Two-dimensional Lattice Research Articles

Designer Spin Models in Tunable Two-Dimensional Nanographene Lattices.

Motivated by recent experimental breakthroughs, we propose a strategy for designing two-dimensional spin-lattices with competing interactions that lead to nontrivial emergent quantum states. We consider S = 1/2 nanographenes with C3 symmetry as building blocks, and we leverage the potential to control both the sign and the strength of exchange with first neighbors to build a family of spin models. Specifically, we consider the case of a Heisenberg model in a triangle-decorated honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions whose ratio can be varied in a wide range. On the basis of the exact diagonalization of both Fermionic and spin models, we predict a quantum phase transition between a valence bond crystal of spin singlets with triplon excitations living in a Kagomé lattice and a Néel phase of effective S = 3/2 in the limit of dominant ferromagnetic interactions.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

Amino acid chiral amplification using Monte Carlo dynamic.

This study investigates the stability of chiral-molecule solution phases, with a specific focus on amino acids. The model framework is based on a two-dimensional square lattice model, where individual sites may be occupied by oriented chiral molecules or structureless solvent particles. Utilizing the Glauber dynamics and statistical mechanical formalism, as previously introduced and examined by Lombardo et al., we explore the influence of temperature, amino acid concentration, enantiomeric excess, and homochiral interaction strength on nucleation mechanisms, equilibrium phase behavior, and crystal composition. Our findings offer thermodynamic insights into the chiral amplification process of amino acids, contributing to a deeper understanding of the underlying processes.

Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model.

We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum MonteCarlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.

Computation insights of kagome structure for probing electronic and thermodynamic properties by applying external factors such as strain, spin-orbital coupling, and external magnetic field

In this study, we explored the electronic properties of a two-dimensional (2D) kagome lattice in the presence of an external magnetic field, spin-orbit coupling (SOC), and strain. Our focus was on investigating the energy-dependent behavior of the electronic heat capacity and paramagnetic spin susceptibility in response to changing factors. Employing the Green's function approach, we successfully determined the energy dependence of the electronic heat capacity and paramagnetic susceptibility using the tight-binding model. Notably, at low energies, the electronic heat capacity almost reaches the Schottky anomaly peak, while the paramagnetic susceptibility sharply decreases. Furthermore, we conducted a detailed investigation of the energy-dependent paramagnetic susceptibility and electronic heat capacity of a kagome lattice monolayer, considering the influences of SOC and magnetic field factors. Our investigation of the density of states (DOS) in the presence of SOC suggests that semimetal-to-insulator phase transitions occur. Additionally, throughout our study, we observed variations in the DOS spectrum, indicating the influence of both compressive and tensile strains. We found that these alterations, along with the splitting of levels under different conditions, led to changes in the material's electrical properties.

Room temperature polaritonic soft-spin XY Hamiltonian in organic–inorganic halide perovskites

Abstract Exciton–polariton condensates, due to their nonlinear and coherent characteristics, have been employed to construct spin Hamiltonian lattices for potentially studying spin glass, critical dephasing, and even solving optimization problems. Here, we report the room-temperature polariton condensation and polaritonic soft-spin XY Hamiltonian lattices in an organic–inorganic halide perovskite microcavity. This is achieved through the direct integration of high-quality single-crystal samples within the cavity. The ferromagnetic and antiferromagnetic couplings in both one- and two-dimensional condensate lattices have been observed clearly. Our work shows a nonlinear organic–inorganic hybrid perovskite platform for future investigations as polariton simulators.

Chiral breathing-valley locking in two-dimensional kagome lattice Ta3I8

The exploration of valley-related physics is essential to the development and refinement of valleytronics. Here, a paradigm called chiral breathing-valley locking (CBVL) is proposed, in which two chiral “breathing” phases are completely locked to their valley indexes. Utilizing first-principles calculations, a two-dimensional (2D) kagome lattice with large spontaneous valley polarization (VP), namely, monolayer Ta3I8, is proposed to realize CBVL. There are two breathing phases with chiral symmetry in Ta3I8, and they can change to each other under some conditions. The valley indexes change between “−K” and “K” along the breathing of the two chiral symmetric phases, so CBVL can be obtained. Remarkably, the VP is up to 199.7 meV, so CBVL can cause the obvious switching of the anomalous valley Hall effect (AVHE). Additionally, a 2D Janus Kagome structure TaI4X4 is constructed to confirm experimentally the feasibility of electric field modulation on the CBVL. The built-in electric field and the breathing mode can mutually influence each other in TaI4X4, which provides a synergistic regulation of the AVHE. Our findings broaden the horizon for exploring AVHE materials and provide a platform for future valleytronic applications.

