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1.
Proc Natl Acad Sci U S A ; 121(28): e2401579121, 2024 Jul 09.
Artigo em Inglês | MEDLINE | ID: mdl-38968123

RESUMO

Iron is an essential element for life owing to its ability to participate in a diverse array of oxidation-reduction reactions. However, misregulation of iron-dependent redox cycling can also produce oxidative stress, contributing to cell growth, proliferation, and death pathways underlying aging, cancer, neurodegeneration, and metabolic diseases. Fluorescent probes that selectively monitor loosely bound Fe(II) ions, termed the labile iron pool, are potentially powerful tools for studies of this metal nutrient; however, the dynamic spatiotemporal nature and potent fluorescence quenching capacity of these bioavailable metal stores pose challenges for their detection. Here, we report a tandem activity-based sensing and labeling strategy that enables imaging of labile iron pools in live cells through enhancement in cellular retention. Iron green-1 fluoromethyl (IG1-FM) reacts selectively with Fe(II) using an endoperoxide trigger to release a quinone methide dye for subsequent attachment to proximal biological nucleophiles, providing a permanent fluorescent stain at sites of elevated labile iron. IG1-FM imaging reveals that degradation of the major iron storage protein ferritin through ferritinophagy expands the labile iron pool, while activation of nuclear factor-erythroid 2-related factor 2 (NRF2) antioxidant response elements (AREs) depletes it. We further show that lung cancer cells with heightened NRF2 activation, and thus lower basal labile iron, have reduced viability when treated with an iron chelator. By connecting labile iron pools and NRF2-ARE activity to a druggable metal-dependent vulnerability in cancer, this work provides a starting point for broader investigations into the roles of transition metal and antioxidant signaling pathways in health and disease.


Assuntos
Elementos de Resposta Antioxidante , Ferro , Humanos , Ferro/metabolismo , Corantes Fluorescentes/química , Fator 2 Relacionado a NF-E2/metabolismo , Ferritinas/metabolismo , Estresse Oxidativo , Oxirredução , Linhagem Celular Tumoral , Antioxidantes/metabolismo
2.
Proc Natl Acad Sci U S A ; 121(30): e2407146121, 2024 Jul 23.
Artigo em Inglês | MEDLINE | ID: mdl-39018196

RESUMO

Surface reconstruction determines the fate of catalytic sites on the near-surface during the oxygen evolution reaction. However, deciphering the conversion mechanism of various intermediate-states during surface reconstruction remains a challenge. Herein, we employed an optical imaging technique to draw the landscape of dynamic surface reconstruction on individual Co3O4 nanoparticles. By regulating the surface states of Co3O4 nanoparticles, we explored dynamic growth of the CoOx(OH)y sublayer on single Co3O4 nanoparticles and directly identified the conversion between two dynamics. Rich oxygen vacancies induced more active sites on the surface and prolonged surface reconstruction, which enhanced electrochemical redox and oxygen evolution. These results were further verified by in situ electrochemical extinction spectroscopy of single Co3O4 nanoparticles. We elucidate the heterogeneous evolution of surface reconstruction on individual Co3O4 nanoparticles and present a unique perspective to understand the fate of catalytic species on the nanosurface, which is of enduring significance for investigating the heterogeneity of multielectron-transfer events.

3.
Proc Natl Acad Sci U S A ; 121(23): e2401757121, 2024 Jun 04.
Artigo em Inglês | MEDLINE | ID: mdl-38820004

RESUMO

We experimentally demonstrate the creation of defects in monolayer WSe2 via nanopillar imprinting and helium ion irradiation. Based on the first method, we realize atomically thin vertical tunneling light-emitting diodes based on WSe2 monolayers hosting quantum emitters at deterministically specified locations. We characterize these emitters by investigating the evolution of their emission spectra in external electric and magnetic fields, as well as by inducing electroluminescence at low temperatures. We identify qualitatively different types of quantum emitters and classify them according to the dominant electron-hole recombination paths, determined by the mechanisms of intervalley mixing occurring in fundamental conduction and/or valence subbands.

