Band structures of strained kagome lattices

Materials with kagome lattices have attracted significant research attention due to their nontrivial features in energy bands.We theoretically investigate the evolution of electronic band structures of kagome lattices in response to uniaxial strain using both a tight-binding model and an antidot model based on a periodic muffin-tin potential.It is found that the Dirac points move with applied strain.Furthermore,the flat band of unstrained kagome lattices is found to develop into a highly anisotropic shape under a stretching strain along y direction,forming a partially flat band with a region dispersionless along ky direction while dispersive along kx direction.Our results shed light on the possibility of engineering the electronic band structures of kagome materials by mechanical strain.

Band structures of transverse waves in nanoscale multilayered phononic crystals with nonlocal interface imperfections by using the radial basis function method

A radial basis function collocation method based on the nonlocal elastic continuum theory is developed to compute the band structures of nanoscale multilayered phononic crystals. The effects of nonlocal imperfect interfaces on band structures of transverse waves propagating obliquely or vertically in the system are studied. The correctness of the present method is verified by comparing the numerical results with those obtained by applying the transfer matrix method in the case of nonlocal perfect interface. Furthermore, the influences of the nanoscale size, the impedance ratio and the incident angle on the cut-off frequency and band structures are investigated and discussed in detail. Numerical results show that the nonlocal interface imperfections have significant effects on the band structures in the macroscopic and microscopic scale.

Synthesis and Crystal and Band Structures of YbCu_6In_6 with 3D Framework

A new intermetallic compound,YbCu6In6,has been synthesized by solid-state reaction of the corresponding pure elements in a welded tantalum tube at high temperature.Its crystal structure was established by single-crystal X-ray diffraction.YbCu6In6 crystallizes in tetragonal space group I4/mmm with a = 9.2283（5）,c = 5.4015（4）,V = 460.00（5） 3,Z = 2,Mr = 1243.20,Dc = 8.976 g/cm3,μ = 38.243 mm-1,F（000） = 1076,and the final R = 0.0258 and wR = 0.0602 for 173 observed reflections with I 〉 2σ（I）.The structure of YbCu6In6 belongs to the ThMn12 type.It is isostructural with RECu6In6（RE = Y,Ce,Pr,Nd,Gd,Tb,Dy）,containing one-dimensional（1D） [Cu10In6] cluster chain along the c axis,which is interconnected via sharing the Cu（1） atoms to form a three-dimensional（3D） [Cu6In6] framework with Yb atoms encapsulated in the 1D tunnels along the c axis.Band structure calculations based on Density Functional Theory（DFT） method indicate that YbCu6In6 is metallic.

Band Structures and Two-photon Absorption of ZnGeP_2 and AgGaS_2 Crystals

Band structure and bonding properties have been investigated in terms of periodic density functional theory（DFT） method,and two-photon absorption（TPA） spectra have been simulated by two-band model for ZnGeP2 and AgGaS2 crystals.It has been predicted that the AgGaS2 crystal has a wider window of nonlinear transmission,and the laser pumping energy larger than 1.02 and 1.35 eV will lead to deleterious TPA of higher nonlinear effect for ZnGeP2 and AgGaS2 crystals,respectively.Electron origin of TPA for them is also discussed.

Photonic band structures of quadrangular multiconnected networks

By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks （QMNs） with a different number of connected waveguide segments （NCWSs） and various matching ratio of waveguide length （MRWL）. It is found that all photonic bands are wide bands when the MRWL is integer. If the integer attribute of MRWL is broken, narrow bands will be created from the wide band near the centre of band structure. For two-segment-connected networks and three-segment-connected networks, it obtains a series of formulae of the band number and width. On the other hand, it proposes a so-called concept of two-segment-connected quantum subsystem and uses it to discuss the complexity of the band structures of QMNs. Based on these formulae, one can dominate the number, width and position of photonic bands within designed frequencies by adjusting the NCWS and MRWL. There would be potential applications for designing optical switches, optical narrow-band filters, dense wavelength-division-multiplexing devices and other correlative waveguide network devices.

