2D Crystals Research Articles

On the reduction in the effects of radiation damage to two-dimensional crystals of organic and biological molecules at liquid-helium temperature

We have studied the fading of electron diffraction spots from two-dimensional (2D) crystals of paraffin (C44H90), purple membrane (bacteriorhodopsin) and aquaporin 4 (AQP4) at stage temperatures between 4K and 100K. We observed that the diffraction spots at resolutions between 3 Å and 20 Å fade more slowly at liquid-helium temperatures compared to liquid-nitrogen temperatures, by a factor of between 1.2 and 1.8, depending on the specimens. If the reduction in the effective rate of radiation damage for 2D crystals at liquid-helium temperature (as measured by spot fading) can be shown to extend to macromolecular assemblies embedded in amorphous ice, this would suggest that valuable improvements to electron cryomicroscopy (cryoEM) of biological specimens could be made by reducing the temperature of the specimens under irradiation below what is obtainable using standard liquid-nitrogen cryostats.

Small angle symmetry splitting of helicene-based molecular wires on pyrolytic graphite

Synthesis of inherently chiral materials and investigation of their self-assembly into molecular wires or 2D crystals belongs to hot topics in nanotechnology. Here we report an inherent splitting of orientational symmetry of 10–500 nm long molecular wires assembled from 3 nm chiral helicene-based macrocycles on atomically flat HOPG surface. The symmetry splitting of molecular wire orientation by a small angle of (6.5 ± 0.5)° is attributed to interaction of individual helicene-based macrocycle with HOPG. There is a good correlation between experimental AFM data and theoretical simulations using ReaxFF force field and Lennard-Jones (L-J) potential. In particular the new 1000 times faster computational method based on L-J potential and sequential addition of molecules is able to simulate formation of molecular wires and emergence of their symmetry splitting, which was not possible to do by conventional molecular dynamics. The method is also sensitive to chirality of the studied molecules; enantiomers and racemates placed on HOPG form different arrangements. This opens new possibilities for simulations of large molecular systems.

2D Pb‐Halide Perovskites Can Self‐Heal Photodamage Better than 3D Ones

AbstractAdding a 2D character to halide perovskite (HaP) active layers in ambient‐protected cells can improve their stability drastically, which is not obvious from the hydrophobicity of the large cations that force the HaP into a 2D structure. Results of two‐photon confocal microscopy are reported to study inherent photo‐stability of 2D Pb iodide HaPs in the interior of single crystals. Compared to 3D HaP crystals, 2D ones have higher photo‐stability and, under a few sun‐equivalent conditions, self‐heal efficiently after photo‐damage. Using both photoluminescence (PL) intensities (as function of time after photo‐damage) and spectra, self‐healing dynamics of 2D HaP (C4H9NH3)2PbI4, 2D/3D (C4H9NH3)2(CH3NH3)2Pb3I10 and 3D MAPbI3 are compared. Differences in response to photo‐damage and self‐healing ability from different degrees of photo‐damage are found between these HaPs. Based on the findings, a possible chemical mechanism for photo‐damage and self‐healing of the 2D HaPs is suggested: the layered lattice arrangement limits out‐diffusion of degradation products, facilitating damage reversal, leading to better 2D HaP photo‐stability and self‐healing uniformity than for 2D/3D HaPs. One implication of the layered structures’ resilience to photo‐damage is transfer of their increased stability to devices made with them, such as photovoltaic solar cells and light‐emitting diodes.

Recent advances in graphene and other 2D materials

The isolation of the first two-dimensional material, graphene – a monolayer of carbon atoms arranged in a hexagonal lattice - opened new exciting opportunities in the field of condensed matter physics and materials. Its isolation and subsequent studies demonstrated that it was possible to obtain sheets of atomically thin crystals and that these were stable, and they also began to show its outstanding properties, thus opening the door to a whole new family of materials, known as two-dimensional materials or 2D materials. The great interest in different 2D materials is motivated by the variety of properties they show, being candidates for numerous applications. Additionally, the combination of 2D crystals allows the assembly of composite, on-demand materials, known as van der Waals heterostructures, which take advantage of the properties of those materials to create functionalities that otherwise would not be accessible. For example, the combination of 2D materials, which can be done with high precision, is opening up opportunities for the study of new challenges in fundamental physics and novel applications. Here we review the latest fundamental discoveries in the area of 2D materials and offer a perspective on the future of the field.

