How Substitutional Point Defects in Two-Dimensional WS2 Induce Charge Localization, Spin-Orbit Splitting, and Strain

Can Iron Be Embedded between Zigzag Mo Chains of the 1T'-MoTe2 Monolayer To Induce Magnetism?: A First-Principles Study

Molybdenum dichalcogenides are remarkable two-dimensional materials with promising applications in electronics, optoelectronics, and energy storage. Modifying a synthesized MoTe2 layer by embedding extra metal atoms into lattice voids induces novel electronic and magnetic properties, enabling quantum phenomena. Our density functional theory (DFT) calculations explore post-growth Fe deposition in 2H- and 1T'-MoTe2 phases, evaluating adatom, interstitial (Int), and substitutional (Sub) configurations. Formation energy results indicate that Fe favors Int sites under Te-limited conditions in both phases, with higher affinity and enhanced magnetism in 1T'. Simulated scanning tunneling microscopy images align with Fe-doping experiments in isoelectronic 1T'-WTe2, showing inconclusive Fe locations. DFT results highlight for the first time the ability to enhance MoTe2 functionality by embedding impurity metals in zigzag chains, enabling applications in quantum technologies and catalysis.

Doped Mott Phase and Charge Correlations in Monolayer 1T-NbSe_{2}

The doped Hubbard model is one of the paradigmatic platforms to engineer exotic quantum many-body states, including charge-ordered states, strange metals, and unconventional superconductors. While undoped and doped correlated phases have been experimentally realized in a variety of twisted van der Waals materials, experiments in monolayer materials, and in particular 1T transition metal dichalcogenides, have solely reached the conventional insulating undoped regime. Correlated phases in monolayer two-dimensional materials have much higher associated energy scales than their twisted counterparts, making doped correlated monolayers an attractive platform for high temperature correlated quantum matter. Here, we demonstrate the realization of a doped Mott phase in a van der Waals dichalcogenide 1T-NbSe_{2} monolayer. The system is electron doped due to electron transfer from a monolayer van der Waals substrate via proximity, leading to a correlated triangular lattice with both half-filled and fully filled sites. We analyze the distribution of the half-filled and filled sites and show the arrangement is unlikely to be controlled by disorder alone, and we show that the presence of competing nonlocal many-body correlations would account for the charge correlations found experimentally. Our results establish 1T-NbSe_{2} as a potential monolayer platform to explore correlated doped Mott physics in a frustrated lattice.

Vibrational and Magnetic States of Point Defects in Bilayer MoSe2

Defects in two-dimensional materials profoundly impact the physicochemical properties of the systems, whose characterization is highly desirable at the atomic scale. Here, using spectroscopic imaging scanning tunneling microscopy, we elucidate the vibrational and magnetic states of MoSe antisite and VMo vacancy with different charge states embedded in ultrathin MoSe2 bilayers supported on graphene substrate. Stringent vibronic states with multimode coupling are resolved on the defects. The spectral intensities are tunable with the electron tunneling rates and well-reproduced by theoretical modeling. Moreover, first-principles calculations suggest that the defects host a local magnetic moment of 2 μB in their neutral state, which is directly confirmed by our spin-flip inelastic electron tunneling spectroscopy. Our study deepens the understanding of defect properties and paves the way of defect-engineering material functionalities and spin-catalytic applications.

Low-Defect-Density Monolayer MoS2 Wafer by Oxygen-Assisted Growth-Repair Strategy

Atomic chalcogen vacancy is the most commonly observed defect category in two dimensional (2D) transition-metal dichalcogenides, which can be detrimental to the intrinsic properties and device performance. Here a low-defect density, high-uniform, wafer-scale single crystal epitaxial technology by in situ oxygen-incorporated "growth-repair" strategy is reported. For the first time, the oxygen-repairing efficiency on MoS2 monolayers at atomic scale is quantitatively evaluated. The sulfur defect density is greatly reduced from (2.71 ± 0.65) × 1013 down to (4.28 ± 0.27) × 1012 cm-2, which is one order of magnitude lower than reported as-grown MoS2. Such prominent defect deduction is owing to the kinetically more favorable configuration of oxygen substitution and an increase in sulfur vacancy formation energy around oxygen-incorporated sites by the first-principle calculations. Furthermore, the sulfur vacancies induced donor defect states is largely eliminated confirmed by quenched defect-related emission. The devices exhibit improved carrier mobility by more than three times up to 65.2 cm2 V-1 s-1 and lower Schottky barrier height reduced by half (less than 20 meV), originating from the suppressed Fermi-level pinning effect from disorder-induced gap state. The work provides an effective route toward engineering the intrinsic defect density and electronic states through modulating synthesis kinetics of 2D materials.

Influence of Substrate-Induced Charge Doping on Defect-Related Excitonic Emission in Monolayer MoS2

Many applications of transition metal dichalcogenides (TMDs) involve transfer to functional substrates that can strongly impact their optical and electronic properties. We investigate the impact that substrate interactions have on free carrier densities and defect-related excitonic (XD) emission from MoS2 monolayers grown by metal-organic chemical vapor deposition. C-plane sapphire substrates mimic common hydroxyl-terminated substrates. We demonstrate that transferring MoS2 monolayers to pristine c-plane sapphire dramatically increases the free electron density within MoS2 layers, quenches XD emission, and accelerates exciton recombination at the optical band edge. In contrast, transferring MoS2 monolayers onto inert hexagonal boron nitride (h-BN) has no measurable influence on these properties. Our findings demonstrate the promise of utilizing substrate engineering to control charge doping interactions and to quench broad XD background emission features that can influence the purity of single photon emitters in TMDs being developed for quantum photonic applications.

Recent Excellent Optoelectronic Applications Based on Two-Dimensional WS2 Nanomaterials: A Review

Tungsten disulfide (WS2) is a promising material with excellent electrical, magnetic, optical, and mechanical properties. It is regarded as a key candidate for the development of optoelectronic devices due to its high carrier mobility, high absorption coefficient, large exciton binding energy, polarized light emission, high surface-to-volume ratio, and tunable band gap. These properties contribute to its excellent photoluminescence and high anisotropy. These characteristics render WS2 an advantageous material for applications in light-emitting devices, memristors, and numerous other devices. This article primarily reviews the most recent advancements in the field of optoelectronic devices based on two-dimensional (2D) nano-WS2. A variety of advanced devices have been considered, including light-emitting diodes (LEDs), sensors, field-effect transistors (FETs), photodetectors, field emission devices, and non-volatile memory. This review provides a guide for improving the application of 2D WS2 through improved methods, such as introducing defects and doping processes. Moreover, it is of great significance for the development of transition-metal oxides in optoelectronic applications.