Viscoelastic mechanics of two-dimensional granular lattices

We study the rate-dependent mechanics of viscoelastic granular packings. Using a two-dimensional, square lattice of particles as a motif mimicking nominally mono-disperse granular packings, we perform a suite of finite element simulations under rate-dependent uniaxial compaction followed by unloading. The focus is on understanding the macroscopic force–displacement relations and the porosity evolution as a function of the viscoelastic relaxation parameters. For the constituent parameters considered here, the force–displacement relations show a two-stage power-law behavior, which is associated with the relative contributions of viscous dissipation and elastic effects at a particular loading rate. For a given loading rate, the nonlinearity of the porosity evolution depends on the constituent parameters and is found to be captured well by a simple analytical model. The heterogeneity of stresses during the compaction and recovery phases provide insights into the emergent complex micromechanics in simple granular motifs. Upon unloading, particles may experience transient tensile pressures, which could have implications on their failure.

Effect of a flat band on a multiband two-dimensional Lieb lattice with intra- and interband interactions

In this study, we explore the effect of a single flat band in the electronic properties of a ferromagnetic two-dimensional Lieb lattice using the multiband Hubbard model with polarized carriers, spin-up and spin-down. We employ the self-consistent dynamical mean field theory and a Green functions cumulant expansion around the atomic limit to obtain the correlated densities of states while varying the intra- and interband interactions. Our findings demonstrate a renormalization of the correlated density of states in both the spin-up and spin-down carriers as we varied the intra- and interband interactions. We conclude that the presence of a flat band enables the system to maintain a metal state with itinerant ferromagnetism in the spin-up carrier.

Photonic Floquet Skin-Topological Effect.

Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.

A study on melting characteristics of micron aluminum particles by lattice Boltzmann method

In this article, a two-dimensional lattice Boltzmann model, utilizing enthalpy as a basis, has been constructed to explore the melting behavior of aluminum particles in the micron size range. The study investigates the impacts of several key factors such as particle size, Rayleigh number, Stefan number, and porosity on temperature distribution, liquid fraction, solid-liquid interface, and melting end time. The findings demonstrate that an increase in particle size stimulates the melting process, with a weakened effect observed as particle size continues to increase. Rayleigh number has a significant effect on natural convection and heat transfer, promoting the development of these processes. Additionally, Stefan number presents a noticeable impact on the melting process, with a more apparent effect in the range of low Stefan numbers. Finally, the increase of porosity proves to be a compelling factor in the promotion of the melting process.

Two-dimensional lattice with an imaginary magnetic field

Two-dimensional lattice with an imaginary magnetic field

An improved axisymmetric interfacial lattice Boltzmann flux solver for large-density-ratio multiphase flows

In this paper, an improved axisymmetric interfacial lattice Boltzmann flux solver abandoning the previous predictor-corrector scheme is proposed. Unlike the previous model starting from the two-dimensional standard lattice Boltzmann method (LBM), the present method is developed using the axisymmetric LBM, which directly incorporates the axisymmetric effects into the distribution functions. As a result, the proposed solver does not need the corrector step involving complicated space derivatives. It makes this method simpler and more computationally efficient. In the present solver, the resultant governing equation is globally resolved by the finite volume method, while the fluxes are reconstructed by local application of the axisymmetric LBM. Therefore, the inconsistency between the local reconstruction and the global governing equation can be eliminated because the global equation can be strictly derived from the axisymmetric LBM, which holds stronger physical basis than the previous method. Numerical experiments about the interface capturing and the multiphase flows are conducted to test the proposed model. Results show that the present method is superior to the fractional step solver in terms of the accuracy, stability, and computational efficiency. In addition, this solver has the capacity of simulating large-density-ratio and complex interfacial change.

Error-correcting codes for fermionic quantum simulation

Utilizing the framework of \mathbb{Z}_2ℤ2 lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any \lfloor \frac{d-1}{2} \rfloor⌊d−12⌋-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

Two-Dimensional Momentum State Lattices

Two-Dimensional Momentum State Lattices

Structure of the two-component S-layer of the archaeon Sulfolobus acidocaldarius.

