Two-dimensional Hexagonal Crystals Research Articles

Simulation Computation of Two-dimensional Hexagonal Honeycomb Photonic Crystals Energy Band Structure Based on COMSOL

This study employs COMSOL software, integrating the plane wave expansion method and finite element method, to simulate and analyze the energy band structure of two-dimensional hexagonal honeycomb photonic crystals. By setting parameters and conducting scans, this paper not only maps out the electric field intensity and energy band distribution but also discovers a significant enhancement of electric field intensity at the lattice's high symmetry points, indicating a higher likelihood of electromagnetic waves' presence at these points. Furthermore, the notable energy gaps between the second and third energy bands provide directions for subsequent research. The findings of this study are of significant value for research and development in optoelectronic integration and communication, demonstrating an effective comprehensive method for analyzing the energy band structure of two-dimensional hexagonal honeycomb photonic crystals.

Quantum transport regimes in quartic dispersion materials with Anderson disorder

Mexican-hat-shaped quartic dispersion manifests itself in certain families of single-layer two-dimensional hexagonal crystals such as compounds of groups III–VI and groups IV–V as well as elemental crystals of group V. A quartic band forms the valence band edge in various of these structures, and some of the experimentally confirmed structures are GaS, GaSe, InSe, SnSb, and blue phosphorene. Here, we numerically investigate strictly one-dimensional and quasi-one dimensional (Q1D) systems with quartic dispersion and systematically study the effects of Anderson disorder on their transport properties with the help of a minimal tight-binding model and Landauer formalism. We compare the analytical expression for the scaling function with simulation data to distinguish the domains of diffusion and localization regimes. In one dimension, it is shown that conductance drops dramatically at the quartic band edge compared to the quadratic case. As for the Q1D nanoribbons, a set of singularities emerge close to the band edge, suppressing conductance and leading to short mean-free-paths and localization lengths. Interestingly, wider nanoribbons can have shorter mean-free-paths because of denser singularities. However, the localization lengths sometimes follow different trends. Our results display the peculiar effects of quartic dispersion on transport in disordered systems.

Large-scale surface hopping simulation of charge transport in hexagonal molecular crystals: role of electronic coupling signs

In large-scale surface hopping simulations with a huge number of electronic states, trivial crossings could easily lead to incorrect long-range charge transfer and induce large numerical errors. We here study the charge transport in two-dimensional hexagonal molecular crystals with a parameter-free full crossing corrected global flux surface hopping method. Fast time-step size convergence and system size independence have been realized in large systems containing thousands of molecular sites. In hexagonal systems, each molecular site has six nearest neighbours. We find that the signs of their electronic couplings have a strong impact on the charge mobility and delocalization strength. In particular, changing the signs of electronic couplings can even lead to a transition from hopping to band-like transport. In comparison, such phenomena cannot be observed in extensively studied two-dimensional square systems. This is attributed to symmetry of the electronic Hamiltonian and distribution of the energy levels. Due to its high performance, the proposed approach is promising to be applied to more realistic and complex systems for molecular design.

Engineering Majorana corner modes from two-dimensional hexagonal crystals

Second order topological insulator can be engineered from two-dimensional materials with strong spin-orbit coupling and in-plane Zeeman field. In proximity to superconductor, topological superconducting phase could be induced in the two-dimensional materials, which host Majorana corner modes at the intersection between two zigzag edges. Two types of tight binding models in hexagonal lattice, which include $p_{z}$ or $p_{x,y}$ orbit(s) in each lattice site, are applied to engineer two-dimensional materials in topological superconducting phase. In both models, the condition that induces the second order topological superconductor requires nonuniform value of either in-plane Zeeman fields or superconductor pairing parameters in two sublattices. The finite size effect of the second model is weaker than that of the first model.