4.
Proc Natl Acad Sci U S A ; 120(46): e2310883120, 2023 Nov 14.
Artigo em Inglês | MEDLINE | ID: mdl-37934818

RESUMO

Development of single-component organic phosphor attracts increasing interest due to its wide applications in optoelectronic technologies. Theoretically, activating efficient intersystem crossing (ISC) via 1(π, π*) to 3(π, π*) transitions, rather than 1(n, π*) → 3(π, π*) transitions, is an alternative access to purely organic phosphors but remains challenging. Herein, we designed and successfully synthesized the sila-8-membered ring fused biaryl benzoskeleton by transition metal catalysis, which served as a new organic phosphor with efficient 1(π, π*) to 3(π, π*) ISC. We first found that such a compound exhibits a record-long phosphorescence lifetime of 6.5 s at low temperature for single-component organic systems. Then, we developed two strategies to tune their decay channels to evolve such nonemissive molecules into bright phosphors with elongated lifetimes at room temperature: 1) Physic-based design, where quantitative analyses of electron-phonon coupling led us to reveal and hinder the major nonradiative channels, thus lighted up room temperature phosphorescence (RTP) with a lifetime of 480 ms at 298 K; 2) chemical geometry-driven molecular engineering, where a geometry-based descriptor ΔΘT1-S0/ΘS0 was developed for rational screening RTP candidates and further improved the RTP lifetime to 794 ms. This study clearly shows the power of interdiscipline among synthetic methodology, physics-based rational design, and computational modeling, which represents a paradigm for the development of an organic emitter.

5.
Proc Natl Acad Sci U S A ; 120(15): e2221725120, 2023 Apr 11.
Artigo em Inglês | MEDLINE | ID: mdl-37014859

RESUMO

The coupling of light to electrical charge carriers in semiconductors is the foundation of many technological applications. Attosecond transient absorption spectroscopy measures simultaneously how excited electrons and the vacancies they leave behind dynamically react to the applied optical fields. In compound semiconductors, these dynamics can be probed via any of their atomic constituents with core-level transitions into valence and conduction band. Typically, the atomic species forming the compound contribute comparably to the relevant electronic properties of the material. One therefore expects to observe similar dynamics, irrespective of the choice of atomic species via which it is probed. Here, we show in the two-dimensional transition metal dichalcogenide semiconductor MoSe2, that through a selenium-based core-level transition we observe charge carriers acting independently from each other, while when probed through molybdenum, the collective, many-body motion of the carriers dominates. Such unexpectedly contrasting behavior can be explained by a strong localization of electrons around molybdenum atoms following absorption of light, which modifies the local fields acting on the carriers. We show that similar behavior in elemental titanium metal [M. Volkov et al., Nat. Phys. 15, 1145-1149 (2019)] carries over to transition metal-containing compounds and is expected to play an essential role for a wide range of such materials. Knowledge of independent particle and collective response is essential for fully understanding these materials.

6.
Proc Natl Acad Sci U S A ; 120(43): e2304274120, 2023 Oct 24.
Artigo em Inglês | MEDLINE | ID: mdl-37856542

RESUMO

Coupling together distinct correlated and topologically nontrivial electronic phases of matter can potentially induce novel electronic orders and phase transitions among them. Transition metal dichalcogenide compounds serve as a bedrock for exploration of such hybrid systems. They host a variety of exotic electronic phases, and their Van der Waals nature enables to admix them, either by exfoliation and stacking or by stoichiometric growth, and thereby induce novel correlated complexes. Here, we investigate the compound 4Hb-TaS2 that interleaves the Mott-insulating state of 1T-TaS2 and the putative spin liquid it hosts together with the metallic state of 2H-TaS2 and the low-temperature superconducting phase it harbors using scanning tunneling spectroscopy. We reveal a thermodynamic phase diagram that hosts a first-order quantum phase transition between a correlated Kondo-like cluster state and a depleted flat band state. We demonstrate that this intrinsic transition can be induced by an electric field and temperature as well as by manipulation of the interlayer coupling with the probe tip, hence allowing to reversibly toggle between the Kondo-like cluster and the depleted flat band states. The phase transition is manifested by a discontinuous change of the complete electronic spectrum accompanied by hysteresis and low-frequency noise. We find that the shape of the transition line in the phase diagram is determined by the local compressibility and the entropy of the two electronic states. Our findings set such heterogeneous structures as an exciting platform for systematic investigation and manipulation of Mott-metal transitions and strongly correlated phases and quantum phase transitions therein.