Atomically Resolved Defect-Engineering Scattering Potential in 2D Semiconductors

Engineering atomic-scale defects has become an important strategy for the future application of transition metal dichalcogenide (TMD) materials in next-generation electronic technologies. Thus, providing an atomic understanding of the electron-defect interactions and supporting defect engineering development to improve carrier transport is crucial to future TMDs technologies. In this work, we utilize low-temperature scanning tunneling microscopy/spectroscopy (LT-STM/S) to elicit how distinct types of defects bring forth scattering potential engineering based on intervalley quantum quasiparticle interference (QPI) in TMDs. Furthermore, quantifying the energy-dependent phase variation of the QPI standing wave reveals the detailed electron-defect interaction between the substitution-induced scattering potential and the carrier transport mechanism. By exploring the intrinsic electronic behavior of atomic-level defects to further understand how defects affect carrier transport in low-dimensional semiconductors, we offer potential technological applications that may contribute to the future expansion of TMDs.

Conversion of Layered WS2 Crystals into Mixed-Domain Electrochemical Catalysts by Plasma-Assisted Surface Reconstruction

Electrocatalytic water splitting is crucial to generate clean hydrogen fuel, but implementation at an industrial scale remains limited due to dependence on expensive platinum (Pt)-based electrocatalysts. Here, an all-dry process to transform electrochemically inert bulk WS2 into a multidomain electrochemical catalyst that enables scalable and cost-effective implementation of the hydrogen evolution reaction (HER) in water electrolysis is reported. Direct dry transfer of WS2 flakes to a gold thin film deposited on a silicon substrate provides a general platform to produce the working electrodes for HER with tunable charge transfer resistance. By treating the mechanically exfoliated WS2 with sequential Ar-O2 plasma, mixed domains of WS2, WO3, and tungsten oxysulfide form on the surfaces of the flakes, which gives rise to a superior HER with much greater long-term stability and steady-state activity compared to Pt. Using density functional theory, ultraefficient atomic sites formed on the constituent nanodomains are identified, and the quantification of atomic-scale reactivities and resulting HER activities fully support the experimental observations.

Determination and investigation of defect domains in multi-shape monolayer tungsten disulfide

Single-layer tungsten disulfide (WS2) is among the most widely investigated two-dimensional materials. Synthesizing it over large areas would enable the exploitation of its appealing optical and electronic properties in industrial applications. However, defects of different nature, concentration and distribution profoundly affect the optical as well as the electronic properties of this crystal. Controlling the defect density distribution can be an effective way to tailor the local dielectric environment and therefore the electronic properties of the system. In this work we investigate the defects in single-layer WS2, grown in different shapes by liquid phase chemical vapor deposition, where the concentration of certain defect species can be controlled by the growth conditions. The properties of the material are surveyed by means of optical spectroscopy, photoelectron spectroscopy and Kelvin probe force microscopy. We determine the chemical nature of the defects and study their influence on the optical and electronic properties of WS2. This work contributes to the understanding of the microscopic nature of the intrinsic defects in WS2, helping the development of defect-based technologies which rely on the control and engineering of defects in dielectric 2D crystals.

A substitutional quantum defect in WS2 discovered by high-throughput computational screening and fabricated by site-selective STM manipulation

Point defects in two-dimensional materials are of key interest for quantum information science. However, the parameter space of possible defects is immense, making the identification of high-performance quantum defects very challenging. Here, we perform high-throughput (HT) first-principles computational screening to search for promising quantum defects within WS2, which present localized levels in the band gap that can lead to bright optical transitions in the visible or telecom regime. Our computed database spans more than 700 charged defects formed through substitution on the tungsten or sulfur site. We found that sulfur substitutions enable the most promising quantum defects. We computationally identify the neutral cobalt substitution to sulfur (CoS 0 ) and fabricate it with scanning tunneling microscopy (STM). The CoS 0 electronic structure measured by STM agrees with first principles and showcases an attractive quantum defect. Our work shows how HT computational screening and nanoscale synthesis routes can be combined to design promising quantum defects.

Charge state-dependent symmetry breaking of atomic defects in transition metal dichalcogenides

The functionality of atomic quantum emitters is intrinsically linked to their host lattice coordination. Structural distortions that spontaneously break the lattice symmetry strongly impact their optical emission properties and spin-photon interface. Here we report on the direct imaging of charge state-dependent symmetry breaking of two prototypical atomic quantum emitters in mono- and bilayer MoS2 by scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM). By changing the built-in substrate chemical potential, different charge states of sulfur vacancies (VacS) and substitutional rhenium dopants (ReMo) can be stabilized. VacS - 1 as well as ReMo 0 and ReMo - 1 exhibit local lattice distortions and symmetry-broken defect orbitals attributed to a Jahn-Teller effect (JTE) and pseudo-JTE, respectively. By mapping the electronic and geometric structure of single point defects, we disentangle the effects of spatial averaging, charge multistability, configurational dynamics, and external perturbations that often mask the presence of local symmetry breaking.

Mechanism of Fermi Level Pinning for Metal Contacts on Molybdenum Dichalcogenide

The high contact resistance of transition metal dichalcogenide (TMD)-based devices is receiving considerable attention due to its limitation on electronic performance. The mechanism of Fermi level (EF) pinning, which causes the high contact resistance, is not thoroughly understood to date. In this study, the metal (Ni and Ag)/Mo-TMD surfaces and interfaces are characterized by X-ray photoelectron spectroscopy, atomic force microscopy, scanning tunneling microscopy and spectroscopy, and density functional theory systematically. Ni and Ag form covalent and van der Waals (vdW) interfaces on Mo-TMDs, respectively. Imperfections are detected on Mo-TMDs, which lead to electronic and spatial variations. Gap states appear after the adsorption of single and two metal atoms on Mo-TMDs. The combination of the interface reaction type (covalent or vdW), the imperfection variability of the TMD materials, and the gap states induced by contact metals with different weights are concluded to be the origins of EF pinning.

