Van Der Waals Structures Research Articles

Plasmonic Biosensing with Nano-Engineered Van der Waals Interfaces.

Observing a Goos-Hänchen (GH) shift of the incident light beam provides a simple and convenient method of detecting fast phase variations without the need for cumbersome direct phase measurements. Here, we show that few-monolayers-thick van der Waals structures (WS₂ , MoSe₂ and graphene) nano-engineered onto a plasmonic surface can enhance the phase variation sensitivity to analyte presence, leading to more than 3 orders of magnitude increase in the Goos-Hänchen shift (ca. 886 mm/RIU for a WS₂ /graphene/Au multilayer). The detection limit is evaluated to be as low as 0.1 aM (6.7 pg/mL) for bovine serum albumin protein with molecular weight of 67 kDa and 1 fM (24.4 ng/mL) for biotin (244 Da) molecules.

Moiré modulation of charge density waves

Here we investigate how charge density waves (CDWs), inherent to a monolayer, are effected by creating twisted van der Waals structures. Homobilayers of metallic transition metal dichalcogenides (TMDs), at small twist angles where there is significant atomic reconstruction, are utilised as an example to investigate the interplay between the moiré domain structure and CDWs of different periods. For CDWs, there is no geometric constraint to prevent the CDWs from propagating throughout the moiré structure. Whereas for CDWs, to ensure the CDWs in each layer have the most favourable interactions in the domains, the CDW phase must be destroyed in the connecting domain walls. For CDWs with twist angles close to 180∘, moiré-scale triangular structures can form; while close to 0∘, moiré-scale dimer domains occur. The star-of-David CDW () is found to host CDWs in the domains only, since there is one low energy stacking configuration, similar to the CDWs. These predictions are offered for experimental verification in twisted bilayer metallic TMDs which host CDWs, and we hope this will stimulate further research on the interplay between the moiré superlattice and CDW phases intrinsic to the comprising 2D materials.

A potential absorber for PHz electronics using Sn/h-BN Van der Waals structure: A hybrid DFT and macroscopic investigations

The rapid rollout of the next-generation network has sparked discussion about an entirely new set of optical techniques. To prepare the path for future wireless network growth, we must investigate the PHz band’s potential for supporting infrastructures. Engineered materials might play a perceptible role in designing such critical PHz band components. This work demonstrates an efficient Stanene/hexagonal- Boron Nitride heterostructure-based metasurface absorber for the PHz regime. An ab-initio computational approach has been employed to estimate the optical and electronic behavior of Sn/h-BN heterostructure . A high absorption coefficient and excellent optical characteristics are obtained by the proposed metasurface absorber based on Sn/h-BN Van der Waals (vdW) structure. The absorption of PHz waves by a metasurface comprising a bi-periodic array of meta-atoms on top of a dielectric substrate backed by gold is simulated using CST Microwave Studio™. By utilizing the Finite Integral Techniques (FIT), a high absorptance (around 0.98) is achieved over a 0.45 PHz wide spectral regime for normal incidence, regardless of the polarization states. • A Sn/h-BN Van der Waals structure has been investigated for device application. • A hybrid DFT and macroscopic approach is used to design an optical absorber. • High absorption coefficient and anisotropic properties are exhibited by the investigated materials. • A high absorptance (around 98%), were achieved over a 0.45 PHz wide spectral regime for normal incidence.

Efficient Inner-to-Outer Wall Energy Transfer in Highly Pure Double-Wall Carbon Nanotubes Revealed by Detailed Spectroscopy.

The coaxial stacking of two single-wall carbon nanotubes (SWCNTs) into a double-wall carbon nanotube (DWCNT), forming a so-called one-dimensional van der Waals structure, leads to synergetic effects that dramatically affect the optical and electronic properties of both layers. In this work, we explore these effects in purified DWCNT samples by combining absorption, wavelength-dependent infrared fluorescence-excitation (PLE), and wavelength-dependent resonant Raman scattering (RRS) spectroscopy. Purified DWCNTs are obtained by careful solubilization that strictly avoids ultrasonication or by electronic-type sorting, both followed by a density gradient ultracentrifugation to remove unwanted SWCNTs that could obscure the DWCNT characterization. Chirality-dependent shifts of the radial breathing mode vibrational frequencies and transition energies of the inner and outer DWCNT walls with respect to their SWCNT analogues are determined by advanced two-dimensional fitting of RRS and PLE data of DWCNT and their reference SWCNT samples. This exhaustive data set verifies that fluorescence from the inner DWCNT walls of well-purified samples is severely quenched through efficient energy transfer from the inner to the outer DWCNT walls. Combined analysis of the PLE and RRS results further reveals that this transfer is dependent on the inner and outer wall chirality, and we identify the specific combinations dominant in our DWCNT samples. These obtained results demonstrate the necessity and value of a combined structural characterization approach including PLE and RRS spectroscopy for bulk DWCNT samples.