Directional etching for high aspect ratio nano-trenches on hexagonal boron nitride by catalytic metal particles

Stimulated by the attractive performance of multi-dimensional heterostructures involving hexagonal boron nitride (hBN), intense attentions have been paid to creation of sharp boundary/interface, which could bring hBN nano-structures additional appealing physical properties. However, the lack of controllable synthesis limits further experimental investigation on hBN nano-structures. Here, the directional etching of transitional metal nano-particles (NPs) on the surface of hBN to produce nano-trenches with sharp edges was systematic investigated. It is found that, only Pt and Ir NPs can produce armchair-oriented nano-trenches at low H2 partial pressure, while other transitional metals lead to zigzag oriented nano-trenches. The density and width of the nano-trenches always increase with etching temperature and the pre-treated solution concentration while the trench orientation depends on both H2 partial pressure and etching temperature. The aspect ratio of nano-trenches may reach several thousand under optimized conditions. The method exhibited here shines a light on edge-selective patterning of 2D crystals.

Global Alignment of Carbon Nanotubes via High Precision Microfluidic Dead‐End Filtration (Adv. Funct. Mater. 10/2022)

1D Crystals The controllable alignment of carbon nanotubes (CNTs) in large-area thin-films has been a longstanding challenge to the scientific community. In article number 2107411, Benjamin S. Flavel and co-workers develop a custom-built micro-fluidic filtration setup that can repeatedly produce globally aligned films over an area of 3.8 cm2 from both positively and negatively charged CNTs.

Microstructured Phononic Crystal Isolates from Ultrasonic Mechanical Vibrations

The functioning of many micro-electromechanical devices with parts oscillating at high frequencies require isolation from external vibration. Phononic crystals, presenting band-gaps in the dispersion spectrum, i.e., interval of frequency in which propagating waves are attenuated, can provide an effective solution for vibration shielding at the microscale. In the present work, we design—through numerical simulations—a 3D phononic crystal with a micrometric unit cell able to work as vibration isolator for a micro system. We exploit the direct writing technique based on two-photon polymerization to realize three prototypes of different dimensions. Experimental measurements performed with a Michelson interferometer demonstrate the effectiveness of the proposal.

Quantized conductance and superconductivity of twisted graphene and other 2D crystals explained with the Eyring’s rate process theory and free volume concept

Theoretical treatment originally intended to address proton transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride has been borrowed to examine conductivity and superconductivity of single layer, bilayer, trilaye, even multilayer graphene or other 2D crystals. The theory was developed based on the Eyring’s rate process theory and free volume concept under an assumption that protons behave exactly same as electrons, thus obtained equations should hold for electron conduction through a 2D crystal, too. These equations show that at high temperature regions conductivity should be scaled as σ=ν1e2h, similar to fractional/integral quantum Hall effect; while at low temperature regions conductivity should be scaled as σ=ν22eh, similar to Josephson junction effect. At high temperature regions, the parameter α, related to electron packing structure and critical to superconductivity, is canceled out and not present in derived equations, indicating that no superconductivity occurs in high temperature regions. While in low temperature regions, superconductivity should appear at temperature about 5 K or even higher, depending on electron packing structures. The fractional parameter f that can vary from fully close status with f=0 or full open status with f=1 should be controlled by the twisted angles. Our equations predict that superconductivity and insulating states are closely adjacent to each other; ”on” and ”off” superconductivity can be observed periodically when twisted angles are precisely varied from one direction to another. The volume ratio of conduction electrons to the conductive area and thickness play a critical role in superconductivity, implying that varying the area and/or thickness could have similar impact as twisted angle does. Our findings shed new lights on conductivity of stacked graphene or other 2D crystals.

Interfacial ferroelectricity in marginally twisted 2D semiconductors

Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of new metamaterials. Here we demonstrate a room temperature ferroelectric semiconductor that is assembled using mono- or few-layer MoS2. These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of atomic arrangement at the interface of two 2D crystals, enables ferroelectric domains with alternating out-of-plane polarization arranged into a twist-controlled network. The last can be moved by applying out-of-plane electrical fields, as visualized in situ using channelling contrast electron microscopy. The observed interfacial charge transfer, movement of domain walls and their bending rigidity agree well with theoretical calculations. Furthermore, we demonstrate proof-of-principle field-effect transistors, where the channel resistance exhibits a pronounced hysteresis governed by pinning of ferroelectric domain walls. Our results show a potential avenue towards room temperature electronic and optoelectronic semiconductor devices with built-in ferroelectric memory functions.