Magnetic doping in transition metal dichalcogenides

Transition metal dichalcogenides (TMDCs) are materials with unique electronic properties due to their two-dimensional nature. Recently, there is a large and growing interest in synthesizing ferromagnetic TMDCs for applications in electronic devices and spintronics. Apart from intrinsically magnetic examples, modification via either intrinsic defects or external dopants may induce ferromagnetism in non-magnetic TMDCs and, hence expand the application of these materials. Here, we review recent experimental work on intrinsically non-magnetic TMDCs that present ferromagnetism as a consequence of either intrinsic defects or doping via self-flux approach, ion implantation or e-beam evaporation. The experimental work discussed here is organized by modification/doping mechanism. We also review current work on density functional theory calculations that predict ferromagnetism in doped systems, which also serve as preliminary data for the choice of new doped TMDCs to be explored experimentally. Implementing a controlled process to induce magnetism in two-dimensional materials is key for technological development and this topical review discusses the fundamental procedures while presenting promising materials to be investigated in order to achieve this goal.

Spontaneous exciton dissociation in transition metal dichalcogenide monolayers

Since the seminal work on MoS2, photoexcitation in atomically thin transition metal dichalcogenides (TMDCs) has been assumed to result in excitons, with binding energies order of magnitude larger than thermal energy at room temperature. Here, we reexamine this foundational assumption and show that photoexcitation of TMDC monolayers can result in a substantial population of free charges. Performing ultrafast terahertz spectroscopy on large-area, single-crystal TMDC monolayers, we find that up to ~10% of excitons spontaneously dissociate into charge carriers with lifetimes exceeding 0.2 ns. Scanning tunneling microscopy reveals that photocarrier generation is intimately related to mid-gap defects, likely via trap-mediated Auger scattering. Only in state-of-the-art quality monolayers, with mid-gap trap densities as low as 109 cm-2, does intrinsic exciton physics start to dominate the terahertz response. Our findings reveal the necessity of knowing the defect density in understanding photophysics of TMDCs.

Engineering the Electrical and Optical Properties of WS2 Monolayers via Defect Control

Two-dimensional (2D) materials as tungsten disulphide (WS2 ) are rising as the ideal platform for the next generation of nanoscale devices due to the excellent electric-transport and optical properties. However, the presence of defects in the as grown samples represents one of the main limiting factors for commercial applications. At the same time, WS2 properties are frequently tailored by introducing impurities at specific sites. Aim of this review paper is to present a complete description and discussion of the effects of both intentional and unintentional defects in WS2 , by an in depth analysis of the recent experimental and theoretical investigations reported in the literature. First, the most frequent intrinsic defects in WS2 are presented and their effects in the readily synthetized material are discussed. Possible solutions to remove and heal unintentional defects are also analyzed. Following, different doping schemes are reported, including the traditional substitution approach and innovative techniques based on the surface charge transfer with adsorbed atoms or molecules. The plethora of WS2 monolayer modifications presented in this review and the systematic analysis of the corresponding optical and electronic properties, represent strategic degrees of freedom the researchers may exploit to tailor WS2 optical and electronic properties for specific device applications.

Atomically precise vacancy-assembled quantum antidots

Patterning antidots, which are regions of potential hills that repel electrons, into well-defined antidot lattices creates fascinating artificial periodic structures, leading to anomalous transport properties and exotic quantum phenomena in two-dimensional systems. Although nanolithography has brought conventional antidots from the semiclassical regime to the quantum regime, achieving precise control over the size of each antidot and its spatial period at the atomic scale has remained challenging. However, attaining such control opens the door to a new paradigm, enabling the creation of quantum antidots with discrete quantum hole states, which, in turn, offer a fertile platform to explore novel quantum phenomena and hot electron dynamics in previously inaccessible regimes. Here we report an atomically precise bottom-up fabrication of a series of atomic-scale quantum antidots through a thermal-induced assembly of a chalcogenide single vacancy in PtTe2. Such quantum antidots consist of highly ordered single-vacancy lattices, spaced by a single Te atom, reaching the ultimate downscaling limit of antidot lattices. Increasing the number of single vacancies in quantum antidots strengthens the cumulative repulsive potential and consequently enhances the collective interference of multiple-pocket scattered quasiparticles inside quantum antidots, creating multilevel quantum hole states with a tunable gap from the telecom to far-infrared regime. Moreover, precisely engineered quantum hole states of quantum antidots are geometry protected and thus survive on oxygen substitutional doping. Therefore, single-vacancy-assembled quantum antidots exhibit unprecedented robustness and property tunability, positioning them as highly promising candidates for advancing quantum information and photocatalysis technologies.

Probing charge traps at the 2D semiconductor/dielectric interface

The family of 2-dimensional (2D) semiconductors is a subject of intensive scientific research due to their potential in next-generation electronics. While offering many unique properties like atomic thickness and chemically inert surfaces, the integration of 2D semiconductors with conventional dielectric materials is challenging. The charge traps at the semiconductor/dielectric interface are among many issues to be addressed before these materials can be of industrial relevance. Conventional electrical characterization methods remain inadequate to quantify the traps at the 2D semiconductor/dielectric interface since the estimations of the density of interface traps, Dit, by different techniques may yield more than an order-of-magnitude discrepancy, even when extracted from the same device. Therefore, the challenge to quantify Dit at the 2D semiconductor/dielectric interface is about finding an accurate and reliable measurement method. In this review, we discuss characterization techniques which have been used to study the 2D semiconductor/dielectric interface. Specifically, we discuss the methods based on small-signal AC measurements, subthreshold slope measurements and low-frequency noise measurements. While these approaches were developed for silicon-based technology, 2D semiconductor devices possess a set of unique challenges requiring a careful re-evaluation when using these characterization techniques. We examine the conventional methods based on their efficacy and accuracy in differentiating various types of trap states and provide guidance to find an appropriate method for charge trap analysis and estimation of Dit at 2D semiconductor/dielectric interfaces.