Performance analysis of the salinity based on hexagonal two-dimensional photonic crystal: computational study

We have designed a unique structure for a liquid sensor based on two-dimensional PCs with a triangular lattice constant in the periodicity by drilling a hexagonal cylinder in a dielectric host material. Using the COMSOL multiphysics approach, we investigated the given structure and sensing performance based on the finite element method. We will optimize two-dimensional hexagonal photonic crystals to localize the photonic band gap region in the mid and far infra-red frequency range, as water is a good absorber for this range of frequencies. Then, we inject the central hexagonal cylinder with saline water and calculate the sensor parameters for different values of the refractive index of saline water at different frequencies related to photonic band gaps. We could reach the optimum conditions of the salinity sensor as the half diagonal of the hexagonal shape (R) = 500 nm, the perpendicular distance between the two diagonal hexagonal (D) = 250 nm, and the number of periods (N) = 5, which gives a high efficiency with sensitivity (S) = 525 nm/RIU, figure of merit (FOM) = 80.7 RIU−1, and quality factor (Q) = 375. The effects of structural characteristics on sensing performance are investigated, with new approaches for improving salinity sensors proposed. Furthermore, traditional salinity sensors may be replaced by the proposed method in the photo-sensing application, which is simple and practical for use in the thermal desalination techniques.

Novel insights into the unique intrinsic sensing essences of 2D tin chalcogenides for ethanol: From hexagonal SnS2 to orthorhombic SnS

Introducing orthorhombic SnS phase into two-dimensional (2D) hexagonal SnS2 crystal to form in-plane heterojunctions has become a promising approach to facilitate the sensitivity of SnS2 towards trace gases. However, its surface sensitization mechanism remains to be exploited in addition to the heterointerface effect. Hence, to dig into it, we explored the surface adsorption of SnS and SnS2 from unique surface electron configurations by combing experimental, computational and bionic approaches. Taking ethanol vapor as the target gas, orthorhombic SnS shows rapid detection of trace ethanol with a sub-ppm level at room temperature (RT). In contrast, hexagonal SnS2 is more suitable for detecting ethanol vapor with much higher concentrations (above 50 ppm). First-principles calculations and porcupine quill models further reveal that unlike the inactive symmetry of electrons on SnS2 surface, the rotational symmetry breaking of the stereochemically-active SnS surface leads to the oriented rearrangement of its surface electrons, which greatly facilitates the adsorption of trace ethanol molecules on SnS. On these basis, we renew the design concept of SnS–SnS2 in-plane heterostructures. This work reveals the structure-property relationship between the crystalline structures and gas-sensitive characteristics of 2D tin chalcogenides from a brand-new perspective, and helps the design and research of novel lateral heterostructures.

Higher-Order Topological Spin Hall Effect of SoundSupported by the National Natural Science Foundation of China (Grant Nos. 11675116 and 11904060), the Jiangsu Distinguished Professor Fund, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

We theoretically propose a reconfigurable two-dimensional (2D) hexagonal sonic crystal with higher-order topology protected by the six-fold, C6, rotation symmetry. The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit cell. In the nontrivial phase, the sonic crystal realizes the topological spin Hall effect in a higher-order fashion: (i) the edge states emerging in the bulk band gap exhibit partial spin-momentum correlation and are gapped due to the reduced spatial symmetry at the edges. (ii) The gapped edge states, on the other hand, stabilize the topological corner states emerging in the edge band gap. The partial spin-momentum correlation is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta, where the pseudospin is emulated by the acoustic orbital angular momentum. We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.

Poisson’s ratio of two-dimensional hexagonal crystals: A mechanics model study

The Poisson’s ratio of two-dimensional hexagonal crystals has been widely studied due to its fundamental and fantastic nature. However, the issue involved in the regulation strategy and in the bounds of Poisson’s ratio of two-dimensional hexagonal crystals has not been addressed. In this work, we predict that the Poisson’s ratio of two-dimensional hexagonal crystals can be controlled by modifying the structural interaction therein, where the lower bound and upper bound are −1∕3 and +1, respectively. Furthermore, molecular simulations verify these predictions. Finally, the underlying mechanism is revealed as the interplay between two deformation modes (i.e., bond stretching and angle changing). This work provides an universal regulation strategy to tune the Poisson’s ratio of two-dimensional hexagonal crystals, and determines fundamental limits on the Poisson’s ratio of two-dimensional hexagonal crystals.

Unusual Effect of Iodine Ions on the Self-Assembly of Poly(ethylene glycol)-Capped Gold Nanoparticles.