Nanometric Moiré Stripes on the Surface of Bi2Se3 Topological Insulator.

Mismatch between adjacent atomic layers in low-dimensional materials, generating moiré patterns, has recently emerged as a suitable method to tune electronic properties by inducing strong electron correlations and generating novel phenomena. Beyond graphene, van der Waals structures such as three-dimensional (3D) topological insulators (TIs) appear as ideal candidates for the study of these phenomena due to the weak coupling between layers. Here we discover and investigate the origin of 1D moiré stripes on the surface of Bi2Se3 TI thin films and nanobelts. Scanning tunneling microscopy and high-resolution transmission electron microscopy reveal a unidirectional strained top layer, in the range 14–25%, with respect to the relaxed bulk structure, which cannot be ascribed to the mismatch with the substrate lattice but rather to strain induced by a specific growth mechanism. The 1D stripes are characterized by a spatial modulation of the local density of states, which is strongly enhanced compared to the bulk system. Density functional theory calculations confirm the experimental findings, showing that the TI surface Dirac cone is preserved in the 1D moiré stripes, as expected from the topology, though with a heavily renormalized Fermi velocity that also changes between the top and valley of the stripes. The strongly enhanced density of surface states in the TI 1D moiré superstructure can be instrumental in promoting strong correlations in the topological surface states, which can be responsible for surface magnetism and topological superconductivity.

Enhanced shift current bulk photovoltaic effect in ferroelectric Rashba semiconductor α-GeTe: ab initio study from three- to two-dimensional van der Waals layered structures

The ferroelectric Rashba semiconductors (FERSCs) are endowed with a unique combination of ferroelectricity and the spin degree of freedom, resulting in a long carrier lifetime and impressive bulk photovoltaic (BPV) efficiency that reached 25% in organometal halide perovskites. The BPV efficiency can be further improved by using low-dimensional ferroelectrics however, it is inhibited by the ferroelectric instability in low-dimensional perovskites and toxicity along with phase instability of the lead-halide perovskites. To address these challenges, the α-GeTe could be of great importance which is the simplest known lead-free FERSC with an intrinsic layered structure. Therefore, in this work, we investigate the BPV properties of three- to two-dimensional van der Waals structures of α-GeTe by calculating the shift current (SHC). We predict that the mono (1.56 Å) and bi-layers (5.44–6.14 Å) α-GeTe with the buckled honeycomb structure are dynamically stable and possess the characteristic features of the bulk up to the nanoscale limit. The SHC of ∼70 μA V−2 is calculated in bulk α-GeTe which is 20 times larger than that obtained in organometal halides in the visible light. The SHC increases with decreasing the number of layers, reaching a maximum amplitude of ∼300 μA V−2 at 2.67 eV in the monolayer which is more than double that obtained in monolayer GeS. We find that the SHC in monolayer α-GeTe can be further enhanced and redshifted by applying a compressive strain; which is correlated with the strong absorption of the xx-polarized light, stimulated by the more delocalized p x /y orbital character of the density of states. Furthermore, in the bilayer structures, the magnitude of the SHC is sensitive to the layers’ stacking arrangement and a maximum SHC (∼250 μA V−2) can be achieved with an AB-type stacking arrangement. Combining these results with the benefits of being environmental-friendly material makes α-GeTe a good candidate for next-generation solar cells application.

A Capillary-Force-Assisted Transfer for Monolayer Transition-Metal-Dichalcogenide Crystals with High Utilization.