7.
J Biol Chem ; 300(8): 107589, 2024 Jul 19.
Artigo em Inglês | MEDLINE | ID: mdl-39032653

RESUMO

Transition metal ions are critically important across all kingdoms of life. The chemical properties of iron, copper, zinc, manganese, cobalt, and nickel make them very attractive for use as cofactors in metalloenzymes and/or metalloproteins. Their versatile chemistry in aqueous solution enables them to function both as electron donors and acceptors, and thus participate in both reduction and oxidation reactions respectively. Transition metal ions can also function as nonredox multidentate coordination sites that play essential roles in macromolecular structure and function. Malfunction in transition metal transport and homeostasis has been linked to a wide number of human diseases including cancer, diabetes, and neurodegenerative disorders. Transition metal transporters are central players in the physiology of transition metals whereby they move transition metals in and out of cellular compartments. In this review, we provide a comprehensive overview of in vitro reconstitution of the activity of integral membrane transition metal transporters and discuss strategies that have been successfully implemented to overcome the challenges. We also discuss recent advances in our understanding of transition metal transport mechanisms and the techniques that are currently used to decipher the molecular basis of transport activities of these proteins. Deep mechanistic insights into transition metal transport systems will be essential to understand their malfunction in human diseases and target them for potential therapeutic strategies.

8.
Proc Natl Acad Sci U S A ; 119(39): e2208830119, 2022 09 27.
Artigo em Inglês | MEDLINE | ID: mdl-36122203

RESUMO

Recent developments in the area of resonant dielectric nanostructures have created attractive opportunities for concentrating and manipulating light at the nanoscale and the establishment of the new exciting field of all-dielectric nanophotonics. Transition metal dichalcogenides (TMDCs) with nanopatterned surfaces are especially promising for these tasks. Still, the fabrication of these structures requires sophisticated lithographic processes, drastically complicating application prospects. To bridge this gap and broaden the application scope of TMDC nanomaterials, we report here femtosecond laser-ablative fabrication of water-dispersed spherical TMDC (MoS2 and WS2) nanoparticles (NPs) of variable size (5 to 250 nm). Such NPs demonstrate exciting optical and electronic properties inherited from TMDC crystals, due to preserved crystalline structure, which offers a unique combination of pronounced excitonic response and high refractive index value, making possible a strong concentration of electromagnetic field in the NPs. Furthermore, such NPs offer additional tunability due to hybridization between the Mie and excitonic resonances. Such properties bring to life a number of nontrivial effects, including enhanced photoabsorption and photothermal conversion. As an illustration, we demonstrate that the NPs exhibit a very strong photothermal response, much exceeding that of conventional dielectric nanoresonators based on Si. Being in a mobile colloidal state and exhibiting superior optical properties compared to other dielectric resonant structures, the synthesized TMDC NPs offer opportunities for the development of next-generation nanophotonic and nanotheranostic platforms, including photothermal therapy and multimodal bioimaging.


Assuntos
Nanosferas , Medicina de Precisão , Refratometria , Molibdênio , Nanosferas/uso terapêutico , Medicina de Precisão/instrumentação , Água
9.
Proc Natl Acad Sci U S A ; 119(45): e2206756119, 2022 Nov 08.
Artigo em Inglês | MEDLINE | ID: mdl-36331995

RESUMO

Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental-computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS2 and MoSe2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).