We use synchrotron X-ray reflectivity and grazing incidence small-angle X-ray scattering to investigate the surface assembly of the poly(ethylene glycol) (PEG)-grafted gold nanoparticles (PEG-AuNPs) induced by different salts. We find that NaCl and CsCl behave as many other electrolytes, namely, drive the PEG-AuNPs to the vapor/suspension interface to form a layer of single-particle depth and organize them into very high-quality two-dimensional (2D) hexagonal crystals. By contrast, NaI induces the migration of PEG-AuNPs to the aqueous surface at much higher surface densities than the other salts (at similar concentrations). The resulting 2D ordering at moderate NaI concentrations is very short ranged, and at a higher NaI concentration, the high-density monolayer is amorphous. Considering NaCl, CsCl and the majority of salts behave similarly, this implicates the anomaly of iodine ion (I-) in this unusual surface population. We argue that the influence of most electrolytes on the PEG corona preserves the polymer in the θ-point with sufficient flexibility to settle into a highly ordered state, whereas I- has a much more severe effect on the corona by collapsing it. The collapsed PEG renders the grafted AuNP a nonspherical shaped complex that, although packs at high density, cannot organize into a 2D ordered arrangement.

Mesoscale Analysis of Homogeneous Dislocation Nucleation

Abstract We perform atomistic simulations of dislocation nucleation in two-dimensional (2D) and three-dimensional (3D) defect-free hexagonal crystals during nanoindentation with circular (2D) or spherical (3D) indenters. The incipient embryo structure in the critical eigenmode of the mesoregions is analyzed to study homogeneous dislocation nucleation. The critical eigenmode or dislocation embryo is found to be localized along a line (or plane in 3D) of atoms with a lateral extent, ξ, at some depth, Y*, below the surface. The lowest energy eigenmode for mesoregions of varying radius, rmeso, centered on the localized region of the critical eigenmode is computed. The energy of the lowest eigenmode, λmeso, decays very rapidly with increasing rmeso and λmeso ≈ 0 for rmeso≳ξ. The analysis of a mesoscale region in the material can reveal the presence of incipient instability even for rmeso≲ξ but gives reasonable estimate for the energy and spatial extent of the critical mode only for rmeso≳ξ. When the mesoregion is not centered at the localized region, we show that the mesoregion should contain a critical part of the embryo (and not only the center of embryo) to reveal instability. This scenario indicates that homogeneous dislocation nucleation is a quasilocal phenomenon. Also, the critical eigenmode for the mesoscale region reveals instability much sooner than the full system eigenmode. We use mesoscale analysis to verify the scaling laws shown previously by Garg and Maloney in 2D [2016, “Universal Scaling Laws for Homogeneous Dissociation Nucleation During Nano-Indentation,” J. Mech. Phys. Solids, 95, pp. 742–754.] for the size, ξ, and depth from the surface, Y*, of the dislocation embryo with respect to indenter radius, R, in full 3D simulations.

Highly efficient subwavelength imaging in mid-IR range using high dielectric hexagonal lattice photonic crystals

Two-dimensional hole-type hexagonal lattice photonic crystals with low and high dielectric materials have been investigated for the aim of achieving all-angle negative refraction for subwavelength imaging. Structures composed of Si (eSi = 12 at IR) and PbTe (ePbTe = 36 at mid-IR) have been regarded, as sample materials. All-angle negative refraction has been achieved for the TM polarization in the second band under the light line in a broad bandwidth of 26% and 31% for low and high dielectric materials, respectively. The optimized radii for low and high dielectric PCs equal to 0.31a and 0.35a and provide the spatial full width at half maximum of 0.37λ and 0.38λ, respectively. The structures present TE gap in the operating wavelength range, and this feature of the structures can be applied to design polarization beam splitters in integrated space division multiplexing.

