Triangular Lattice Research Articles

Role of biquadratic exchange on thermodynamic quantities in anisotropic Heisenberg model

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within Oguchi approximation. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.

Dumbbell Impurities in 2D Crystals of Repulsive Colloidal Spheres Trap Dislocations.

Impurity-induced defects play a crucial role for the properties of crystals, but little is known about impurities with anisotropic shape. Here, we study how colloidal dumbbells distort and interact with a hexagonal crystal of charged colloidal spheres at a fluid interface. We find that subtle differences in the dumbbell length determine whether it induces a local distortion of the lattice or traps a dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes toward controlling material properties and understanding fundamental questions in phase transitions through particle-bound dislocations.

Supersymmetry on the honeycomb lattice: Resonating charge stripes, superfrustration, and domain walls

Supersymmetry on the honeycomb lattice: Resonating charge stripes, superfrustration, and domain walls

Chemical Design of Spin Frustration to Realize Topological Spin Glasses.

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal-organic framework (MOF) platform, Ni3(pymca)3X3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni2+-based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin-spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Phase-modulation-induced reconfigurable rotating photonic lattices in atomic vapors.

We propose a method to prepare optically induced rotating hexagonal and honey-comb photonic lattices by employing the phase modulated three-beam interference in atomic vapors with electromagnetically induced transparency. The phase differences among the three beams are dynamically elaborated to synthesize the circular motion (in transverse dimensions) of waveguides in the photonic lattices. Further, we verify this model experimentally in the case of low-speed modulation. A weak Gaussian probe field is sent into the constructed helical photonic lattices to image their structures under electromagnetically induced transparency (EIT). The motion trajectories of the sites on the discretized output patterns exhibit repeated circles, advocating the formation of rotating lattices. By introducing phase modulations to involved beams, we provide a continent way for producing transverse motions in waveguide arrays with reconfigurability in rotational direction, radius, and speed. This work looks forward to promising applications in topological photonics with great popularity.

Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems.

The generalized Wigner crystal (GWC) is a novel quantum phase of matter driven by further-range interaction at fractional fillings of a lattice. The role of further-range interaction as the driver for the incompressible state is akin to the Wigner crystal. On the other hand, the significant role of commensurate filling is akin to the Mott insulator. Recent progress in simulator platforms presents unprecedented opportunities to investigate quantum melting in the strongly interacting regime through synergy between theory and experiments. However, the earlier theory literature presents diverging predictions. We study the quantum freezing of GWC through large-scale density matrix renormalization group simulations of a triangular lattice extended Hubbard model. We find a single first-order phase transition between the Fermi liquid and the sqrt[3]×sqrt[3] GWC state. The GWC state shows long-range antiferromagnetic 120° Néel order. Our results present the simplest answers to the question of the quantum phase transition into the GWC phase and the properties of the GWC phase.

Investigating the role of graphene in the formation and stability of [formula omitted]-phase antimonene islands

Two-dimensional materials have shown tremendous potential for various technological applications. Particularly, 2D antimony exhibits high applicability in electronics, sensors, and batteries. This 2D material, known as antimonene, presents two stable phases: α (rectangular lattice) and β (honeycomb lattice), whose formation depends on the substrate where antimony is deposited. In this study, we investigated the growth of antimonene islands on graphene, forming an antimonene/graphene heterostructure. To demonstrate the significance of graphene in the synthesis of antimonene, we also studied antimony deposited on a bare copper foil similar to the one used for the graphene substrate. Antimony deposition exhibits the β phase antimonene structure when deposited on top of monolayer graphene, but not when deposited on a bare copper foil, nor on top of multilayer graphene. Additionally, we investigated the stability of the heterostructure after exposure to air. Pure antimony islands are formed when evaporated in high vacuum on top of graphene and copper substrates, and antimony atoms oxidize upon exposure to air. After annealing the sample in ultra-high-vacuum at temperatures lower than 200 °C, more than half of pure antimony is recovered and almost all oxidized antimony is desorbed from the graphene substrate. In contrast, almost none of the oxidized antimony is desorbed from the bare copper substrate, highlighting the key role of the heterostructure on the formation and preservation of the physical and chemical properties of the deposited 2D material.