Assuntos
Fraturas Ósseas , Humanos , Reprodutibilidade dos Testes
10.
Proc Natl Acad Sci U S A ; 119(43): e2202736119, 2022 10 25.
Artigo em Inglês | MEDLINE | ID: mdl-36252013

RESUMO

Copper is an essential metal nutrient for life that often relies on redox cycling between Cu(I) and Cu(II) oxidation states to fulfill its physiological roles, but alterations in cellular redox status can lead to imbalances in copper homeostasis that contribute to cancer and other metalloplasias with metal-dependent disease vulnerabilities. Copper-responsive fluorescent probes offer powerful tools to study labile copper pools, but most of these reagents target Cu(I), with limited methods for monitoring Cu(II) owing to its potent fluorescence quenching properties. Here, we report an activity-based sensing strategy for turn-on, oxidation state-specific detection of Cu(II) through metal-directed acyl imidazole chemistry. Cu(II) binding to a metal and oxidation state-specific receptor that accommodates the harder Lewis acidity of Cu(II) relative to Cu(I) activates the pendant dye for reaction with proximal biological nucleophiles and concomitant metal ion release, thus avoiding fluorescence quenching. Copper-directed acyl imidazole 649 for Cu(II) (CD649.2) provides foundational information on the existence and regulation of labile Cu(II) pools, including identifying divalent metal transporter 1 (DMT1) as a Cu(II) importer, labile Cu(II) increases in response to oxidative stress induced by depleting total glutathione levels, and reciprocal increases in labile Cu(II) accompanied by decreases in labile Cu(I) induced by oncogenic mutations that promote oxidative stress.


Assuntos
Cobre , Corantes Fluorescentes , Cobre/metabolismo , Corantes Fluorescentes/química , Glutationa/metabolismo , Imidazóis , Oncogenes , Oxirredução
11.
Nano Lett ; 2024 Aug 19.
Artigo em Inglês | MEDLINE | ID: mdl-39158041

RESUMO

Achieving robust electrical contacts is crucial for realizing the promise of monolayer 2D semiconductors such as semiconducting transition metal dichalcogenides (s-TMDs) in electronics. Despite recent breakthroughs, a gap remains between the experimental and theoretical understanding of metal-s-TMDs contacts. This study explores bismuth semimetal contacts to monolayer MoSe2, using a platform that minimizes experimental sources of uncertainty; we combine contact-front and contact-end measurements to measure key parameters like specific resistivity (ρc) and transfer length (Lt). We find that the resistivity of MoSe2 under the contacts is enhanced due to charge transfer that can be modeled using a self-consistent approach. In contrast, ab initio calculations of the interlayer charge transfer rate are inconsistent with the measured value of ρc, highlighting the need for new theoretical approaches.

12.
Nano Lett ; 2024 Jun 10.
Artigo em Inglês | MEDLINE | ID: mdl-38855978

RESUMO

Integration of 2D semiconductors with photonic crystal slabs provides an attractive approach to achieving strong light-matter coupling and exciton-polariton formation in a chip-compatible geometry. However, for the development of practical devices, it is crucial that polariton excitations are easily tunable and exhibit a strong nonlinear response. Here we study neutral and charged exciton-polaritons in an electrostatically gated photonic crystal slab with an embedded monolayer semiconductor MoSe2 and experimentally demonstrate a novel approach to optical control based on polariton nonlinearity. We show that spatial modulation of the dielectric environment within the photonic crystal unit cell results in the formation of two distinct excitonic species with significantly different nonlinear responses of the corresponding charged exciton-polaritons under optical pumping. This behavior enables optical switching with ultrashort laser pulses and can be sensitively controlled via an electrostatic gate voltage. Our results open new avenues toward the development of active polaritonic devices in a compact chip-compatible implementation.

13.
Nano Lett ; 24(9): 2789-2797, 2024 Mar 06.
Artigo em Inglês | MEDLINE | ID: mdl-38407030

RESUMO

Two-dimensional materials are expected to play an important role in next-generation electronics and optoelectronic devices. Recently, twisted bilayer graphene and transition metal dichalcogenides have attracted significant attention due to their unique physical properties and potential applications. In this study, we describe the use of optical microscopy to collect the color space of chemical vapor deposition (CVD) of molybdenum disulfide (MoS2) and the application of a semantic segmentation convolutional neural network (CNN) to accurately and rapidly identify thicknesses of MoS2 flakes. A second CNN model is trained to provide precise predictions on the twist angle of CVD-grown bilayer flakes. This model harnessed a data set comprising over 10,000 synthetic images, encompassing geometries spanning from hexagonal to triangular shapes. Subsequent validation of the deep learning predictions on twist angles was executed through the second harmonic generation and Raman spectroscopy. Our results introduce a scalable methodology for automated inspection of twisted atomically thin CVD-grown bilayers.