The capillary-force-assisted transfer has shown application potential for constructing two-dimensional (2D) electronic and optoelectronic devices for the advantage of free of spin coating the organic compound and etching the substrate. Currently, the transfer mechanism remains obscure. The capillary adhesion mechanism and capillary invasion separation mechanism were proposed independently and rarely discussed in a comprehensive manner. What is more, the integrity and utilization remain to be improved. Here, we developed the capillary-force-assisted transfer method with high utilization and integrity. Uniformity of water transport was improved by introducing water from the sidewall of the small polydimethylsiloxane (PDMS) stamp driven by capillary force. The transfer integrity rate increased, and the location of the complete samples became predictable. The transfer utilization increased as the limited water transportation minimized the impact on the surrounding WS2. The monolayer triangle WS2 crystals from adjacent areas on the sapphire substrate were transferred one after another. Besides, local mechanical exfoliation of the continuous WS2 thin films was demonstrated, implying that the capillary adhesion is strong enough to break the strong in-plane covalent bond and overcome the van der Waals force between WS2 and sapphire substrate. Finally, the water transport model between two surfaces with different hydrophobicity combinations was derived on the basis of the Young-Laplace equation. The analysis of water transport between different interfaces reveals how capillary adhesion and capillary invasion work together to achieve capillary force transfer. This study highlights the potential of the capillary-force-assisted transfer as an efficient technique for fabricating van der Waals structures based on two-dimensional atomic crystals, especially periodic structures.

Imaging topological and correlated insulating states in twisted monolayer-bilayer graphene

Flat bands in Van der Waals heterostructure provide an ideal platform for unveiling emergent quantum electronic phases. One celebrated example is twisted monolayer-bilayer graphene, in which the effects of electronic correlation have been observed. Here, we report the observation via scanning tunnelling microscopy and spectroscopy of correlated insulating states in twisted monolayer-bilayer graphene, leading to the formation of an electron crystal phase. At integer fillings, the strong Coulomb interaction redistributes flat-band electrons within one moiré unit cell, producing an insulating state with vanishing density of states at the Fermi level. Moreover, our approach enables the direct visualization of an ordered lattice of topological torus-shaped states, generated by the interaction between the electron crystal and the non-trivial band topology of twisted monolayer-bilayer graphene. Our results illustrate an efficient strategy for entwining topological physics with strong electron correlation in twisted van der Waals structures.

Tuning the optical properties of molybdenum oxide using electric field: A theoretical and experimental study

Molybdenum Oxide (MoO3) with van der Waals structure can lead to the exotic properties under the action of external physical perturbation. Here, a combined density functional theory and an experimental study were performed to analyze the response of MoO3 under electric field. The electric field with the strength varying from 0.05 V/Å to 0.23 V/Å was applied across the MoO3 cell which induced the splitting in the valence and conduction band and decreases the bandgap. A critical electric field of 0.23 V/Å resulted a closing of the bandgap of MoO3 and led semiconductor to metal transition. The results of DFT regarding decrease in the bandgap of MoO3 were further supported experimentally. For this, MoO3 films were fabricated using thermal evaporation and their chemical and optical properties were analyzed using X-ray photoelectron spectroscopy and Electroreflectance (ER). To analyze the optical response, an ER analysis with external voltage varying from 10 to 50 volts was performed on Aluminum/MoO3/Aluminum heterostructure. The resultant ER spectra revealed three distinct critical points that correspond to the fundamental as well as defect related optical transitions involved in MoO3. The Third derivative functional form model applied on the ER spectra depicted a monotonical decrease in the critical points of MoO3 at lower voltage. At high voltage of about 80 volts, the existence of high built-in electric field results the delocalization in the electrons and hole wave function and gives rise to the Franz-Keldysh oscillations.

Regulating interfacial morphology and charge-carrier utilization of Ti3C2 modified all-sulfide CdS/ZnIn2S4 S-scheme heterojunctions for effective photocatalytic H2 evolution

