect pinning. Second, the precise control of stacking angles below 1° remains technically demanding, requiring advanced in situ monitoring techniques. Recent advances in epitaxial confinement and laser-assisted stacking may provide solutions, but their generalizability across material systems needs further exploration. For heterostructure assembly, interface contamination and lattice mismatch can compromise the designed symmetry breaking. However, the interlayer coupling mechanisms in artificially stacked systems are not fully understood, particularly for mixed-dimensional or multi-component heterostructures.^66,67

The third category—alternative symmetry-breaking routes—faces distinct challenges. Self-intercalation (e.g., Ta_1+xS₂) often suffers from inhomogeneous distribution of intercalants, while etching approaches (e.g., MoS₂ kirigami) struggle with edge-defect proliferation. Moreover, the development of universal characterization protocols is crucial to quantify the degree of symmetry breaking across different material systems and fabrication methods. Despite these challenges, recent advances, such as coherently confined single-metal-atom chains in 2D atomic crystals,⁶⁸ nano-folding edge engineering,⁶⁹ and high-entropy alloys,^70–73 bring fresh insights into the centrosymmetry breaking.

From a fundamental perspective, several open questions demand attention. The critical thickness limit for maintaining noncentrosymmetric properties in thinned crystals is poorly understood for many material systems. In stacked heterostructures, the role of Moiré potentials in modifying symmetry-governed properties (e.g., nonlinear optical response) requires systematic investigation. For chemically modified systems (intercalated or etched), the trade-off between defect density and symmetry-breaking efficiency needs rigorous assessment.

Looking ahead, the field is poised to make transformative advances through convergent methodologies. The integration of machine learning with high-throughput synthesis could accelerate the discovery of optimal symmetry-breaking parameters. In situ microscopy techniques may unravel atomic-scale dynamics during thinning, stacking, or intercalation processes. For applications, the co-design of materials and devices will be essential—for instance, developing etching protocols tailored for photonic circuits or stacking sequences optimized for quantum emitters.

Ultimately, the goal is to establish design rules that connect specific symmetry-breaking methods (thinning, stacking, or chemical modification) with target functionalities (piezoelectricity, valleytronics, or nonlinear optics). As the field matures, the focus should shift from proof-of-concept demonstrations to reproducible fabrication and device integration, enabling practical applications in quantum information, energy conversion, and ultracompact optoelectronics. The three-pronged strategy outlined here—thinning, stacking, and alternative routes—provides a comprehensive framework to advance this exciting field toward both fundamental discoveries and technological breakthroughs.

Author contributions

Yongshuai Wang: writing – original draft; Qing Zhang: writing – review & editing, funding acquisition; Lin Li: writing – review & editing; Fan Wu: writing – review & editing; Dechao Geng: writing – review & editing, supervision, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this study's findings are available from the corresponding author upon reasonable request.

Acknowledgements

This work was supported by the National Key R&D Program (2023YFB3609001 and 2021YFA0717900), the Natural Science Foundation of China (grants 52472168), the Natural Science Foundation of Tianjin (grants 22JCJQJC00080), the Haihe Laboratory of Sustainable Chemical Transformations, the Beijing National Laboratory for Molecular Sciences (BNLMS202309), the Hebei Natural Science Foundation (E2024208084), the Chinese Postdoctoral Science Foundation (2024M760101 and GZB20230004), and the Fundamental Research Funds for the Central Universities.

Notes and references

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