14.
Nano Lett ; 24(9): 2931-2938, 2024 Mar 06.
Artigo em Inglês | MEDLINE | ID: mdl-38377049

RESUMO

Plasmon-induced hot-electron transfer at the metallic nanoparticle/semiconductor interface is the basis of plasmon-enhanced photocatalysis and energy harvesting. However, limited by the nanoscale size of hot spots and femtosecond time scale of hot-electron transfer, direct observation is still challenging. Herein, by using spatiotemporal-resolved photoemission electron microscopy with a two-color pump-probe beamline, we directly observed such a process with a concise system, the Au nanoparticle/monolayer transition-metal dichalcogenide (TMD) interface. The ultrafast hot-electron transfer from Au nanoparticles to monolayer TMDs and the plasmon-enhanced transfer process were directly measured and verified through an in situ comparison with the Au film/TMD interface and free TMDs. The lifetime at the Au nanoparticle/MoSe2 interface decreased from 410 to 42 fs, while the photoemission intensities exhibited a 27-fold increase compared to free MoSe2. We also measured the evolution of hot electrons in the energy distributions, indicating the hot-electron injection and decay happened in an ultrafast time scale of ∼50 fs without observable electron cooling.

15.
Nano Lett ; 24(4): 1431-1438, 2024 Jan 31.
Artigo em Inglês | MEDLINE | ID: mdl-38252694

RESUMO

Transition metal dichalcogenides (TMDCs) have garnered considerable interest over the past decade as a class of semiconducting layered materials. Most studies on the carrier dynamics in these materials have focused on the monolayer due to its direct bandgap, strong photoluminescence, and strongly bound excitons. However, a comparative understanding of the carrier dynamics in multilayer (e.g., >10 layers) flakes is still absent. Recent computational studies have suggested that excitons in bulk TMDCs are confined to individual layers, leading to room-temperature stable exciton populations. Using this new context, we explore the carrier dynamics in MoSe2 flakes that are between ∼16 and ∼125 layers thick. We assign the kinetics to exciton-exciton annihilation (EEA) and Shockley-Read-Hall recombination of free carriers. Interestingly, the average observed EEA rate constant (0.003 cm2/s) is nearly independent of flake thickness and 2 orders of magnitude smaller than that of an unencapsulated monolayer (0.33 cm2/s) but very similar to values observed in encapsulated monolayers. Thus, we posit that strong intralayer interactions minimize the effect of layer thickness on recombination dynamics, causing the multilayer to behave like the monolayer and exhibit an apparent EEA rate intrinsic to MoSe2.

16.
Nano Lett ; 24(1): 493-500, 2024 Jan 10.
Artigo em Inglês | MEDLINE | ID: mdl-38148179

RESUMO

Compositional tunability, an indispensable parameter for modifying the properties of materials, can open up new applications for van der Waals (vdW) layered materials such as transition-metal dichalcogenides (TMDCs). To date, multielement alloy TMDC layers are obtained via exfoliation from bulk polycrystalline powders. Here, we demonstrate direct deposition of high-entropy alloy disulfide, (VNbMoTaW)S2, layers with controllable thicknesses on free-standing graphene membranes and on bare and hBN-covered Al2O3(0001) substrates via ultra-high-vacuum reactive dc magnetron sputtering of the VNbMoTaW target in Kr and H2S gas mixtures. Using a combination of density functional theory calculations, Raman spectroscopy, X-ray diffraction, scanning transmission electron microscopy coupled with energy dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy, we determine that the as-deposited layers are single-phase, 2H-structured, and 0001-oriented (V0.10Nb0.16Mo0.19Ta0.28W0.27)S2.44. Our synthesis route is general and applicable for heteroepitaxial growth of a wide variety of TMDC alloys and potentially other multielement alloy vdW compounds with the desired compositions.