MORPHOLOGY EVOLUTION IN PTFE AS A FUNCTION OF MELT TIME AND TEMPERATURE——Ⅱ.LOW MOLECULAR WEIGHT FOLDED CHAIN SINGLE CRYSTALS AND BAND STRUCTURES

The effect of sintering dispersed and bulk,low molecular weight(M_n=50,000 Da),nano-emulsionpolytetrafluoroethylene(PTFE)particles near their melting point is described.With the nascent particles consisting of ca.75 nm diameter,hexagonal,single crystals,sintering at,e.g.,350℃,results,initially,in merger of neighboring particles,followed by individual molecular motion on the substrate and the formation of folded chain,lamellar single crystals andspherulites,and on-edge ribbons.It is suggested these structures develop,with time,in the mesomorphic“melt”.Sintering ofthe bulk resin yields extended chain,band structures,as well as folded chain lamellae;end-surface to end-surface merger,possibly by end-to-end polymerization,occurs with increasing time.

Synthesis,Crystal and Band Structures,and Optical Properties of Mercury Pnictide Halide Hg_(19)As_(10)Br_(18)

A mercury pnictide halide semiconductor Hg19As10Br18（1） has been prepared by the solid-state reaction and structurally characterized by single-crystal X-ray diffraction analysis.Compound 1 crystallizes in triclinic,space group P with a = 11.262（4）,b = 11.352（4）,c = 12.309（5） ,α = 105.724（2）,β = 105.788（4）,γ = 109.0780（10）° and V = 1314.3（8） 3.The structure of 1 is composed of parallel perovskite-like layers bridged by the linearly coordinated Br atoms to form a three-dimensional framework.The optical properties were investigated in terms of the diffuse reflectance spectrum.The electronic band structure along with density of states（DOS） calculated by DFT method indicates that compound 1 is a semiconductor with an indirect band gap,and that the optical absorption is mainly originated from the charge transitions from Br-4p and As-4p to the Hg-6s states.

Electronic Band Structures of TiO_2 with Heavy Nitrogen Doping

The first-principles density-functional calculation was conducted to investigate the electronic band structures of titanium dioxide with heavy nitrogen doping （TiO2-xNx）.The calculation results indicate that when x≤0.25,isolated N 2p states appear above the valence-band maximum of TiO2 without a band-gap narrowing between O 2p and Ti 3d states.When x≥0.50,an obvious band gap narrowing between O 2p and Ti 3d states was observed along with the existence of isolated N 2p states above the valence-band of TiO2,indicating that the mechanism proposed by Asahi et al operates under heavy nitrogen doping condition.

Persistence of charge density wave against variation of band structures in V_(x)Ti_(1−x)Se_(2)(x=0–0.1)

Charge density wave(CDW)is a phenomenon that occurs in materials,accompanied by changes in their intrinsic electronic properties.The study of CDW and its modulation in materials holds tremendous significance in materials research,as it provides a unique approach to controlling the electronic properties of materials.TiSe_(2) is a typical layered material with a CDW phase at low temperatures.Through V substitution for Ti in TiSe_(2),we tuned the carrier concentration in V_(x)Ti_(1-x)Se_(2) to study how its electronic structures evolve.Angle-resolved photoemission spectroscopy(ARPES)shows that the band-folding effect is sustained with the doping level up to 10%,indicating the persistence of the CDW phase,even though the band structure is strikingly different from that of the parent compound TiSe_(2).Though CDW can induce the band fold effect with a driving force from the perspective of electronic systems,our studies suggest that this behavior could be maintained by lattice distortion of the CDW phase,even if band structures deviate from the electron-driven CDW scenario.Our work provides a constraint for understanding the CDW mechanism in TiSe_(2),and highlights the role of lattice distortion in the band-folding effect.

Reanalysis of energy band structure in the type-II quantum wells

Band structure analysis holds significant importance for understanding the optoelectronic characteristics of semiconductor structures and exploring their potential applications in practice. For quantum well structures, the energy of carriers in the well splits into discrete energy levels due to the confinement of barriers in the growth direction. However, the discrete energy levels obtained at a fixed wave vector cannot accurately reflect the actual energy band structure. In this work, the band structure of the type-II quantum wells is reanalyzed. When the wave vectors of the entire Brillouin region(corresponding to the growth direction) are taken into account, the quantized energy levels of the carriers in the well are replaced by subbands with certain energy distributions. This new understanding of the energy bands of low-dimensional structures not only helps us to have a deeper cognition of the structure, but also may overturn many viewpoints in traditional band theories and serve as supplementary to the band theory of low-dimensional systems.