Origins of Fermi Level Pinning for Ni and Ag Metal Contacts on Tungsten Dichalcogenides

Tungsten transition metal dichalcogenides (W-TMDs) are intriguing due to their properties and potential for application in next-generation electronic devices. However, strong Fermi level (EF) pinning manifests at the metal/W-TMD interfaces, which could tremendously restrain the carrier injection into the channel. In this work, we illustrate the origins of EF pinning for Ni and Ag contacts on W-TMDs by considering interface chemistry, band alignment, impurities, and imperfections of W-TMDs, contact metal adsorption mechanism, and the resultant electronic structure. We conclude that the origins of EF pinning at a covalent contact metal/W-TMD interface, such as Ni/W-TMDs, can be attributed to defects, impurities, and interface reaction products. In contrast, for a van der Waals contact metal/TMD system such as Ag/W-TMDs, the primary factor responsible for EF pinning is the electronic modification of the TMDs resulting from the defects and impurities with the minor impact of metal-induced gap states. The potential strategies for carefully engineering the metal deposition approach are also discussed. This work unveils the origins of EF pinning at metal/TMD interfaces experimentally and theoretically and provides guidance on further enhancing and improving the device performance.

Dilute Rhenium Doping and its Impact on Defects in MoS2

Substitutionally doped 2D transition metal dichalcogenides are primed for next-generation device applications such as field effect transistors (FET), sensors, and optoelectronic circuits. In this work, we demonstrate substitutional rhenium (Re) doping of MoS2 monolayers with controllable concentrations down to 500 ppm by metal-organic chemical vapor deposition (MOCVD). Surprisingly, we discover that even trace amounts of Re lead to a reduction in sulfur site defect density by 5-10×. Ab initio models indicate the origin of the reduction is an increase in the free-energy of sulfur-vacancy formation at the MoS2 growth-front when Re is introduced. Defect photoluminescence (PL) commonly seen in undoped MOCVD MoS2 is suppressed by 6× at 0.05 atomic percent (at. %) Re and completely quenched with 1 at. % Re. Furthermore, we find that Re-MoS2 transistors exhibit a 2× increase in drain current and carrier mobility compared to undoped MoS2, indicating that sulfur vacancy reduction improves carrier transport in the Re-MoS2. This work provides important insights on how dopants affect 2D semiconductor growth dynamics, which can lead to improved crystal quality and device performance.

Single Atomic Defect Conductivity for Selective Dilute Impurity Imaging in 2D Semiconductors

Precisely controlled impurity doping is of fundamental significance in modern semiconductor technologies. Desired physical properties are often achieved at impurity concentrations well below parts per million level. For emergent two-dimensional semiconductors, development of reliable doping strategies is hindered by the inherent difficulty in identifying and quantifying impurities in such a dilute limit where the absolute number of atoms to be detected is insufficient for common analytical techniques. Here we report rapid high-contrast imaging of dilute single atomic impurities by using conductive atomic force microscopy. We show that the local conductivity is enhanced by more than 100-fold by a single impurity atom due to resonance-assisted tunneling. Unlike the closely related scanning tunneling microscopy, the local conductivity sensitively depends on the impurity energy level, allowing minority defects to be selectively imaged. We further demonstrate subsurface impurity detection with single monolayer depth resolution in multilayer materials.

Defect Engineering of Nanomaterials for Catalysis

Defect chemistry is a branch of materials science that deals with the study of the properties and behavior of defects in crystalline solids [...].

Structure modulation of two-dimensional transition metal chalcogenides: recent advances in methodology, mechanism and applications

Together with the development of two-dimensional (2D) materials, transition metal dichalcogenides (TMDs) have become one of the most popular series of model materials for fundamental sciences and practical applications. Due to the ever-growing requirements of customization and multi-function, dozens of modulated structures have been introduced in TMDs. In this review, we present a systematic and comprehensive overview of the structure modulation of TMDs, including point, linear and out-of-plane structures, following and updating the conventional classification for silicon and related bulk semiconductors. In particular, we focus on the structural characteristics of modulated TMD structures and analyse the corresponding root causes. We also summarize the recent progress in modulating methods, mechanisms, properties and applications based on modulated TMD structures. Finally, we demonstrate challenges and prospects in the structure modulation of TMDs and forecast potential directions about what and how breakthroughs can be achieved.

Deep learning based atomic defect detection framework for two-dimensional materials

Defects to popular two-dimensional (2D) transition metal dichalcogenides (TMDs) seriously lower the efficiency of field-effect transistor (FET) and depress the development of 2D materials. These atomic defects are mainly identified and researched by scanning tunneling microscope (STM) because it can provide precise measurement without harming the samples. The long analysis time of STM for locating defects in images has been solved by combining feature detection with convolutional neural networks (CNN). However, the low signal-noise ratio, insufficient data, and a large amount of TMDs members make the automatic defect detection system hard to be applied. In this study, we propose a deep learning-based atomic defect detection framework (DL-ADD) to efficiently detect atomic defects in molybdenum disulfide (MoS₂) and generalize the model for defect detection in other TMD materials. We design DL-ADD with data augmentation, color preprocessing, noise filtering, and a detection model to improve detection quality. The DL-ADD provides precise detection in MoS₂ (F2-scores is 0.86 on average) and good generality to WS₂ (F2-scores is 0.89 on average).

Spatial Control of Substitutional Dopants in Hexagonal Monolayer WS2 : The Effect of Edge Termination

The ability to control the density and spatial distribution of substitutional dopants in semiconductors is crucial for achieving desired physicochemical properties. Substitutional doping with adjustable doping levels has been previously demonstrated in 2D transition metal dichalcogenides (TMDs); however, the spatial control of dopant distribution remains an open field. In this work, edge termination is demonstrated as an important characteristic of 2D TMD monocrystals that affects the distribution of substitutional dopants. Particularly, in chemical vapor deposition (CVD)-grown monolayer WS₂ , it is found that a higher density of transition metal dopants is always incorporated in sulfur-terminated domains when compared to tungsten-terminated domains. Two representative examples demonstrate this spatial distribution control, including hexagonal iron- and vanadium-doped WS₂ monolayers. Density functional theory (DFT) calculations are further performed, indicating that the edge-dependent dopant distribution is due to a strong binding of tungsten atoms at tungsten-zigzag edges, resulting in the formation of open sites at sulfur-zigzag edges that enable preferential dopant incorporation. Based on these results, it is envisioned that edge termination in crystalline TMD monolayers can be utilized as a novel and effective knob for engineering the spatial distribution of substitutional dopants, leading to in-plane hetero-/multi-junctions that display fascinating electronic, optoelectronic, and magnetic properties.