Crystallization-Driven Controlled Two-Dimensional (2D) Assemblies from Chromophore-Appended Poly(L-lactide)s: Highly Efficient Energy Transfer on a 2D Surface.

A rational approach towards precision two-dimensional (2D) assemblies by crystallization-driven self-assembly (CDSA) of poly(L-lactides) (PLLAs), end-capped with dipolar dyes like merocyanine (MC) or naphthalene monoimide (NMI) and hydrophobic pyrene (PY) or benzene (Bn) is described. PLLA chains crystallize into diamond-shaped platelets in isopropanol, which forces the terminal dyes to assemble into a 2D array on the platelet surface by either dipolar interactions or π-stacking and exhibit tunable emission. Dipolar dyes play a critical role in imparting colloidal stability and structural uniformity to the 2D crystals, which is partly compromised for hydrophobic ones. Co-crystallization between NMI- and PY-labeled PLLAs yields similar diamond-shaped co-platelets with highly efficient (≈80 %) Förster Resonance Energy Transfer on the 2D surface. Further, the "living" CDSA method confers enlarged, segmented block co-platelets using one of the homopolymers as "seed" and the other as "unimer".

Crystallization‐Driven Controlled Two‐Dimensional (2D) Assemblies from Chromophore‐Appended Poly(L‐lactide)s: Highly Efficient Energy Transfer on a 2D Surface

AbstractA rational approach towards precision two‐dimensional (2D) assemblies by crystallization‐driven self‐assembly (CDSA) of poly(L‐lactides) (PLLAs), end‐capped with dipolar dyes like merocyanine (MC) or naphthalene monoimide (NMI) and hydrophobic pyrene (PY) or benzene (Bn) is described. PLLA chains crystallize into diamond‐shaped platelets in isopropanol, which forces the terminal dyes to assemble into a 2D array on the platelet surface by either dipolar interactions or π‐stacking and exhibit tunable emission. Dipolar dyes play a critical role in imparting colloidal stability and structural uniformity to the 2D crystals, which is partly compromised for hydrophobic ones. Co‐crystallization between NMI‐ and PY‐labeled PLLAs yields similar diamond‐shaped co‐platelets with highly efficient (≈80 %) Förster Resonance Energy Transfer on the 2D surface. Further, the “living” CDSA method confers enlarged, segmented block co‐platelets using one of the homopolymers as “seed” and the other as “unimer”.

Size Dependence of Charge-Density-Wave Orders in Single-Layer NbSe2 Hetero/Homophase Junctions.

Controlling charge-density-wave (CDW) orders in two-dimensional (2D) crystals has attracted a great deal of interest because of their fundamental physics and their demand inse in miniaturized devices. In this work, we systematically studied the size-dependent CDW orders in single-layer hetero/homo-NbSe2 stacking junctions. We found that the CDW orders in the top 1T-NbSe2 layer of the junctions are highly dependent on its lateral size. For the 1T/2H-NbSe2 heterojunction, the critical lateral size of 1T-NbSe2 islands for the formation of well-defined CDW orders is ∼26 nm, whereas below 15 nm, the CDW orders melt. However, for the 1T/1T-NbSe2 homojunction, the CDW orders in the islands can persist even with a lateral size of <11 nm. Our findings illuminate the fresh phenomenon of size-dependent CDW orders existing in 2D van der Waals hetero/homojunctions and provide useful information for the control of CDW orders.

Oriented Growth of Thin Films of Covalent Organic Frameworks with Large Single-Crystalline Domains on the Water Surface.