Complex band structures of 1D anisotropic graphene photonic crystal

The complex band structures of a 1D anisotropic graphene photonic crystal are investigated, and the dispersion relations are confirmed using the transfer matrix method and simulation of commercial software. It is found that the result of using effective medium theory can fit the derived dispersion curves in the low wave vector.Transmission, absorption, and reflection at oblique incident angles are studied for the structure, respectively.Omni-gaps exist for angles as high as 80° for two polarizations. Physical mechanisms of the tunable dispersion and transmission are explained by the permittivity of graphene and the effective permittivity of the multilayerstructure.

Calculation of valence band structures of InAs/GaAs quantum ring and quantum dot:using numerical Fourier transform method

This article puts forward a new method in calculating the band structures of low-dimensional semiconductor structures. In this study, the valence band structures of InAs/GaAs quantum ring and lens-shaped quantum dot are calculated with four-band model, in the framework of effective-mass envelope function theory. To determine the Hamiltonian matrix elements, this article develops the numerical Fourier transform method instead of the widely used analytical integral method. The valence band mixing is considered. The hole energy levels change dramatically with the geometrical parameters of the quantum ring and quantum dot. It is demonstrated that numerical Fourier transform method can be adopted in low-dimensional structures with any shape. The results of Fourier transform method are consistent with the ones of analytical integral in literature; and they are helpful for studying and fabricating optoelectronic devices.

Theoretical studies on the band structures of superconducting solid compounds: Nb3X (X=Si, Ge, Sn, Pb)

The band structures of several analogous superconducting A-15 type solid compounds, Nb3X (X=Si, Ge, Sn, Pb), have been calculated by use of the tight-binding method within the Extended Huckel approximation (EHT). By analysis of their energy bands, densities of states and crystal orbital overlap populations, the dependence of the superconducting transition temperatures (Tc) on the electronic structures and bondings is qualitatively elucidated.

Band structure engineering in metal halide perovskite nanostructures for optoelectronic applications

Metal halide perovskite nanostructures have emerged as low-dimensional semiconductors of great significance in many fields such as photovoltaics,photonics,and optoelectronics.Extensive efforts on the controlled synthesis of perovskite nanostructures have been made towards potential device applications.The engineering of their band structures holds great promise in the rational tuning of the electronic and optical properties of perovskite nanostructures,which is one of the keys to achieving efficient and multifunctional optoelectronic devices.In this article,we summarize recent advances in band structure engineering of perovskite nanostructures.A survey of bandgap engineering of nanostructured perovskites is firstly presented from the aspects of dimensionality tailoring,compositional substitution,phase segregation and transition,as well as strain and pressure stimuli.The strategies of electronic doping are then reviewed,including defect-induced self-doping,inorganic or organic molecules-based chemical doping,and modification by metal ions or nanostructures.Based on the bandgap engineering and electronic doping,discussions on engineering energy band alignments in perovskite nanostructures are provided for building high-performance perovskite p-n junctions and heterostructures.At last,we provide our perspectives in engineering band structures of perovskite nanostructures towards future low-energy optoelectronics technologies.

Using coupling slabs to tailor surface-acoustic-wave band structures in phononic crystals consisting of pillars attached to elastic substrates

The propagation of surface acoustic waves(SAWs) in two-dimensional phononic crystals(PnCs) with and without coupling-enhancement slabs was theoretically investigated using a three-dimensional finite element method.Different piezoelectric substrates,for example,lithium niobate(LiNbO_3),gallium nitride(GaN),and aluminium nitride(A1N),were taken into account.Compared to the PnCs without coupling-enhancement slabs,the coupling between each pillar and its nearest neighbor was largely enhanced in the presence of slabs.The bandwidth of the first directional band gap increased markedly compared with its initial value for the PnCs without a slab(within square symmetry).In addition,with increasing thicknesses of the slabs bonded between neighboring pillars,the first directional band-gap and second directional band gap of the PnCs tend to merge.Therefore,the structure with coupling-enhancement slabs can be used as an excellent electrical band elimination filter for most electro-SAW devices,offering a new strategy to realize chip-scale applications in electroacoustic signal processing,optoacoustic modulation,and even SAW microfluidic devices.