Tip-enhanced nanoscopy of two-dimensional transition metal dichalcogenides: progress and perspectives

The optoelectronic properties of two-dimensional (2D) transition metal dichalcogenide (TMD) thin layers prepared by exfoliation or chemical vapour deposition are strongly modulated by defects at the nanoscale. The mediated electronic and optical properties are expected to be spatially localised in a nanoscale width neighbouring the defects. Characterising such localised properties requires an analytical tool with nanoscale spatial resolution and high optical sensitivity. In recent years, tip-enhanced nanoscopy, represented by tip-enhanced Raman spectroscopy (TERS) and tip-enhanced photoluminescence (TEPL), has emerged as a powerful tool to characterise the localised phonon and exciton behaviours of 2D TMDs and heterojunctions (HJs) at the nanoscale. Herein, we first summarise the recent progress of TERS and TEPL in the characterisation of several typical defects in TMDs, such as edges, wrinkles, grain boundaries and other defects generated in transfer and growth processes. Then the local strain and its dynamic control of phonon and exciton behaviours characterised by TERS and TEPL will be reviewed. The recent progress in characterising TMD HJs using TERS and TEPL will be subsequently summarised. Finally, the progress of TERS and TEPL combined with optoelectronic sensitive electronic scanning probe microscopy (SPM) in the applications of TMDs will be reviewed.

Low-defect-density WS2 by hydroxide vapor phase deposition

Two-dimensional (2D) semiconducting monolayers such as transition metal dichalcogenides (TMDs) are promising channel materials to extend Moore's Law in advanced electronics. Synthetic TMD layers from chemical vapor deposition (CVD) are scalable for fabrication but notorious for their high defect densities. Therefore, innovative endeavors on growth reaction to enhance their quality are urgently needed. Here, we report that the hydroxide W species, an extremely pure vapor phase metal precursor form, is very efficient for sulfurization, leading to about one order of magnitude lower defect density compared to those from conventional CVD methods. The field-effect transistor (FET) devices based on the proposed growth reach a peak electron mobility ~200 cm2/Vs (~800 cm2/Vs) at room temperature (15 K), comparable to those from exfoliated flakes. The FET device with a channel length of 100 nm displays a high on-state current of ~400 µA/µm, encouraging the industrialization of 2D materials.

Strain engineering of electronic properties and anomalous valley hall conductivity of transition metal dichalcogenide nanoribbons

Strain engineering is a powerful technique for tuning electronic properties and valley degree of freedom in honeycomb structure of two-dimensional crystals. Carriers in + k and − k (opposite Berry curvature) in transition metal dichalcogenide (TMD) with broken inversion symmetry act as effective magnetic fields, where this polarized valleys are suitable for encoding information. In this work, we study the strained TMD nanoribbons by Slater-Koster tight-binding model, which acquires electronic bands in whole Brillouin zone. From this, we derive a generic profile of strain effect on the electronic band structure of TMD nanoribbons, which shows indirect band gap, and also exhibits a phase transition from semiconductor to metallic by applying uniaxial X-tensile and Y-arc type of strain. Midgap states in strained TMD nanoribbons are determined by calculation of localized density of electron states. Moreover, our findings of anomalous valley Hall conductivity reveal that the creation of pseudogauge fields using strained TMD nanoribbons affect the Dirac electrons, which generate the new quantized Landau level. Furthermore, we demonstrate in strained TMD nanoribbons that strain field can effectively tune both the magnitude and sign of valley Hall conductivity. Our work elucidates the valley Hall transport in strained TMDs due to pseudo-electric and pseudo-magnetic filed will be applicable as information carries for future electronics and valleytronics.

Directly Visualizing Photoinduced Renormalized Momentum-Forbidden Electronic Quantum States in an Atomically Thin Semiconductor

Resolving the momentum degree of freedom of photoexcited charge carriers and exploring the excited-state physics in the hexagonal Brillouin zone of atomically thin semiconductors have recently attracted great interest for optoelectronic technologies. We demonstrate a combination of light-modulated scanning tunneling microscopy and the quasiparticle interference (QPI) technique to offer a directly accessible approach to reveal and quantify the unexplored momentum-forbidden electronic quantum states in transition metal dichalcogenide (TMD) monolayers. Our QPI results affirm the large spin-splitting energy at the spin-valley-coupled Q valleys in the conduction band (CB) of a tungsten disulfide monolayer. Furthermore, we also quantify the photoexcited carrier density-dependent band renormalization at the Q valleys. Our findings directly highlight the importance of the excited-state distribution at the Q valley in the band renormalization in TMDs and support the critical role of the CB Q valley in engineering the quantum electronic valley degree of freedom in TMD devices.

Laser-ablation assisted strain engineering of gold nanoparticles for selective electrochemical CO2 reduction

Strain engineering can endow versatile functions, such as refining d-band center and inducing lattice mismatch, on catalysts for a specific reaction. To this end, effective strain engineering for introducing strain on the catalyst is highly sought in various catalytic applications. Herein, a facile laser ablation in liquid (LAL) strategy is adopted to synthesize gold nanoparticles (Au NPs) with rich compressive strain (Au-LAL) for electrochemical CO₂ reduction. It is demonstrated that the rich compressive strain can greatly promote the electrochemical CO₂ reduction performance of Au, achieving a CO partial current density of 24.9 mA cm^-2 and a maximum CO faradaic efficiency of 97% at -0.9 V for Au-LAL, while it is only 2.77 mA cm^-2 and 16.2% for regular Au nanoparticles (Au-A). As revealed by the in situ Raman characterization and density functional theory calculations, the presence of compressive strain can induce a unique electronic structure change in Au NPs, significantly up-shifting the d-band center of Au. Such a phenomenon can greatly enhance the adsorption strength of Au NPs toward the key intermediate of CO₂ reduction (i.e., *COOH). More interestingly, we demonstrate that, an important industrial chemical feedstock, syngas, can be obtained by simply mixing Au-LAL with Au-A in a suitable ratio. This work provides a promising method for introducing strain in metal NPs and demonstrates the important role of strain in tuning the performance and selectivity of catalysts.