It has been a longstanding challenge to rationally synthesize thin films of organic two-dimensional (2D) crystals with large single-crystalline domains. Here, we present a general strategy for the creation of 2D crystals of covalent organic frameworks (COFs) on the water surface, assisted by a charged polymer. The morphology of the preorganized monomers underneath the charged polymer on the water surface and their diffusion were crucial for the formation of the organic 2D crystals. Thin films of 2D COFs with an average single-crystalline domain size of around 3.57 ± 2.57 μm2 have been achieved, and their lattice structure, molecular structure, and grain boundaries were identified with a resolution down to 3 Å. The swing of chain segments and lattice distortion were revealed as key factors in compensating for the misorientation between adjacent grains and facilitating error corrections at the grain boundaries, giving rise to larger single-crystalline domains. The generality of the synthesis method was further proved with three additional 2D COFs. The oriented single-crystalline domains and clear grain boundaries render the films as model materials to study the dependence of the vertical conductivity of organic 2D crystals on domain sizes and chemical structures, and significant grain boundary effects were illustrated. This study presents a breakthrough in the controlled synthesis of organic 2D crystals with structural control at the molecular level. We envisage that this work will inspire further investigation into the microstructure-intrinsic property correlation of 2D COFs and boost their application in electronics.

Machine Learning Guided Synthesis of Flash Graphene.

Advances in nanoscience have enabled the synthesis of nanomaterials, such as graphene, from low-value or waste materials through flash Joule heating. Though this capability is promising, the complex and entangled variables that govern nanocrystal formation in the Joule heating process remain poorly understood. In this work, machine learning (ML) models are constructed to explore the factors that drive the transformation of amorphous carbon into graphene nanocrystals during flash Joule heating. An XGBoost regression model of crystallinity achieves an r2 score of 0.8051 ± 0.054. Feature importance assays and decision trees extracted from these models reveal key considerations in the selection of starting materials and the role of stochastic current fluctuations in flash Joule heating synthesis. Furthermore, partial dependence analyses demonstrate the importance of charge and current density as predictors of crystallinity, implying a progression from reaction-limited to diffusion-limited kinetics as flash Joule heating parameters change. Finally, a practical application of the ML models is shown by using Bayesian meta-learning algorithms to automatically improve bulk crystallinity over many Joule heating reactions. These results illustrate the power of ML as a tool to analyze complex nanomanufacturing processes and enable the synthesis of 2D crystals with desirable properties by flash Joule heating.

Systematic investigation of emergent particles in type-III magnetic space groups

In three-dimensional (3D) crystals, emergent particles arise when two or multiple bands contact and form degeneracy (band crossing) in the Brillouin zone. Recently a complete classification of emergent particles in 3D nonmagnetic crystals, which described by the type-II magnetic space groups (MSGs), has been established. However, a systematic investigation of emergent particles in magnetic crystals has not yet been performed, due to the complexity of the symmetries of magnetically ordered structures. Here, we address this challenging task by exploring the possibilities of the emergent particles in the 674 type-III MSGs. Based on effective k.p Hamiltonian and our classification of emergent particles [Yu et al., Sci. Bull. 67, 375 (2022) DOI:10.1016/j.scib.2021.10.023], we identify all possible emergent particles, including spinful and spinless, essential and accidental particles in the type-III MSGs. We find that all emergent particles in type-III MSGs also exist in type-II MSGs, with only one exception, i.e. the combined quadratic nodal line and nodal surface (QNL/NS). Moreover, tabulations of the emergent particles in each of the 674 type-III MSGs, together with the symmetry operations, the small corepresentations, the effective k.p Hamiltonians, and the topological character of these particles, are explicitly presented. Remarkably, combining this work and our homemade SpaceGroupIrep and MSGCorep packages will provide an effcient way to search topological magnetic materials with novel quasiparticles.

A Scalable Network Model for Electrically Tunable Ferroelectric Domain Structure in Twistronic Bilayers of Two-Dimensional Semiconductors.

Moiré structures in small-angle-twisted bilayers of two-dimensional (2D) semiconductors with a broken-symmetry interface form arrays of ferroelectric (FE) domains with periodically alternating out-of-plane polarization. Here, we propose a network theory for the tunability of such FE domain structure by applying an electric field perpendicular to the 2D crystal. Using multiscale analysis, we derive a fully parametrized string-theory-like description of the domain wall network (DWN) and show that it undergoes a qualitative change, after the arcs of partial dislocation (PD) like domain walls merge (near the network nodes) into streaks of perfect screw dislocations (PSD), which happens at a threshold displacement field dependent on the DWN period.