Surface layers (S-layers) are resilient two-dimensional protein lattices that encapsulate many bacteria and most archaea. In archaea, S-layers usually form the only structural component of the cell wall and thus act as the final frontier between the cell and its environment. Therefore, S-layers are crucial for supporting microbial life. Notwithstanding their importance, little is known about archaeal S-layers at the atomic level. Here, we combined single-particle cryo electron microscopy, cryo electron tomography, and Alphafold2 predictions to generate an atomic model of the two-component S-layer of Sulfolobus acidocaldarius. The outer component of this S-layer (SlaA) is a flexible, highly glycosylated, and stable protein. Together with the inner and membrane-bound component (SlaB), they assemble into a porous and interwoven lattice. We hypothesise that jackknife-like conformational changes in SlaA play important roles in S-layer assembly.

Simulating cumulus clouds based on self-organized criticality

Recently it was shown that self-organized criticality is an important component of the dynamics of cumulus clouds (Najafi et al., 2021). Here we introduce a new algorithm to simulate cumulus clouds in two-dimensional square lattices, based on two important facts: the cohesive energy of wet air parcels and a sand-pile-type diffusion of cloud segments. The latter is realized by considering the evaporation/condensation of air parcels in various regions of the cloud, which enables them to diffuse to the neighboring regions. The results stemming from this model are in excellent agreement with observations reported in the above-cited paper, in which the exponents were determined for two-dimensional earth-to-sky RGB cloud images. The exponents obtained at the lowest condensation level in our model are consistent with the exponents observed in nature. We find that the cloud fields obtained from our model are fractal, with the outer perimeter having a fractal dimension of Df=1.25±0.01. Furthermore, the distributions of the radius of gyration and the loop length follow a power-law function with exponents τr=2.3±0.1 and τl=2.1±0.1, respectively. The loop Green function is found to be logarithmic with the radius of gyration of the loops following the observational results. The winding angle statistic of the external perimeter of the cloud field is also analyzed, showing an exponent in agreement with the fractal dimension, which may serve as the conformal invariance of the system.

Realization of two-sublattice exchange physics in the triangular lattice compound Ba3Er(BO3)3

Geometric frustration commonly occurs in materials where magnetic rare-earth ions are arranged on a two-dimensional triangular lattice. These compounds have been gaining significant attention lately, as they hold the promise of revealing unique quantum states of matter. However, little attention has been devoted to cases where spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{2}$$\\end{document} rare-earth ions are substituted with ions exhibiting higher spin multiplicities. Here, we successfully synthesize high-quality single crystal samples of Ba3Er(BO3)3, which is part of the family of triangular lattice compounds. In our experiments, conducted at extremely low temperatures (around 100 millikelvin), we observe two sublattice exchange interactions in Ba3Er(BO3)3, resulting in the hexagonal lattice spins exhibiting a mixture of ferromagnetic and antiferromagnetic tendencies. Our theoretical analysis suggest that this behavior may be attributed to the distinct positions of magnetic ions within the crystal lattice. However, the presence of quantum effects adds an extra layer of complexity to our findings, calling for further exploration.

Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states

The kagome lattice is a well-known model system for the investigation of strong correlation and topological electronic phenomena due to the intrinsic flat band, magnetic frustration, etc. Introducing chirality into the kagome lattice would bring about new physics due to the unique symmetry, which is still yet to be fully explored. Here we report the investigation on a two-dimensional chiral kagome lattice utilizing tight binding band calculation and topological index analysis. It is found that the periodic chiral kagome lattice would bring about a robust zero-energy flat band. Furthermore, in the Su–Schrieffer–Heeger type dimer-/trimerized breathing chiral kagome lattice with particular edge terminations, topological corner states or metallic edge states would appear, implying new candidates for the second-order topological insulator. We also proposed the construction strategy for such lattices employing the scanning tunneling microscope atom manipulation technique.

Realization of all two-dimensional Bravais lattices with metasurface-based interference lithography

Abstract Proximity-field nanopatterning (PnP) have been used recently as a rapid, cost-effective, and large-scale fabrication method utilizing volumetric interference patterns generated by conformal phase masks. Despite the effectiveness of PnP processes, their design diversity has not been thoroughly explored. Here, we demonstrate that the possibility of generating any two-dimensional lattice with diverse motifs. By controlling the amplitude, phase, and polarization of each diffraction beam, we can implement all two-dimensional Bravais lattices in three-dimensional space. The results may provide diverse applications that require three-dimensional nanostructures from optical materials and structural materials to energy storage or conversion materials.