Interplay between Thermal Stress and Interface Binding on Fracture of WS2 Monolayer with Triangular Voids

The defect engineering of two-dimensional (2D) materials has become a pivotal strategy for tuning the electrical and optical properties of the material. However, the reliable application of these atomically thin materials in practical devices require careful control of structural defects to avoid premature failure. Herein, a systematic investigation is presented to delineate the complex interactions among structural defects, the role of thermal mismatch between WS₂ monolayer and different substrates, and their consequent effect on the fracture behavior of the monolayer. Detailed microscopic and Raman/PL spectroscopic observations enabled a direct correlation between thermal mismatch stress and crack patterns originating from the corner of faceted voids in the WS₂ monolayer. Aberration-corrected STEM-HAADF imaging reveals the tensile strain localization around the faceted void corners. Density functional theory (DFT) simulations on interfacial interaction between the substrate (Silicon and sapphire -Al₂O₃) and monolayer WS₂ revealed a binding energy between WS₂ and Si substrate is 20 times higher than that with a sapphire substrate. This increased interfacial interaction in WS₂ and substrate-aided thermal mismatch stress arising due to difference in thermal expansion coefficient to a maximum extent leading to fracture in monolayer WS₂. Finite element simulations revealed the stress distribution near the void in the WS₂ monolayer, where the maximum stress was concentrated at the void tip.

Electronic Properties and Carrier Dynamics at the Alloy Interfaces of WS2x Se2-2x Spiral Nanosheets

Electronic properties at the interfaces between different-composition domains of 2D-alloys are key for their optical, electronic, and optoelectronic applications. Understanding the interfacial electronic structures and carrier dynamics is essential for designing and fabricating devices that use these alloys. Here, WS_2x Se_2-2x spiral nanosheets are prepared using the physical vapor deposition method, and the nonlinear optical and electronic properties, as well as the carrier dynamics at the interfaces between the WS and WSe domains, are studied. Second-harmonic generation tests demonstrate that these nanosheets exhibit a very strong layer-dependent nonlinear optical effect. Atomic-resolution scanning tunneling microscopy (STM) and spectroscopy (STS) measurements reveal that S and Se atoms are non-uniformly distributed, forming WS domains, WSe domains, and defect-related areas. Atomic STM images and STS maps reveal enhanced local density of states by electron scattering at the WS/WSe interfaces, providing a detailed nanoscale interpretation of the S/Se-ratio-dependent lifetimes observed in pump-probe spectroscopy measurements. This work provides valuable interfacial characterization of 2D-alloy materials, using state-of-the-art methods with high temporal and spatial resolutions. The obtained insights are likely to be useful for prospective applications.

Spin-dependent vibronic response of a carbon radical ion in two-dimensional WS2

Atomic spin centers in 2D materials are a highly anticipated building block for quantum technologies. Here, we demonstrate the creation of an effective spin-1/2 system via the atomically controlled generation of magnetic carbon radical ions (CRIs) in synthetic two-dimensional transition metal dichalcogenides. Hydrogenated carbon impurities located at chalcogen sites introduced by chemical doping are activated with atomic precision by hydrogen depassivation using a scanning probe tip. In its anionic state, the carbon impurity is computed to have a magnetic moment of 1 μ_B resulting from an unpaired electron populating a spin-polarized in-gap orbital. We show that the CRI defect states couple to a small number of local vibrational modes. The vibronic coupling strength critically depends on the spin state and differs for monolayer and bilayer WS₂. The carbon radical ion is a surface-bound atomic defect that can be selectively introduced, features a well-understood vibronic spectrum, and is charge state controlled.

Spin-polarized defects in 2D materials are attracting attention for future quantum technology applications, but their controlled fabrication is still challenging. Here, the authors report the creation and characterization of effective spin 1/2 defects via the atomically-precise generation of magnetic carbon radical ions in 2D WS₂.

Gate-Tunable Magnetism via Resonant Se-Vacancy Levels in WSe2

The confined defects in 2D van der Waals (vdW)-layered semiconductors can be easily tailored using charge doping, strain, or an electric field. Nevertheless, gate-tunable magnetic order via intrinsic defects has been rarely observed to date. Herein, a gate-tunable magnetic order via resonant Se vacancies in WSe₂ is demonstrated. The Se-vacancy states are probed via photocurrent measurements with gating to convert unoccupied states to partially occupied states associated with photo-excited carrier recombination. The magneto-photoresistance hysteresis is modulated by gating, which is consistent with the density functional calculations. The two energy levels associated with Se vacancies split with increasing laser power, owing to the robust Coulomb interaction and strong spin-orbit coupling. The findings offer a new approach for controlling the magnetic properties of defects in optoelectronic and spintronic devices using vdW-layered semiconductors.

Sublattice Dependence and Gate Tunability of Midgap and Resonant States Induced by Native Dopants in Bernal-Stacked Bilayer Graphene

The properties of semiconductors can be crucially impacted by midgap states induced by dopants, which can be native or intentionally incorporated in the crystal lattice. For Bernal-stacked bilayer graphene (BLG), which has a tunable band gap, the existence of midgap states induced by dopants or adatoms has been investigated theoretically and observed indirectly in electron transport experiments. Here, we characterize BLG midgap states in real space, with atomic-scale resolution with scanning tunneling microscopy and spectroscopy. We show that the midgap states in BLG-for which we demonstrate gate tunability-appear when the dopant is hosted on the nondimer sublattice sites. We further evidence the presence of narrow resonances at the onset of the high-energy bands (valence or conduction, depending on the dopant type) when the dopants lie on the dimer sublattice sites. Our results are supported by tight-binding calculations that agree remarkably well with the experimental findings.

Exciton-Photonics: From Fundamental Science to Applications

Semiconductors in all dimensionalities ranging from 0D quantum dots and molecules to 3D bulk crystals support bound electron-hole pair quasiparticles termed excitons. Over the past two decades, the emergence of a variety of low-dimensional semiconductors that support excitons combined with advances in nano-optics and photonics has burgeoned an advanced area of research that focuses on engineering, imaging, and modulating the coupling between excitons and photons, resulting in the formation of hybrid quasiparticles termed exciton-polaritons. This advanced area has the potential to bring about a paradigm shift in quantum optics, as well as classical optoelectronic devices. Here, we present a review on the coupling of light in excitonic semiconductors and previous investigations of the optical properties of these hybrid quasiparticles via both far-field and near-field imaging and spectroscopy techniques. Special emphasis is given to recent advances with critical evaluation of the bottlenecks that plague various materials toward practical device implementations including quantum light sources. Our review highlights a growing need for excitonic material development together with optical engineering and imaging techniques to harness the utility of excitons and their host materials for a variety of applications.