Preparation and Properties of Graphene-based Inorganic Nanocomposites

Graphene is a two-dimensional hexagonal monoatomic layer crystal composed of carbon atoms, which exhibits the shape of a honeycomb and plays an important role in the fields of optics and mechanics. It also has the advantages of high specific surface area, strong chemical stability and special planar structure. It is an ideal carrier for carrying various inorganic compounds and is suitable for the development of high performance graphene-based inorganic nanocomposites.[1] Based on this, the paper introduces the characteristics of graphene, expounds the related content of graphene-based inorganic nanocomposites, and studies the preparation methods and properties of graphene-based inorganic nanocomposites.

Antiferromagnetic spin valve based on a heterostructure of two-dimensional hexagonal crystals

Spin valves consisting of heterostructures of single-layer hexagonal crystal on an antiferromagnetic substrate or of bilayer hexagonal crystal intercalated between two (anti)ferromagnetic insulators, with the current-in-plane geometry, are proposed. The two-dimensional hexagonal crystals such as graphene, silicene, germanene, and stanene are modeled by the tight binding model of honeycomb lattice. The magnetization orientation of the antiferromagnetic substrate(s) controls the band gap and topological properties of bulk, which in turn control the transport of three types of spin valve geometries: (i) the in-plane transport of bulk; (ii) the transport of topological edge states along nanoribbon with bulk gap; (iii) the transport of chiral edge state along domain wall. The heterostructures are investigated by a tight binding model with an (anti)ferromagnetic exchange field, Hubbard interaction and(or) spin-orbital coupling. For the first type of spin valve geometry, the Hubbard interaction could enlarged the effective band gap of bulk, which in turn improve the sensitivity of the spin valves to the antiferromagnetic exchange field. For the second and third types of spin valve geometries, the topological phase diagrams of varying types of heterostructures with spin-orbital coupling serve as guideline for designing the spin valve. The coexistence of the Hubbard interaction and the spin-orbital coupling could enlarge the topological gap in bulk and improve the quality of the chiral edge states at the domain walls between regions with different topological numbers.

Effect of Polydispersity on the Phase Diagram of Colloid Systems

A theoretical model is proposed that describes the experimentally observed phase diagram of colloidal dispersions of disk-shaped polydisperse particles. In the framework of the phenomenological theory of phase transitions, it is shown that if disk-shaped particles have polydispersity comparable in thickness and disk diameter, then the following sequence of phase transitions should be expected with increasing volume fraction of ϕ particles: an isotropic liquid (I); a nematic liquid crystal (N), in which the director n sets the preferred orientation of the disk normal; and the discotic (columnar) phase (C), in which the disklike molecules aggregate into liquid columns, and the latter form a two-dimensional hexagonal crystal consisting of liquid columns. However, when the particles forming the colloidal dispersion do not have any polydispersity in thickness (but the polydispersity in the particle diameter is preserved), another sequence of phase transitions takes place, in which the columnar phase is replaced by a smectic liquid crystal (S); that is, particles form a system of equidistant liquid layers. This work proposes and discusses the mechanisms of this behavior and new predictions that follow from this consideration.

Controlled growth and Atomic-scale Characterization of Two-dimensional hexagonal boron nitride crystals

Two-dimensional (2D) hexagonal boron nitride (h-BN) is a fascinating material for variety of applications such as graphene-based devices, transparent/bendable electronics, and deep ultraviolet emitters. However, its technological applications are contingent upon tunable and scalable growth. Here, we demonstrate reproducible and tunable growth of high-quality h-BN crystals on Cu via chemical vapor deposition (CVD) through a precise control of the BN precursor’s flow during growth. We present synthesis of both epitaxially-grown triangular flakes and large-area continuous films with tunable thickness ranging from monolayer to 11-layer thick. Using a combination of electron microscopy imaging, spectroscopy, and diffraction analysis, we thoroughly study morphology, thickness, chemistry, grain size, and atomic structure of the grown h-BN crystals. This study could pave the way for developing controlled and reproducible growth of high-quality h-BN crystals with tunable thickness and morphology.