Topologically protected bound modes in non-neighboring hexagonal lattices

In the last decade, the study of wave localization and guiding has gained a renewed interest thanks to the introduction of the concept of topological protection. Originally developed in the field of quantum mechanics, topological protection has successively inspired the search for its analogue in other physical domains, including elasticity. In this context, periodic hexagonal lattices have been proposed as ideal candidates to realize these concepts. In this work, we explore the dynamic behavior of discrete hexagonal lattices with third nearest neighbor connections. First, the formation and transition of multiple Dirac cones above a critical value of the relative stiffness between the first and third nearest neighbor connections is derived. Then, the formation of extremely localized modes (i.e., bound modes) at the interface between regions formed by lattices which are inverted copies of each other is demonstrated. Our results show that this localization derives from a type of interface satisfying a point reflection symmetry for which the considered chain decouples into two identical copies at the high symmetry point of the Brillouin zone. Our findings open novel avenues for topological waveguiding and confinement with potential applications in surface acoustic wave devices.

Designed honeycomb lattice for improving vibration control

Honeycombs represent common cellular structures characterised by two-dimensional arrays of unit cells arranged in-plane and stacked parallelly in the out-of-plane direction, exhibiting a periodic structure. Due to the interconnected network of these unit cells, honeycombs possess higher porosity and lower mass density than their matrix materials, resulting in superior specific stiffness/strength and specific energy absorption. The arrangement of repeating unit cells profoundly impacts the mechanical properties of these lightweight materials. This study explores a 2D metamaterial cellular system inspired by the lightweight characteristics of honeycombs. In this system, squared honeycomb cells with additional lumped masses can influence vibrating modes. Unlike conventional methods employing discrete mass-spring resonators, this approach intentionally adds masses to create complete or incomplete stop bands wherein wave propagation is either wholly or partially suppressed along specific directions. The dispersion curves of wave bands and the sensitivity of bandgaps concerning design parameters are estimated using the finite element method and Block's theorem. Numerical simulations demonstrate the stop band behaviour, providing insights for optimisation strategies and a deeper comprehension of these remarkable cellular material systems and improvements in the design with enhanced vibro-acoustics performance and control.

High-resolution mid-infrared image transport by a chalcogenide multi-core fiber

Abstract We have successfully demonstrated high-resolution mid-infrared image transport by a multi-core fiber made of chalcogenide glasses.
The fiber cores are arranged on a triangular lattice, and adjacent cores have different core diameters to reduce cross-talk between them.
We tested the resolution of the fiber using different fineness patterns and found that it can resolve better than 25 lp/mm at a wavelength of 9.3 μm.
This demonstrates the potential of the fiber for high-resolution thermal imaging inside the human body.

Synthesis and characterization of a two-dimensional antiferromagnet KNiB4O6F3 with triangular spin lattice

We prepared a layered antiferromagnet KNiB4O6F31 by hydrothermal synthesis, and characterized its structure and physical properties by X-ray diffraction, magnetization and specific heat measurements as well as thermal stability, FTIR and UV-vis-NIR measurements. 1 consists of layers of composition [NiB4O6F3]- separated by layers of K+ cations. And Ni2+ ions are arranged in slightly distorted triangular pattern in each [NiB4O6F3]- layer. The magnetic susceptibility measurements indicate no divergence between the zero-field-cooled and field-cooled curves down to 7.9 K, below which a long-range order takes place as verified by specific heat measurements. The M(H) curve linearly increases when the field is weak (below ∼2 T), confirming that the ground state of 1 is antiferromagnetic. At 7 T, the magnetization of 1 is 1.67 μB which is lower than the saturation magnetization.

Nonlinear elasticity tailoring and failure mode manipulation of functionally graded honeycombs under large deformation

Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.