A High-Efficiency Wavelength-Tunable Monolayer LED with Hybrid Continuous-Pulsed Injection

High-efficiency and wavelength-tunable light-emitting diode (LED) devices will play an important role in future advanced optoelectronic systems. Traditional semiconductor LED devices typically have a fixed emission wavelength that is determined by the energy of the emission states. Here, a novel high-efficiency and wavelength-tunable monolayer WS₂ LED device, which operates in the hybrid mode of continuous-pulsed injection, is developed. This hybrid injection enables highly enhanced emission efficiency (>20 times) and effective size of emission area (>5 times) at room temperature. The emission wavelength of the WS₂ monolayer LED device can be tuned over more than 40 nm by driving AC voltages, from exciton emission to trion emission, and further to defect emission. The quantum efficiency of defect electroluminescence (EL) emission is measured to be more than 24.5 times larger than that from free exciton and trion EL emission. The separate carrier injection in the LED also demonstrates advantages in allowing defect species to be visualized and distinguished in real space. Those defects are assigned to be negatively charged defects. The results open a new route to develop high-performance and wavelength-tunable LED devices for future advanced optoelectronic applications.

Flexo-photoelectronic effect in n-type/p-type two-dimensional semiconductors and a deriving light-stimulated artificial synapse

Flexoelectricity and photoelectricity with their coupled effect (the so-called flexo-photoelectronic effect), are of increasing interest in the study of electronics and optoelectronics in van der Waals layered semiconductors. However, the related device design is severely restricted owing to the ambiguous underlying physical nature of flexo-photoelectronic effects originating from the co-manipulation of light and strain-gradients. Here, flexoelectric polarization and the flexo-photoelectronic effect of few-layered semiconductors have been multi-dimensionally investigated from high-resolution microscopic characterization on the nanoscale, physics analysis, and deriving a device design. We found that two back-to-back built-in electric fields form in bent InSe and WSe₂, and greatly modulate the transport behaviors of photogenerated carriers, further facilitating the separation of photogenerated electron-hole pairs and trapping the holes/electrons in InSe or WSe₂ channels, recorded in realtime by a home-made technique of lighting Kelvin probe force microscopy (KPFM). The slow release of trapped carriers contributes to the photoconductance relaxation after illumination. Utilizing the photoconductance relaxation, a light-stimulated artificial synapse based on the flexo-photoelectronic effect of bent InSe has been achieved. Significantly, all the pair-pulse facilitation (PPF) behavior, spike frequency-dependent excitatory post-synaptic current (EPSC) and the transition from short-term memory (STM) to long-term memory (LTM) have been successfully realized in this artificial synapse. This work adds to the investigation of flexo-photoelectronic effects on 2D optoelectronics, and moves towards the development of 2D neuromorphic electronics.

Wafer-Scale Oxygen-Doped MoS2 Monolayer

Monolayer MoS₂ is an emergent 2D semiconductor for next-generation miniaturized and flexible electronics. Although the high-quality monolayer MoS₂ is already available at wafer scale, doping of it uniformly remains an unsolved problem. Such doping is of great importance in view of not only tailoring its properties but also facilitating many potential large-scale applications. In this work, the uniform oxygen doping of 2 in wafer-scale monolayer MoS₂ (MoS_{2- x} O_x ) with tunable doping levels is realized through an in situ chemical vapor deposition process. Interestingly, ultrafast infrared spectroscopy measurements and first-principles calculations reveal a reduction of bandgaps of monolayer MoS_{2- x} O_x with increased oxygen-doping levels. Field-effect transistors and logic devices are also fabricated based on these wafer-scale MoS_{2- x} O_x monolayers, and excellent electronic performances are achieved, exhibiting promise of such doped MoS₂ monolayers.

Steric Hindrance- and Work Function-Promoted High Performance for Electrochemical CO Methanation on Antisite Defects of MoS2 and WS2

CO methanation from electrochemical CO reduction reaction (CORR) is significant for sustainable environment and energy, but electrocatalysts with excellent selectivity and activity are still lacking. Selectivity is sensitive to the structure of active sites, and activity can be tailored by work function. Moreover, intrinsic active sites usually possess relatively high concentration compared to artificial ones. Here, antisite defects Mo_S2 and W_S2 , intrinsic atomic defects of MoS₂ and WS₂ with a transition metal atom substituting a S₂ column, were investigated for CORR by density functional theory calculations. The steric hindrance from the special bowl structure of Mo_S2 and W_S2 ensured good selectivity towards CO methanation. Coordination environment variation of the active sites, the under-coordinated Mo or W atoms, effectively lowered the work function, making Mo_S2 and W_S2 highly active for CO methanation with the required potential of -0.47 and -0.49 V vs. reversible hydrogen electrode, respectively. Moreover, high concentration of active sites and minimal structural deformation during the catalytic process of Mo_S2 and W_S2 enhanced their attraction for future commercial application.

Hybridized Defects in Solid-State Materials as Artificial Molecules

Two-dimensional materials can be crafted with structural precision approaching the atomic scale, enabling quantum defects-by-design. These defects are frequently described as "artificial atoms" and are emerging optically addressable spin qubits. However, interactions and coupling of such artificial atoms with each other, in the presence of the lattice, warrants further investigation. Here we present the formation of "artificial molecules" in solids, introducing a chemical degree of freedom in control of quantum optoelectronic materials. Specifically, in monolayer hexagonal boron nitride as our model system, we observe configuration- and distance-dependent dissociation curves and hybridization of defect orbitals within the bandgap into bonding and antibonding orbitals, with splitting energies ranging from ∼10 meV to nearly 1 eV. We calculate the energetics of cis and trans out-of-plane defect pairs CH_B-CH_B against an in-plane defect pair C_B-C_B and find that in-plane defect pair interacts more strongly than out-of-plane pairs. We demonstrate an application of this chemical degree of freedom by varying the distance between C_B and V_N of C_BV_N and observe changes in the predicted peak absorption wavelength from the visible to the near-infrared spectral band. We envision leveraging this chemical degree of freedom of defect complexes to precisely control and tune defect properties toward engineering robust quantum memories and quantum emitters for quantum information science.