Optimizing band structure of CoP nanoparticles via rich-defect carbon shell toward bifunctional electrocatalysts for overall water splitting

Transition-metal phosphides(TMPs)with high catalytic activity are widely used in the design of electrodes for water splitting.However,a major challenge is how to achieve the trade-off between activity and stability of TMPs.Herein,a novel method for synthesizing CoP nanoparticles encapsu-lated in a rich-defect carbon shell(CoP/DCS)is developed through the self-assembly of modified polycyclic aromatic molecules.The graft and removal of high-activity C-N bonds of aromatic molecules render the controllable design of crystallite defects of carbon shell.The density functional theory calculation indicates that the carbon defects with unpaired electrons could effectively tailor the band structure of CoP.Benefiting from the improved activity and corrosion resistance,the CoP/DCS delivers outstanding difunctional hydrogen evolution reaction(88 mV)and oxygen evolution reaction(251 mV)performances at 10 mA cm^(−2)current density.Furthermore,the coupled water electrolyzer with CoP/DCS as both the cathode and anode presents ultralow cell voltages of 1.49 V to achieve 10 mA cm^(−2)with long-time stability.This strategy to improve TMPs electrocatalyst with rich-DCS and heterogeneous structure will inspire the design of other transition metal compound electrocatalysts for water splitting.

Wavelet-Based Boundary Element Method for Calculating the Band Structures of Two-Dimensional Phononic Crystals

A wavelet-based boundary element method is employed to calculate the band structures of two-dimensional phononic crystals,which are composed of square or triangular lattices with scatterers of arbitrary cross sections.With the aid of structural periodicity,the boundary integral equations of both the scatterer and the matrix are discretized in a unit cell.To make the curve boundary compatible,the second-order scaling functions of the B-spline wavelet on the interval are used to approximate the geometric boundaries,while the boundary variables are interpolated by scaling functions of arbitrary order.For any given angular frequency,an effective technique is given to yield matrix values related to the boundary shape.Thereafter,combining the periodic boundary conditions and interface conditions,linear eigenvalue equations related to the Bloch wave vector are developed.Typical numerical examples illustrate the superior performance of the proposed method by comparing with the conventional BEM.

Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures

Artificially constructed van der Waals heterostructures(vdWHs)provide an ideal platform for realizing emerging quantum phenomena in condensed matter physics.Two methods for building vdWHs have been developed:stacking two-dimensional(2D)materials into a bilayer structure with different lattice constants,or with different orientations.The interlayer coupling stemming from commensurate or incommensurate superlattice pattern plays an important role in vdWHs for modulating the band structures and generating new electronic states.In this article,we review a series of novel quantum states discovered in two model vdWH systems—graphene/hexagonal boron nitride(hBN)hetero-bilayer and twisted bilayer graphene(tBLG),and discuss how the electronic structures are modified by such stacking and twisting.We also provide perspectives for future studies on hetero-bilayer materials,from which an expansion of 2D material phase library is expected.

An Efficient Calculation of Photonic Crystal Band Structures Using Taylor Expansions

In this paper we present an efficient algorithm for the calculation of photonic crystal band structures and band structures of photonic crystal waveguides.Our method relies on the fact that the dispersion curves of the band structure are smooth functions of the quasi-momentum in the one-dimensional Brillouin zone.We show the derivation and computation of the group velocity,the group velocity dispersion,and any higher derivative of the dispersion curves.These derivatives are then employed in a Taylor expansion of the dispersion curves.We control the error of the Taylor expansion with the help of a residual estimate and introduce an adaptive scheme for the selection of nodes in the one-dimensional Brillouin zone at which we solve the underlying eigenvalue problem and compute the derivatives of the dispersion curves.The proposed algorithm is not only advantageous as it decreases the computational effort to compute the band structure but also because it allows for the identification of crossings and anti-crossings of dispersion curves,respectively.This identification is not possible with the standard approach of solving the underlying eigenvalue problem at a discrete set of values of the quasi-momentum without taking the mode parity into account.

Interface-induced topological phase and doping-modulated bandgap of two-dimensioanl graphene-like networks

Biphenylene is a new topological material that has attracted much attention recently.By amplifying its size of unit cell,we construct a series of planar structures as homogeneous carbon allotropes in the form of polyphenylene networks.We first use the low-energy effective model to prove the topological three periodicity for these allotropes.Then,through first-principles calculations,we show that the topological phase has the Dirac point.As the size of per unit cell increases,the influence of the quaternary rings decreases,leading to a reduction in the anisotropy of the system,and the Dirac cone undergoes a transition from type II to type I.We confirm that there are two kinds of non-trivial topological phases with gapless and gapped bulk dispersion.Furthermore,we add a built-in electric field to the gapless system by doping with B and N atoms,which opens a gap for the bulk dispersion.Finally,by manipulating the built-in electric field,the dispersion relations of the edge modes will be transformed into a linear type.These findings provide a hopeful approach for designing the topological carbon-based materials with controllable properties of edge states.