Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice

Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional （3D） Weyl semimetals, 3D Dirac semimetMs, and 3D node-line semimetals （NLSs）. In particular, several compounds （e.g., certain 3D graphene networks, Cu3PdN, Ca3P2 ） were discovered to be 3D NLSs, in which the conduction and valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional （2D） Dirac semimetal （e.g., graphene）, 2D topological semimetals are much less investigated. Here we propose a new concept of a 2D NLS and suggest that this state could be realized in a new mixed lattice （named as HK lattice） composed by Kagome and honeycomb lattices. It is found that A3B2 （A is a group-liB cation and B is a group-VA anion） compounds （such as Hg3As2） with the HK lattice are 2D NLSs due to the band inversion between the cation Hg-s orbital and the anion As-pz orbital with respect to the mirror symmetry. Since the band inversion occurs between two bands with the same parity, this peculiar 2D NLS could be used as transparent conductors. In the presence of buckling or spin-orbit coupling, the 2D NLS state may turn into a 2D Dirac semimetal state or a 2D topological crystalline insulating state. Since the band gap opening due to buckling or spin-orbit coupling is small, Hg3As3 with the HK lattice can still be regarded as a 2D NLS at room temperature. Our work suggests a new route to design topological materials without involving states with opposite parities.

Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

Research on two-dimensional(2D) materials and related van der Waals heterostructures(vdWHs) is intense and remains one of the leading topics in condensed matter physics.Lattice vibrations or phonons of a vdWH provide rich information,such as lattice structure,phonon dispersion,electronic band structure and electron–phonon coupling.Here,we provide a mini review on the lattice vibrations in vdWHs probed by Raman spectroscopy.First,we introduced different kinds of vdWHs,including their structures,properties and potential applications.Second,we discussed interlayer and intralayer phonon in twist multilayer graphene and MoS2.The frequencies of interlayer and intralayer modes can be reproduced by linear chain model(LCM)and phonon folding induced by periodical moiré potentials,respectively.Then,we extended LCM to vdWHs formed by distinct 2D materials,such as MoS2/graphene and hBN/WS2 heterostructures.We further demonstrated how to calculate Raman intensity of interlayer modes in vdWHs by interlayer polarizability model.

Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry＇s theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.

Two-Dimensional Breather Lattice Solutions and Compact-Like Discrete Breathers and Their Stability in Discrete Two-Dimensional Monatomic β-FPU Lattice

We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.

Localized self-trapping in two-dimensional molecular lattice with interaction between Wannier-Mott excitons and phonon lattice

We investigate the interactions of lattice pbonons with Wannier-Mott exciton, the exciton that has a large radius in two-dimensional molecular lattice, by the method of continuum limit approximation, and obtain that the self-trapping can also appear in two-dimensional molecular lattice with a harmonic and nonlinear potential. The exciton effect on molecular lattice does not distort the molecular lattice but only makes it localized and the localization can also react, again through phonon coupling, to trap the energy and prevents its dispersion.

Localized self-trapping in the two-dimensional discrete molecular lattice with the interaction between Frenkel excitons and phonons

We investigate the interactions of lattice phonons with Frenkel exciton, which has a small radius in a twodimensional discrete molecular lattice, by the virtue of the quasi-discreteness approximation and the method of multiplescale, and obtain that the self-trapping can also appear in the two-dimensional discrete molecular lattice with harmonic and nonlinear potential. The excitons＇ effect on the molecular lattice does not distort it but only causes it to localize which enables it to react again through phonon coupling to trap the energy and prevent its dispersion.

Density of States in Two-Dimensional Square Lattices Around Half Filling with Strong Impurities

We calculate the lowest-order quantum-interference correction to the density of states (DOS) of weakly-disordered two-dimensional (2D) tight-binding square lattices around half filling. The impurities are assumed to be randomly distributed on small fractions of the sites, and have a-strong potential yielding a unitary-limit scattering. In addition to the usual diffusive modes in the retarded-advanced channel, there appear diffusive pi modes in the retarded-retarded (or advanced-advanced) channel due to the existence of particle-hole symmetry. It is found that the pi-mode diffuson gives rise to a logarithmic suppression to the DOS near the band center, which prevails over the positive correction contributed by pi-mode cooperon. As a result, the DOS is subject to a negative total correction. This result is qualitatively different from the divergent behavior of the DOS at the band center predicted previously for disordered 2D two-sublattice models with the particle-hole symmetry.