Scalable Substitutional Re-Doping and its Impact on the Optical and Electronic Properties of Tungsten Diselenide

Reliable, controlled doping of 2D transition metal dichalcogenides will enable the realization of next-generation electronic, logic-memory, and magnetic devices based on these materials. However, to date, accurate control over dopant concentration and scalability of the process remains a challenge. Here, a systematic study of scalable in situ doping of fully coalesced 2D WSe₂ films with Re atoms via metal-organic chemical vapor deposition is reported. Dopant concentrations are uniformly distributed over the substrate surface, with precisely controlled concentrations down to <0.001% Re achieved by tuning the precursor partial pressure. Moreover, the impact of doping on morphological, chemical, optical, and electronic properties of WSe₂ is elucidated with detailed experimental and theoretical examinations, confirming that the substitutional doping of Re at the W site leads to n-type behavior of WSe₂ . Transport characteristics of fabricated back-gated field-effect-transistors are directly correlated to the dopant concentration, with degrading device performances for doping concentrations exceeding 1% of Re. The study demonstrates a viable approach to introducing true dopant-level impurities with high precision, which can be scaled up to batch production for applications beyond digital electronics.

In Situ Oxygen Doping of Monolayer MoS2 for Novel Electronics

In 2D semiconductors, doping offers an effective approach to modulate their optical and electronic properties. Here, an in situ doping of oxygen atoms in monolayer molybdenum disulfide (MoS₂ ) is reported during the chemical vapor deposition process. Oxygen concentrations up to 20-25% can be reliable achieved in these doped monolayers, MoS_{2- x} O_x . These oxygen dopants are in a form of substitution of sulfur atoms in the MoS₂ lattice and can reduce the bandgap of intrinsic MoS₂ without introducing in-gap states as confirmed by photoluminescence spectroscopy and scanning tunneling spectroscopy. Field effect transistors made of monolayer MoS_{2- x} O_x show enhanced electrical performances, such as high field-effect mobility (≈100 cm² V^-1 s^-1 ) and inverter gain, ultrahigh devices' on/off ratio (>10⁹ ) and small subthreshold swing value (≈80 mV dec^-1 ). This in situ oxygen doping technique holds great promise on developing advanced electronics based on 2D semiconductors.

Electrically driven photon emission from individual atomic defects in monolayer WS2

Quantum dot-like single-photon sources in transition metal dichalcogenides (TMDs) exhibit appealing quantum optical properties but lack a well-defined atomic structure and are subject to large spectral variability. Here, we demonstrate electrically stimulated photon emission from individual atomic defects in monolayer WS2 and directly correlate the emission with the local atomic and electronic structure. Radiative transitions are locally excited by sequential inelastic electron tunneling from a metallic tip into selected discrete defect states in the WS2 bandgap. Coupling to the optical far field is mediated by tip plasmons, which transduce the excess energy into a single photon. The applied tip-sample voltage determines the transition energy. Atomically resolved emission maps of individual point defects closely resemble electronic defect orbitals, the final states of the optical transitions. Inelastic charge carrier injection into localized defect states of two-dimensional materials provides a powerful platform for electrically driven, broadly tunable, atomic-scale single-photon sources.

Bound Hole States Associated to Individual Vanadium Atoms Incorporated into Monolayer WSe_{2}

Doping a two-dimensional semiconductor with magnetic atoms is a possible route to induce magnetism in the material. We report on the atomic structure and electronic properties of monolayer WSe_{2} intentionally doped with vanadium atoms by means of scanning transmission electron microscopy and scanning tunneling microscopy and spectroscopy. Most of the V atoms incorporate at W sites. These V_{W} dopants are negatively charged, which induces a localized bound state located 140 meV above the valence band maximum. The overlap of the electronic potential of two charged V_{W} dopants generates additional in-gap states. Eventually, the negative charge may suppress the magnetic moment on the V_{W} dopants.

Spatial defects nanoengineering for bipolar conductivity in MoS2

Understanding the atomistic origin of defects in two-dimensional transition metal dichalcogenides, their impact on the electronic properties, and how to control them is critical for future electronics and optoelectronics. Here, we demonstrate the integration of thermochemical scanning probe lithography (tc-SPL) with a flow-through reactive gas cell to achieve nanoscale control of defects in monolayer MoS₂. The tc-SPL produced defects can present either p- or n-type doping on demand, depending on the used gasses, allowing the realization of field effect transistors, and p-n junctions with precise sub-μm spatial control, and a rectification ratio of over 10⁴. Doping and defects formation are elucidated by means of X-Ray photoelectron spectroscopy, scanning transmission electron microscopy, and density functional theory. We find that p-type doping in HCl/H₂O atmosphere is related to the rearrangement of sulfur atoms, and the formation of protruding covalent S-S bonds on the surface. Alternatively, local heating MoS₂ in N₂ produces n-character.

Bipolar conductivity is fundamental for electronic devices based on two-dimensional semiconductors. Here, the authors report on-demand p- and n-doping of monolayer MoS₂ via defects engineering using thermochemical scanning probe lithography, and achieve a p-n junction with rectification ratio over 10⁴.

Atomistic Positioning of Defects in Helium Ion Treated Single-Layer MoS2

Structuring materials with atomic precision is the ultimate goal of nanotechnology and is becoming increasingly relevant as an enabling technology for quantum electronics/spintronics and quantum photonics. Here, we create atomic defects in monolayer MoS₂ by helium ion (He-ion) beam lithography with a spatial fidelity approaching the single-atom limit in all three dimensions. Using low-temperature scanning tunneling microscopy (STM), we confirm the formation of individual point defects in MoS₂ upon He-ion bombardment and show that defects are generated within 9 nm of the incident helium ions. Atom-specific sputtering yields are determined by analyzing the type and occurrence of defects observed in high-resolution STM images and compared with Monte Carlo simulations. Both theory and experiment indicate that the He-ion bombardment predominantly generates sulfur vacancies.

Ultrafast Electron Cooling and Decay in Monolayer WS2 Revealed by Time- and Energy-Resolved Photoemission Electron Microscopy

A comprehensive understanding of the ultrafast electron dynamics in two-dimensional transition metal dichalcogenides (TMDs) is necessary for their applications in optoelectronic devices. In this work, we contribute a study of ultrafast electron cooling and decay dynamics in the supported and suspended monolayer WS₂ by time- and energy-resolved photoemission electron microscopy (PEEM). Electron cooling in the Q valley of the conduction band is clearly resolved in energy and time, on a time scale of 0.3 ps. Electron decay is mainly via a defect trapping process on a time scale of several picoseconds. We observed that the trap states can be produced and increased by laser illumination under an ultrahigh vacuum, and the higher local optical-field intensity led to the faster increase of trap states. The enhanced defect trapping could significantly modify the carrier dynamics and should be paid attention to in photoemission experiments for two-dimensional materials.