17.
Nano Lett ; 24(6): 1835-1842, 2024 Feb 14.
Artigo em Inglês | MEDLINE | ID: mdl-38315833

RESUMO

Strain engineering modifies the optical and electronic properties of atomically thin transition metal dichalcogenides. Highly inhomogeneous strain distributions in two-dimensional materials can be easily realized, enabling control of properties on the nanoscale; however, methods for probing strain on the nanoscale remain challenging. In this work, we characterize inhomogeneously strained monolayer MoS2 via Kelvin probe force microscopy and electrostatic gating, isolating the contributions of strain from other electrostatic effects and enabling the measurement of all components of the two-dimensional strain tensor on length scales less than 100 nm. The combination of these methods is used to calculate the spatial distribution of the electrostatic potential resulting from piezoelectricity, presenting a powerful way to characterize inhomogeneous strain and piezoelectricity that can be extended toward a variety of 2D materials.

18.
Nano Lett ; 24(22): 6592-6600, 2024 Jun 05.
Artigo em Inglês | MEDLINE | ID: mdl-38787539

RESUMO

Monolayer transition metal dichalcogenides exhibit valley-dependent excitonic characters with a large binding energy, acting as the building block for future optoelectronic functionalities. Herein, combined with pump-probe ultrafast transient transmission spectroscopy and theoretical simulations, we reveal the chirality-dependent trion dynamics in h-BN encapsulated monolayer tungsten disulfide. By resonantly pumping trions in a single valley and monitoring their temporal evolution, we identify the temperature-dependent competition between two relaxation channels driven by chirality-dependent scattering processes. At room temperature, the phonon-assisted upconversion process predominates, converting excited trions to excitons within the same valley on a sub-picosecond (ps) time scale. As temperature decreases, this process becomes less efficient, while alternative channels, notably valley depolarization process for trions, assume importance, leading to an increase of trion density in the unpumped valley within a ps time scale. Our time-resolved valley-contrast results provide a comprehensive insight into trion dynamics in 2D materials, thereby advancing the development of novel valleytronic devices.

19.
Nano Lett ; 24(31): 9575-9582, 2024 Aug 07.
Artigo em Inglês | MEDLINE | ID: mdl-39051155

RESUMO

Interlayer excitons (IXs) in van der Waals heterostructures with static out of plane dipole moment and long lifetime show promise in the development of exciton based optoelectronic devices and the exploration of many body physics. However, these IXs are not always observed, as the emission is very sensitive to lattice mismatch and twist angle between the constituent materials. Moreover, their emission intensity is very weak compared to that of corresponding intralayer excitons at room temperature. Here we report the room-temperature realization of twist angle independent momentum direct IX in the heterostructures of bulk PbI2 and bilayer WS2. Momentum conserving transitions combined with the large band offsets between the constituent materials enable intense IX emission at room temperature. A long lifetime (∼100 ns), noticeable Stark shift, and tunability of IX emission from 1.70 to 1.45 eV by varying the number of WS2 layers make these heterostructures promising to develop room temperature exciton based optoelectronic devices.

20.
Nano Lett ; 24(31): 9658-9665, 2024 Aug 07.
Artigo em Inglês | MEDLINE | ID: mdl-39052446

RESUMO

Dielectric phase gradient metasurfaces have emerged as promising candidates to shrink bulky optical elements to subwavelength thickness scale based on dielectric meta-atoms. These meta-atoms strongly interact with light, thus offering excellent phase manipulation of incident light. However, to fulfill 2π phase control using meta-atoms, the metasurface thickness, to date, is limited to the order of 102 nm. Here, we present the thickness scaling down of phase gradient metasurfaces to <λ/20 by using excitonic van der Waals metasurfaces. High-refractive-index enabled by exciton resonances and symmetry-breaking nanostructures in the patterned layered tungsten disulfide (WS2) corporately enable quasibound states in the continuum in WS2 metasurfaces, which consequently yield complete phase regulation of 2π with the thickness down to 35 nm. To illustrate the concept, we have experimentally demonstrated beam steering, focusing, and holographic display using WS2 metasurfaces. We envision our results unveiling new venues for ultimate thin phase gradient metasurfaces.

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