The separation efficiency of electrons and holes and the enhancement of the surface reductive reaction in the metal sulfide semiconductor photocatalysts are important factors in boosting photocatalytic H2 evolution from water. The control of both interface morphology and the charge–carrier utilization of metal sulfide-based photocatalysts can effectively improve the separation efficiency of electrons and holes and increase the surface reaction active sites, which are considered to be effective methods to improve the photocatalytic activity of semiconductors. Here, the Ti3C2 (Mxene) modified all-sulfide 2D/2D S-scheme heterojunction Ti3C2/ ZnIn2S4(ZIS)/CdS composite material was firstly synthesized by a two-step solvothermal method. The formation of all-sulfide S-scheme heterojunction improves the efficiency of electron-hole separation. The intimate 2D/2D van der Waals structure provides a strong interaction force and a large contact area to enhance charge transfer. The addition of 2D Ti3C2 forms the accumulation layer, reducing the recombination of electrons and holes. Under the synergistic promotion, the highest hydrogen production of the prepared Ti3C2/ZIS/CdS composite photocatalyst could reach 8.93 mmol/h/g. This work not only enriches the photocatalytic systems through integrating the ohmic junction and the 2D/2D all-sulfide S-scheme heterojunction, but also provides a satisfactory design strategy for engineering interfacial morphology and charge-carrier utilization.

Intrinsic Mechanisms of Morphological Engineering and Carbon Doping for Improved Photocatalysis of 2D/2D Carbon Nitride Van Der Waals Heterojunction

Van der Waals (VDW) heterojunctions in a 2D/2D contact provide the highest area for the separation and transfer of charge carriers. In this work, a top‐down strategy with a gas erosion process was employed to fabricate a 2D/2D carbon nitride VDW heterojunction in carbon nitride (g‐C3N4) with carbon‐rich carbon nitride. The created 2D semiconducting channel in the VDW structure exhibits enhanced electric field exposure and radiation absorption, which facilitates the separation of the charge carriers and their mobility. Consequently, compared with bulk g‐C3N4 and its nanosheets, the photocatalytic performance of the fabricated carbon nitride VDW heterojunction in the water splitting reaction to hydrogen is improved by 8.6 and 3.3 times, respectively, while maintaining satisfactory photo‐stability. Mechanistically, the finite element method (FEM) was employed to evaluate and clarify the contributions of the formation of VDW heterojunction to enhanced photocatalysis, in agreement quantitatively with experimental ones. This study provides a new and effective strategy for the modification and more insights to performance improvement on polymeric semiconductors in photocatalysis and energy conversion.

London Dispersion‐Corrected Density Functionals Applied to van der Waals Stacked Layered Materials: Validation of Structure, Energy, and Electronic Properties

AbstractMost density functionals lack to correctly account for long‐range London dispersion interactions, and numerous a posteriori correction schemes have been proposed in recent years. In van der Waals structures, the interlayer distance controls the proximity effect on the electronic structure, and the interlayer interaction energy indicates the possibility to mechanically exfoliate a layered material. For upcoming twisted van der Waals heterostructures, a reliable but efficient and scalable theoretical scheme to correctly predict the interlayer distance is required. Therefore, the performance of a series of popular London dispersion corrections combined with computationally affordable density functionals is validated. As reference data, the experimental interlayer distance of layered bulk materials is used, and corresponding interlayer interaction energies are calculated using the random phase approximation. We demonstrate that the SCAN‐rVV10 and PBE‐rVV10L functionals predict interlayer interaction energies and interlayer distances of the studied layered systems within the range of the defined error limits of 10 meV per atom and 0.12 Å, respectively. Semi‐empirical and empirical dispersion‐corrected functionals show significantly larger error bars, with PBE+dDsC performing best with comparable quality of geometries, but with higher interlayer interaction energy error limits of ≈20 meV per atom.

Domino-like stacking order switching in twisted monolayer-multilayer graphene.

Atomic reconstruction has been widely observed in two-dimensional van der Waals structures with small twist angles1-7. This unusual behaviour leads to many novel phenomena, including strong electronic correlation, spontaneous ferromagnetism and topologically protected states1,5,8-14. Nevertheless, atomic reconstruction typically occurs spontaneously, exhibiting only one single stable state. Using conductive atomic force microscopy, here we show that, for small-angle twisted monolayer-multilayer graphene, there exist two metastable reconstruction states with distinct stacking orders and strain soliton structures. More importantly, we demonstrate that these two reconstruction states can be reversibly switched, and the switching can propagate spontaneously in an unusual domino-like fashion. Assisted by lattice-resolved conductive atomic force microscopy imaging and atomistic simulations, the detailed structure of the strain soliton networks has been identified and the associated propagation mechanism is attributed to the strong mechanical coupling among solitons. The fine structure of the bistable states is critical for understanding the unique properties of van der Waals structures with tiny twists, and the switching mechanism offers a viable means for manipulating their stacking states.