Design and numerical investigation of the 3D reinforced re-entrant auxetic and hexagonal lattice structures for energy absorption properties

Lattice Structures (LS) are widely recognized for their light weight and excellent mechanical properties. In this study, strut reinforcement technique is applied to enhance the energy absorption properties of 3D re-entrant auxetic (Aux) and hexagonal (Hex) LS. Numerical investigation using finite element analysis (FEA) was carried out to understand the mechanical and energy absorption properties of the novel designs through quasi-static compression test. The uniaxial loading results of the reinforced designs were compared to the traditional 3D hexagonal and re-entrant auxetic LS. In order to numerically simulate the mechanical behaviour of 3D printed LS, mechanical properties of experimentally studied PA2200 matrix material (manufactured via additive manufacturing) was used. Study of the mechanical behaviour of the 3D printed LS parts is essential because additive manufacturing has the capacity to fabricate the complex LS compared to conventional manufacturing processes, and innovative LS design can provide high specific strength of parts. The stress–strain and energy absorption curve results indicate that the purposed new designs are excellent choice for energy absorption properties at large strain. The findings of this study contribute towards the novel design of 3D hexagonal and re-entrant auxetic LS for superior mechanical strength and specific energy absorption properties.

Algebraic and Geometric Methods for Construction of Topological Quantum Codes from Lattices

Current work provides an algebraic and geometric technique for building topological quantum codes. From the lattice partition derived of quotient lattices Λ′/Λ of index m combined with geometric technique of the projections of vector basis Λ′ over vector basis Λ, we reproduce surface codes found in the literature with parameter [[2m2,2,|a|+|b|]] for the case Λ=Z2 and m=a2+b2, where a and b are integers that are not null, simultaneously. We also obtain a new class of surface code with parameters [[2m,2,|a|+|b|]] from the Λ=A2-lattice when m can be expressed as m=a2+ab+b2, where a and b are integer values. Finally, we will show how this technique can be extended to the construction of color codes with parameters [[18m,4,6(|a|+|b|)]] by considering honeycomb lattices partition A2/Λ′ of index m=9(a2+ab+b2) where a and b are not null integers.

Berezinskii–Kosterlitz–Thouless Transition of the Two-Dimensional XY Model on the Honeycomb Lattice

Abstract The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional $XY$ model on the honeycomb lattice is investigated using both the techniques of Neural network (NN) and Monte Carlo simulations. It is demonstrated in the literature that, with certain plausible assumptions, the associated critical temperature $T_{\text{BKT,H}}$ is found to be ${1}/{\sqrt{2}}$ exactly. Surprisingly, the value of $T_{\text{BKT,H}}$ obtained from our NN calculations is 0.572(3), which deviates significantly from ${1}/{\sqrt{2}}$. In addition, based on the helicity modulus, the $T_{\text{BKT,H}}$ determined is 0.576(4), agreeing well with that resulting from the NN estimation. It will be interesting to carry out a more detailed analytic calculation to obtain a theoretical value consistent with the numerical result reached here.

Percolation and jamming properties in an object growth model on a triangular lattice with finite-size impurities

Percolation and jamming properties in an object growth model on a triangular lattice with finite-size impurities

Two-dimensional tetragonal carbon nitride semiconductors with fascinating electronic/optical properties and low thermal conductivity

Abstract Exploring two-dimensional (2D) tetragonal carbon nitride materials is significant for unlocking new physical properties beyond those offered by traditional hexagonal lattices. In this work, we propose three theoretically stable 2D carbon nitride monolayers with tetragonal lattices, namely T-C3N, P-C3N, and PH-C5N4. Electronic structure calculations indicate that all three monolayers exhibit semiconducting characteristics, with T-C3N showing interesting flat band features. Additionally, these three carbon nitrides exhibit anisotropic and high carrier mobilities and excellent light absorption capabilities in the visible-light and near-infrared regions. Meanwhile, the calculated thermal conductivity (κp) of PH-C5N4 is 63.9 Wm−1K−1 at room temperature, significantly outperforming T-C3N (12.2 Wm−1K−1) and P-C3N (18.9 Wm−1K−1). Phonon scattering rates and Grüneisen parameters confirm the origin for the relatively high κp in PH-C5N4. Our study proposes three tetragonal carbon nitride structures with novel physical properties, which lays a theoretical foundation for the multifunctional applications of 2D carbon nitride materials.