Effect of Magnetic-Impurity Scattering in Disordered Two-Dimensional Square Lattices Around Half Filling

Abstract Weak-localization effect in the presence of magnetic impurities is studied in disordered two-dimensional tight-binding square lattices around half filling. Both the magnetic and nonmagnetic impurities are assumed to be randomly distributed on small fractions of the sites, while the nonmagnetic impurities have a strong potential yielding a unitary-limit scattering. We derive in details the expressions of diffusive π modes in the retarded-retarded （or advanced- advanced） channel, which result from the existence of particle-hole symmetry. The quantum interference correction to the density of states is calculated. While the magnetic-impurity scattering suppresses the quantum correction from π-mode cooperon, it does not affect the contribution of π-mode diffuson.

A Note on Casoratian Solutions to Two-Dimensional Toda Lattice

In this short paper we generalize the conditions that Casoratian entries satisfy for the two-dlmenslonal Toda lattice. Although we finally conclude that our generalization is trivial in some sense for getting new solutions, our discussion is still helpful for the study of Wronskian technique.

Experimental realization of two-dimensional single-layer ultracold gases of ^(87)Rb in an accordion lattice

We experimentally realize two-dimensional(2D) single-layer ultracold gases of ^(87)Rb by dynamically tuning the periodicity of a standing wave, known as accordion lattice. In order to load ^(87)Rb Bose-Einstein condensate into single dark fringe node of the blue detuning optical lattice, we reduce the lattice periodicity from 26.7 μm to 3.5 μm with the help of an acousto-optic deflector(AOD) to compress the three-dimensional BEC adiabatically into a flat and uniform quasi-2D single-layer. We describe the experimental procedure of the atoms loading into the accordion lattice in detail and present the characteristics of the quasi-2D ultracold gases. This setup provides an important platform for studying in-and out-of equilibrium physics, phase transition and 2D topological matter.

The interaction of nonlinear waves in two-dimensional lattice

This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincarge-Lighthill-Kuo perturbation method, it obtains two Korteweg-de Vries equations for nonlinear waves in both the ζ and η directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u（υ） up to O（ε^3） order is given.

Periodic,quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein-Gordon lattice

We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.

Generating two-dimensional quantum gases with high stability

Quantum gas microscopy has enabled the study on intriguing properties of ultracold atoms in optical lattices.It provides the cutting-edge technology for manipulating quantum many-body systems.In such experiments,atoms have to be prepared into a two-dimensional(2D)system for being resolved by microscopes with limited depth of focus.Here we report an experiment on slicing a single layer of the atoms trapped in a few layers of pancake-shaped optical traps to create a 2D system.This technique is implemented with a microwave“knife”,i.e.,a microwave field with a frequency defined by the resonant condition with the Zeeman-shifted atomic levels related to a gradient magnetic field.It is crucial to keep a stable preparation of the desired layer to create the 2D quantum gas for future experimental applications.To achieve this,the most important point is to provide a gradient magnetic field with low noises and slow drift in combination with a properly optimized microwave pulse.Monitoring the electric current source and the environmental magnetic field,we applied an actively stabilizing circuit and realized a field drift of 0.042(3)mG/hour.This guarantees creating the single layer of atoms with an efficiency of 99.92(3)%while atoms are hardly seen in other layers within 48 hours,satisfying future experimental demands on studying quantum many-body physics.

Raman scattering study of two-dimensional magnetic van der Waals compound VI3

The layered magnetic van der Waals materials have generated tremendous interest due to their potential applications and importance in fundamental research.Previous x-ray diffraction(XRD)studies on the magnetic van der Waals compound VI3,revealed a structural transition above the magnetic transition but output controversial analysis on symmetry.In this paper we carried out polarized Raman scattering measurements on VI3 from 10 K to 300 K,with focus on the two Ag phonon modes at^71.1 cm^-1 and 128.4 cm-1.Our careful symmetry analysis based on the angle-dependent spectra demonstrates that the crystal symmetry can be well described by C2h rather than D3d both above and below structural phase transition.We further performed temperature-dependent Raman experiments to study the magnetism in VI3.Fano asymmetry and anomalous linewidth drop of two Ag phonon modes at low temperatures,point to a significant spin-phonon coupling.This is also supported by the softening of 71.1-cm^-1 mode above the magnetic transition.The study provides the fundamental information on lattice dynamics and clarifies the symmetry in VI3.And spin-phonon coupling existing in a wide temperature range revealed here may be meaningful in applications.