Strain Switching in van der Waals Heterostructures Triggered by a Spin‐Crossover Metal–Organic Framework

AbstractVan der Waals heterostructures (vdWHs) provide the possibility of engineering new materials with emergent functionalities that are not accessible in another way. These heterostructures are formed by assembling layers of different materials used as building blocks. Beyond inorganic 2D crystals, layered molecular materials remain still rather unexplored, with only few examples regarding their isolation as atomically thin layers. Here, the family of van der Waals heterostructures is enlarged by introducing a molecular building block able to produce strain: the so‐called spin‐crossover (SCO). In these metal–organic materials, a spin transition can be induced by applying external stimuli like light, temperature, pressure, or an electric field. In particular, smart vdWHs are prepared in which the electronic and optical properties of the 2D material (graphene and WSe2) are clearly switched by the strain concomitant to the spin transition. These molecular/inorganic vdWHs represent the deterministic incorporation of bistable molecular layers with other 2D crystals of interest in the emergent fields of straintronics and band engineering in low‐dimensional materials.

Two-tone Doppler cooling of radial two-dimensional crystals in a radio-frequency ion trap

We study the Doppler-cooling of radial two-dimensional (2D) Coulomb crystals of trapped barium ions in a radiofrequency trap. Ions in radial 2D crystals experience micromotion of an amplitude that increases linearly with the distance from the trap center, leading to a position-dependent frequency modulation of laser light in each ion's rest frame. We use two tones of Doppler-cooling laser light separated by approximately 100 MHz to efficiently cool distinct regions in the crystals with differing amplitudes of micromotion. This technique allows us to trap and cool more than 50 ions populating four shells in a radial 2D crystal, where with a single tone of Doppler cooling light we are limited to 30 ions in three shells. We also individually characterize the micromotion of all ions within the crystals and use this information to locate the center of the trap and to determine the Matthieu parameters ${q}_{x}$ and ${q}_{y}$.

Irreversible synthesis of an ultrastrong two-dimensional polymeric material.

Polymers that extend covalently in two dimensions have attracted recent attention1,2 as a means of combining the mechanical strength and in-plane energy conduction of conventional two-dimensional (2D) materials3,4 with the low densities, synthetic processability and organic composition of their one-dimensional counterparts. Efforts so far have proven successful in forms that do not allow full realization of these properties, such as polymerization at flat interfaces5,6 or fixation of monomers in immobilized lattices7-9. Another frequently employed synthetic approach is to introduce microscopic reversibility, at the cost of bond stability, to achieve 2D crystals after extensive error correction10,11. Here we demonstrate a homogenous 2D irreversible polycondensation that results in a covalently bonded 2D polymeric material that is chemically stable and highly processable. Further processing yields highly oriented, free-standing films that have a 2D elastic modulus and yield strength of 12.7 ± 3.8 gigapascals and 488 ± 57 megapascals, respectively. This synthetic route provides opportunities for 2D materials in applications ranging from composite structures to barrier coating materials.

Surface Plasmon Resonance of Two-Dimensional Gold Colloidal Crystals Formed on Gold Plates.

The free electrons inside precious metals such as Au vibrate when the surface of the metal is irradiated with an electromagnetic wave of an appropriate frequency. This oscillation is referred to as surface plasmon resonance (SPR), and the resonance frequency varies with permittivity of the medium around the metal. SPR sensors are widely applied in the fields of bioscience and pharmaceutical sciences, including biosensing for drug discovery, biomarker screening, virus detection, and testing for food safety. Here, we fabricated a metal-insulator-metal (MIM) SPR sensor by constructing two-dimensional (2D) regular array of Au colloidal particles (2D colloidal crystals) on an insulator layer over a thin Au film coated on a glass substrate surface. The 2D crystals were fabricated by electrostatically adsorbing negatively charged three-dimensional crystals onto a positively charged thin insulator formed on Au film. The plasmon peaks/dips from the MIM structure were measured in aqueous solutions of ethylene glycol (EG) at various concentrations. Multiple plasmon peaks/dips were observed due to the localized SPR (LSPR) of the Au particles and the Fano resonance between the Au particles and thin film. The plasmon peaks/dips shifted to higher wavelengths on increasing EG concentrations due to an increase in the refractive index of the media. The observed peak/dip shift was approximately twice that of LSPR from an isolated Au particle. We expect the present MIM substrate will be useful as a highly sensitive sensor in the pharmaceutical field.