Three-dimensional interconnected mesoporous anatase TiO2 exhibiting unique photocatalytic performances

In this article, an ordered two-dimensional (2D) hexagonal mesoporous anatase crystals–silica nanocomposite was first synthesized using synchronous-assembly of surfactant and inorganic precursors molecules, and then a three-dimensional (3D) interconnected mesoporous anatase TiO2 was prepared via an “extracting silica” approach. The results show that the mesopore channels in our titania are highly connected by plenty of 3D uniform intrawall mesopores while retaining mesostructural integrity and regularity. The TiO2 prepared is completely anatase crystalline with uniform nanocrystals (13.0nm in size) and a high specific surface area (∼145m2/g). This method is mild, simple and can be easily repeatable. The photocatalytic degradation rates of Acid Red 1 (0.173min−1) and microcystin−LR (2.57min−1) on the interconnected mesoporous TiO2 are very high, which are 41.6 and 2.85 times higher than that of the parent sample; 29.2 and 7.20 times that of P25 photocatalyst, respectively. These results clearly demonstrated that the 3D interconnected mesostructure played a key role in the activity increments. In addition, our photocatalysts are considerably stable and reusable. To the best of our knowledge, such results have not been seen in the literature before. Furthermore, the fundamentals of this study would provide new insights for the rational design and preparation of 3D highly interlinked mesoporous metal-oxides with unique photocatalytic performances.

Observation of acoustic valley vortex states and valley-chirality locked beam splitting

The Letter reports an experimental observation of the classical version of valley polarized states in a two-dimensional hexagonal sonic crystal, where the inversion-symmetry breaking of scatterers induces an omnidirectional frequency gap. The acoustic valley states, which carry specific linear momenta and orbital angular momenta, were selectively excited by external Gaussian beams and conveniently confirmed by the pressure distribution outside the crystal, according to the criterion of momentum conservation. The vortex nature of such intriguing crystal states was directly characterized by scanning the phase profile inside the crystal. In addition, we observed a peculiar beam splitting phenomenon, in which the separated beams are constructed by different valleys and locked to the opposite vortex chirality. The exceptional sound transport, encoded with valley-chirality locked information, may serve as the basis of designing conceptually novel acoustic devices with unconventional functions.

Room-temperature light emission from an airbridge double-heterostructure microcavity of Er-doped Si photonic crystal

We experimentally demonstrate an efficient enhancement of luminescence from two-dimensional (2D) hexagonal photonic crystal (PC) airbridge double-heterostructure microcavity with Er-doped silicon (Si) as light emitters on siliconon-insulator (SOI) wafer at room temperature. A single sharp resonant peak at 1 529.6 nm dominates the photoluminescence (PL) spectrum with the pumping power of 12.5 mW. The obvious red shift and the degraded quality factor (Q-factor) of resonant peak appear with the pumping power increasing, and the maximum measured Q-factor of 4 905 is achieved at the pumping power of 1.5 mW. The resonant peak is observed to shift depending on the structural parameters of PC, which indicates a possible method to control the wavelength of enhanced luminescence for Si-based light emitters based on PC microcavity.

Zigzag nanoribbons of two-dimensional silicene-like crystals: magnetic, topological and thermoelectric properties

The effects of electron–electron and spin–orbit interactions on the ground-state magnetic configuration and on the corresponding thermoelectric and spin thermoelectric properties in zigzag nanoribbons of two-dimensional hexagonal crystals are analysed theoretically. The thermoelectric properties of quasi-stable magnetic states are also considered. Of particular interest is the influence of Coulomb and spin–orbit interactions on the topological edge states and on the transition between the topological insulator and conventional gap insulator states. It is shown that the interplay of both interactions also has a significant impact on the transport and thermoelectric characteristics of the nanoribbons. The spin–orbit interaction also determines the in-plane magnetic easy axis. The thermoelectric properties of nanoribbons with in-plane magnetic moments are compared to those of nanoribbons with edge magnetic moments oriented perpendicularly to their plane. Nanoribbons with ferromagnetic alignment of the edge moments are shown to reveal spin thermoelectricity in addition to the conventional one.

Theory of thermal expansion in 2D crystals

The thermal expansion in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to is due to anharmonic couplings between in-plane stretching modes and out-of-plane bending (flexural modes). Genuine in-plane anharmonicities give a positive contribution to . The competition between these two effects can lead to a change of sign (crossover) from a negative value of in a temperature (T) range to a positive value of for in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two-dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in-plane and out-of-plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature . Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known.