Two-dimensional Dirac materials:Tight-binding lattice models and material candidates

The discovery of graphene has led to the devotion of intensive efforts,theoretical and experimental,to produce two-dimensional(2D)materials that can be used for developing functional materials and devices.This work provides a brief review of the recent developments in the lattice models of 2D Dirac materials and their relevant real material counterparts that are crucial for understanding the origins of 2D Dirac cones in electronic band structures as well as their material design and device applications.We focus on the roles of lattice symmetry,atomic orbital hybridization,and spin-orbit coupling in the presence of a Dirac cone.A number of lattice models,such as honeycomb,kagome,ruby,star,Cairo,and line-centered honeycomb,with different symmetries are reviewed based on the tight-binding approach.Inorganic and organic 2D materials,theoretically proposed or experimentally synthesized to satisfy these 2D Dirac lattice models,are summarized.

Multi-relaxation-time lattice Boltzmann simulations of lid driven flows using graphics processing unit

Large eddy simulation （LES） using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components （D2Q9） lattice Boltzmann equation （LBE） with multi-relaxation-time （MRT） to simulate incompressible turbulent cavity flows with the Reynolds numbers up to 1 × 10^7. To improve the computation efficiency of LBM on the numerical simulations of turbulent flows, the massively parallel computing power from a graphic processing unit （GPU） with a computing unified device architecture （CUDA） is introduced into the MRT-LBE-LES model. The model performs well, compared with the results from others, with an increase of 76 times in computation efficiency. It appears that the higher the Reynolds numbers is, the smaller the Smagorinsky constant should be, if the lattice number is fixed. Also, for a selected high Reynolds number and a selected proper Smagorinsky constant, there is a minimum requirement for the lattice number so that the Smagorinsky eddy viscosity will not be excessively large.

二维胶体晶体衍射图样的研究及其衬底形变测量

以柔性衬底上自组装的聚苯乙烯微球阵列为研究对象,基于光学衍射方法与晶体结构理论,设计了积木式胶体晶体衍射图样演示及其衬底形变测量装置.该装置不仅可以直观地展现微球排列方式与衍射图样的对应关系,实现宏观衍射图样到微观晶格结构的知识过渡,而且还可以实现衬底形变测量,实验结果与理论预测符合良好.另外,该装置具有可视化、测量精度高、易操作的特点,可作为拓展实验应用于本科实验教学.

Classical spin liquid state in a rhombic lattice metal-organic framework

Discovering more and new geometrically frustrated systems remains an active point of inquiry in fundamental physics for the existence of unusual states of matter.Here,we report spin-liquid-like behavior in a two-dimensional(2D)rhombic lattice Fe-metal-organic framework(Fe-MOF)with frustrated antiferromagnetism.This Fe-MOF exhibits a high frustration factor f=|θCW|/TN≥315,and its long-range magnetic order is suppressed down to 180 mK.Detailed theoretical calculations demonstrate strong antiferromagnetic coupling between adjacent Fe3+ions,indicating the potential of a classical spin-liquid-like behavior.Notably,a T-linear heat capacity parameter,γ,originating from electronic contributions and with magnetic field independence up to 8 T,can be observed in the specific heat capacity measurements at low-temperature,providing further proof for the spin-liquid-like behavior.This work highlights the potential of MOF materials in geometrically frustrated systems,and will promote the research of exotic quantum physics phenomena.

LATTICE BOLTZMANN SCHEME TO SIMULATE TWO-DIMENSIONAL FLUID TRANSIENTS

This paper proposes a lattice Boltzmann scheme to simulate two-dimensionalfluid transients. A set of multi-scale equations, which characterize the relations between thelattice Boltzmann equation and its corresponding macroscopic equations, were derived by using theChapman-Enskog expansion. Based on these multi-scale equations and the basic equations ofmultidimensional fluid transients, two special lattice Boltzmann models were established. Numericalsimulation of one-dimensional pressure wave transmission and reflection, two-dimensional wave cornerdiffraction and hydraulic transients in a concrete spiral case show that the Lattice BoltzmannMethod (LBM) is a feasible and promising approach to simulate multidimensional transient flows.

Two-dimensional novel optical lattices with multi-well traps for cold atoms or molecules

We propose some new schemes to constitute two-dimensional （2D） array of multi-well optical dipole traps for cold atoms （or molecules） by using an optical system consisting of a binary 7r-phase grating and a 2D array of rectangle microlens. We calculate the intensity distribution of each optical well in 2D array of multi-well traps and its geometric parameters and so on. The proposed 2D array of multi-well traps can be used to form novel 2D optical lattices with cold atoms （or molecules）, and form various novel optical crystals with cold atoms （or molecules）, or to perform quantum computing and quantum information processing on an atom chip, even to realize an array of all-optical multi-well atomic （or molecular） Bose- Einstein condensates （BECs） on an all-optical integrated atom （or molecule） chip.