Designing TaC Virtual Substrates for Vertical AlxGa1−xN Power Electronics Devices

Power electronics are critical for a sustainable energy future, playing a key role in electrification and integration of renewable energy sources into the grid. Advances in ultrawide band gap materials are needed to handle higher powers in smaller form factors while reducing electrical and thermal losses. High Al content AlxGa1−xN is theoretically capable of meeting these demands, but its impact in power electronics has been severely restricted by a lack of substrates that can satisfy conductivity, lattice matching, and/or thermal expansion requirements. We demonstrate that electrically conductive TaC can be used as a virtual substrate for AlxGa1−xN heteroepitaxy. Scaleably sputtered TaC grown on Al2O3, followed by high-temperature face-to-face annealing, produces a thin film TaC template with an effective hexagonal lattice constant matched to Al0.70Ga0.30N. Annealing of the TaC promotes recrystallization, significantly improving crystallinity and reducing crystalline defects from as-deposited columnar grains to a step-and-terrace surface morphology, enabling the subsequent growth of high-quality Al0.70Ga0.30N by molecular beam epitaxy. X-ray diffraction and scanning transmission electron microscopy confirm that the AlxGa1−xN layer is heteroepitaxially aligned, strain-free, and lattice-matched, transitioning abruptly from TaC to AlxGa1−xN without intermediate phases. These results demonstrate TaC virtual substrates as electrically conductive, lattice-matched, and thermally compatible templates for vertical AlxGa1−xN devices that can meet the growing power needs of a sustainable energy future. Published by the American Physical Society 2024

Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii Physics in the Triangular Lattice Bilayer Colbaltate.

Motivated by the experiments on the triangular lattice bilayer colbaltate K_{2}Co_{2}(SeO_{3})_{3}, we consider an extended XXZ model to explore the underlying physics. The model is composed of interacting Co^{2+} dimers on the triangular lattice, where the Co^{2+} ion provides an effective spin-1/2 local moment via the spin-orbit coupling and the crystal field effect. The intradimer interaction is dominant and would simply favor the local spin singlet, and the interdimer interactions compete with the interdimer interaction, leading to rich behaviors. With the easy-axis anisotropy, it is shown that, in the ground state manifold of the intradimer Ising interaction, the system realizes an effective quantum Ising model, where the ground state is either a three-sublattice order with a mixture of antiferromagnetic Ising order and a valence-bond spin singlet or Ising disordered. The finite temperature regime realizes the Berezinskii-Kosterlitz-Thouless physics. To explore the full excitations, we incorporate the excited state manifold of the intradimer Ising interaction and establish the emergent Kugel-Khomskii physics. Thus, the triangular lattice bilayer colbaltate is an excellent platform to explore the interplay between geometrical frustration and anisotropic interactions as well as the emergent effective models and the resulting physics.

A novel strategy to produce spherical SBA-15 by polymeric macrospheres as a template for drug delivery

AbstractMesoporous silica SBA-15 has been a material widely studied for drug delivery due to its high biocompatibility and chemical stability, its ordered mesoporous cavities allow drug loading. However, it has a non-spherical particle shape, making it difficult to use in solid dosage forms, where spherical particles are preferred for better flow and distribution. In this regard, this study presented a novel strategy to produce spheric SBA-15 using polymeric macrospheres of a pharmaceutical grade acidic-resistant copolymer (Eudragit®S) stabilized with Pluronic® 123, as a template. The macrospheres of Eudragit®S were fabricated using the double emulsion (W1/O/W2) solvent-diffusion technique and then were used as a template to synthesize macrospheres of SBA-15 following acidic hydrolysis. The physicochemical analysis revealed that the SBA-15 has a spherical morphology (SEM) with pores arranged in a hexagonal lattice (TEM). The XRD showed signals at 0.71, 0.88 y 2.03 °2θ, that were indexed at the Miller indices (100), (110), (200). Nitrogen adsorption-desorption isotherms (type IV, H3) demonstrated mesoporous characteristics with a pore size of 9.3 nm, a wall thickness of 3 nm, a pore volume of 0.7538 cm³g−1, and a surface area of 640 m²g−1. These SBA-15 macrospheres also showed a zero-order release of ibuprofen. The SBA-15 formation using Eudragit®S macrospheres suggests that P123 on the macrosphere acts as a spherical core, as shown by FT-IR analysis. The acid-resistant copolymer maintained macrosphere integrity, enabling the assembly of the SBA-15 mesostructure in a 24-hour manufacturing time under acidic conditions.