Spin freezing in the van der Waals material Mn2Ga2S5

Geometrical frustration in low-dimensional magnetic systems has been an intriguing research aspect, where the suppression of conventional magnetic order may lead to exotic ground states such as spin glass or spin liquid. In this work we report the synthesis and magnetism study of the monocrystalline Mn2Ga2S5, featuring both the van der Waals structure and a bilayered triangular Mn lattice. Magnetic susceptibility reveals a significant antiferromagnetic interaction with a Curie–Weiss temperature θ w ∼ –260 K and a high spin S = 5/2 Mn2+ state. However, no long range magnetic order has been found down to 2 K, and a spin freezing transition is found to occur at around 12 K well below its θ w. This yields a frustration index of f = –θ w/T f ≈ 22, an indication that the system is highly frustrated. The absence of a double-peak structure in magnetic specific heat compared with the TM 2S4 compounds implies that the spin freezing behavior in Mn2Ga2S5 is a result of the competition between exchange interactions and the 2D crystalline structure. Our results suggest that the layered Mn2Ga2S5 would be an excellent candidate for investigating the physics of 2D magnetism and spin disordered state.

Enhanced Versatility of Table-Top X-Rays from Van der Waals Structures.

Van der Waals (vdW) materials have attracted much interest for their myriad unique electronic, mechanical, and thermal properties. In particular, they are promising candidates for monochromatic, table‐top X‐ray sources. This work reveals that the versatility of the table‐top vdW X‐ray source goes beyond what has been demonstrated so far. By introducing a tilt angle between the vdW structure and the incident electron beam, it is theoretically and experimentally shown that the accessible photon energy range is more than doubled. This allows for greater versatility in real‐time tuning of the vdW X‐ray source. Furthermore, this work shows that the accessible photon energy range is maximized by simultaneously controlling both the electron energy and the vdW structure tilt. These results will pave the way for highly tunable, compact X‐ray sources, with potential applications including hyperspectral X‐ray fluoroscopy and X‐ray quantum optics.

Thermoelectric Conversion From Interface Thermophoresis and Piezoelectric Effects

Piezoelectric effect has proved itself to be a promising energy conversion mechanism that can convert mechanical energy into electricity. Here, we propose an indirect thermoelectric conversion mechanism based on a combination of the thermophoresis and piezoelectric effects. We first analyze this thermally driven mechanism using a simplified theoretical model and then numerically analyze a molecular dynamics (MD) simulation of a hybrid system constructed of a single-layer MoS2 nanoribbon and a concentric carbon nanotube. We show that the thermophoresis-induced piezoelectric output voltage can reach 3.5 V, and this value can be tuned using a temperature difference. The output voltage obtained using this mechanism is significantly higher than that obtained by heating piezoelectric materials directly. Given the generality of the thermophoresis effect in Van der Waals structures, this mechanism has potential applications in the conversion of thermal energy into electrical energy at the nanoscale level.

Fermi Level Pinning Dependent 2D Semiconductor Devices: Challenges and Prospects.

Motivated by the high expectation for efficient electrostatic modulation of charge transport at very low voltages, atomically thin 2D materials with a range of bandgaps are investigated extensively for use in future semiconductor devices. However, researchers face formidable challenges in 2D device processing mainly originated from the out-of-plane van der Waals (vdW) structure of ultrathin 2D materials. As major challenges, untunable Schottky barrier height and the corresponding strong Fermi level pinning (FLP) at metal interfaces are observed unexpectedly with 2D vdW materials, giving rise to unmodulated semiconductor polarity, high contact resistance, and lowered device mobility. Here, FLP observed from recently developed 2D semiconductor devices is addressed differently from those observed from conventional semiconductor devices. It is understood that the observed FLP is attributed to inefficient doping into 2D materials, vdW gap present at the metal interface, and hybridized compounds formed under contacting metals. To provide readers with practical guidelines for the design of 2D devices, the impact of FLP occurring in 2D semiconductor devices is further reviewed by exploring various origins responsible for the FLP, effects of FLP on 2D device performances, and methods for improving metallic contact to 2D materials.

Stacking and Twisting of Layered Materials Enabled by Screw Dislocations and Non-Euclidean Surfaces

ConspectusThe rise of van der Waals layered materials such as graphene, hexagonal boron nitride, and transition-metal dichalcogenides opens up enormous opportunities for exploring novel quantum phenomena at the two-dimensional (2D) atomic limit. The physical properties of van der Waals materials are often affected by the symmetry of the crystal lattices. For example, breaking the inversion symmetry can lead to a variety of phenomena, such as second-harmonic generation, valley polarization, and ferroelectricity. The symmetry and symmetry breaking of layered materials are determined by the atomic arrangements within the layer and the layer stackings. The screw-dislocation-driven growth mechanism is general to 2D materials and can provide effective kinetic pathways to influence the layer stacking and generate diverse and complex layer stackings with different symmetry.Furthermore, different van der Waals layered materials can also be stacked vertically to create artificial new structures. In such stacked structures, the interlayer twist angle between stacked layers results in the formation of large-scale moiré superlattices that manipulate the electronic structures of van der Waals materials and provide an additional degree of freedom for tuning their physical properties. The stacking and twisting of layered materials lead to observations of new quantum phenomena, such as unconventional superconductivity, tunable Mott insulators, moiré excitons, and various magnetic and ferroelectric orderings. Previously, such twisted 2D structures were often fabricated by mechanically stacking exfoliated layers, but it was recently demonstrated that twisted van der Waals structures can form via direct growth. Moreover, continuously twisted structures of 2D materials can be realized through two distinct mechanisms that involve screw dislocations. The Eshelby twist mechanism induced by the strain of screw dislocation gives rise to twisted van der Waals nanowires with small interlayer twists. Beyond the Eshelby twist mechanism, supertwisted spirals have recently been enabled by a non-Euclidean twist mechanism which arises from the mismatched geometry between van der Waals crystals and non-Euclidean (curved) surfaces.In this Account, we start with reviewing the stacking configurations in the diverse polytypic structures of layered materials using transition-metal dichalcogenides as examples. We further discuss the twisted structures of layered materials from a structural point of view. After introducing screw-dislocation-driven growth and showing its generality in the crystal growth of layered materials, we further discuss how the unique structures of screw dislocations influence the stacking and symmetry of layered materials. Moreover, we highlight how screw dislocations enable interlayer twisting through the Eshelby twist mechanism and the non-Euclidean twist mechanism. In the end, the challenges and future perspectives are discussed for the study of screw-dislocated layered materials to control the stacking and twist for exotic physical properties.

2D Janus Transition Metal Dichalcogenides: Properties and Applications

The successful fabrication of Janus transition metal dichalcogenide (TMD) monolayer has sparked extensive research interests in various fields, such as nanoelectronics, optoelectronics, valleytronics, and catalysis. Janus TMDs can not only inherit the advantages of conventional TMDs but also produce novel properties which are different from their counterparts. The breaking of vertical mirror symmetry can induce a variety of novel properties, such as Rashba spin splitting, vertical piezoelectricity, and long exciton lifetime. Moreover, the intrinsic electric field that originates from the vertical asymmetry can serve as a superior platform for tuning the interlayer coupling when forming van der Waals structures. In this mini review, the recent key research progresses of 2D Janus TMDs, including the fundamental properties and potential applications, are briefly summarized, and the existing challenges are also presented.

Ultrahigh-Quality Infrared Polaritonic Resonators Based on Bottom-Up-Synthesized van der Waals Nanoribbons.

van der Waals nanomaterials supporting phonon polariton quasiparticles possess extraordinary light confinement capabilities, making them ideal systems for molecular sensing, thermal emission, and subwavelength imaging applications, but they require defect-free crystallinity and nanostructured form factors to fully showcase these capabilities. We introduce bottom-up-synthesized α-MoO3 structures as nanoscale phonon polaritonic systems that feature tailorable morphologies and crystal qualities consistent with bulk single crystals. α-MoO3 nanoribbons serve as low-loss hyperbolic Fabry-Pérot nanoresonators, and we experimentally map hyperbolic resonances over four Reststrahlen bands spanning the far- and mid-infrared spectral range, including resonance modes beyond the 10th order. The measured quality factors are the highest from phonon polaritonic van der Waals structures to date. We anticipate that bottom-up-synthesized polaritonic van der Waals nanostructures will serve as an enabling high-performance and low-loss platform for infrared optical and optoelectronic applications.