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.

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.

Impact of Oxygen Vacancy on Band Structure Engineering of n-p Codoped Anatase TiO2

Doping with various impurities is an effective approach to improve the photoelectrochemical properties of TiO2. Here, we explore the effect of oxygen vacancy on geometric and elec- tronic properties of compensated （i.e. V-N and Cr-C） and non-compensated （i.e. V-C and Cr-N） codoped anatase TiO2 by performing extensive density functional theory calculations. Theoretical results show that oxygen vacancy prefers to the neighboring site of metal dopant （i.e. V or Cr atom）. After introduction of oxygen vacancy, the unoccupied impurity bands located within band gap of these codoped TiO2 will be filled with electrons, and the posi- tion of conduction band offset does not change obviously, which result in the reduction of photoinduced carrier recombination and the good performance for hydrogen production via water splitting. Moreover, we find that oxygen vacancy is easily introduced in V-N codoped TiO2 under O-poor condition. These theoretical insights are helpful for designing codoped TiO2 with high photoelectrochemical performance.

Band structures of TiO_2 doped with N, C and B

This study on the band structures and charge densities of nitrogen (N)-, carbon (C)- and boron (B)-doped titanium dioxide (TiO2) by first-principles simulation with the CASTEP code (Segall et al., 2002) showed that the three 2p bands of im-purity atom are located above the valence-band maximum and below the Ti 3d bands, and that along with the decreasing of im-purity atomic number, the fluctuations become more intensive. We cannot observe obvious band-gap narrowing in our result. Therefore, the cause of absorption in visible light might be the isolated impurity atom 2p states in band-gap rather than the band-gap narrowing.

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.

Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique

A multiple monopole （or multipole） method based on the generalized mul- tipole technique （GMT） is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure is obtained. Some numerical examples are presented to validate the proposed method.

Synthesis,Crystal Structure and Band Structure of Sm_3In_5

A new intermetallic compound, Sm3In5, has been synthesized by solid-state reaction of the corresponding pure elements in a welded niobium tube at high temperature. Its crystal structure was established by single-crystal X-ray diffraction. Sm3In5 crystallizes in orthorhombic, space group Cmcm with a = 10.0137（8）, b = 8.1211（7）, c = 10.3858（8） A, V = 844.60（1） A^3, Z = 4, Mr = 1025.15, Dc = 8.062 g/cm^3, μ = 33.791 mm^-1, F（000） = 1724, the final R = 0.0346 and wR = 0.0775 for 533 observed reflections with I 〉 2σ（I）. The structure of Sm3In5 belongs to the modified Pu3Pd5 type. It is isostructural with La3In5 and β-Y3In5, containing one-dimensional （1D） [In5] cluster chains along the c-axis, which are weakly interconnected via In-In bonds （3.345A） to form a three-dimensional （3D） structure. The samarium cations are located at the voids between the 1D [In5] cluster chains. Band structure calculations based on Density Function Theory （DFT） method indicate that Sm3In5 is metallic.

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.

Synthesis, Crystal Structure and Band Structure of Eu_3Sn_5 with Arachno-type Zintl Anions

A new polar intermetallic compound, Eu3Sn5, has been synthesized by solid-state reaction of the corresponding pure elements in a stoicbiometric ratio in a welded tantalum tube at high temperature. Its crystal structure was established by single-crystal X-ray diffraction. EuaSn5 crystallizes in orthorhombic, space group Cmcm with a = 10.466（11）, b = 8,445（8）, c = 10.662（12）/k, V = 942.4（17）A^3, Z = 4, Mr = 1049.33, De= 7.396 g/cm^3, ,μ = 32.578 mm^-1, F（000） = 1756, the final R = 0.0236 and wR = 0.0472 for 535 observed reflections with I 〉 2σ（I）. Its structure belongs to the modified Pu3Pd5 type. It is isostructural with SraSn5 and Ba3Sn5, featuring [Sn5] square pyramidal clusters described as “arachno” according to the Wade-Mingos electron counting rules. The europium cations are located at the voids between the square pyramidal clusters. Results of the extended Htickel band structure calculations indicate that Eu3Sn5 is metallic.

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.

Study on Band Structure of YbB_6 and Analysis of Its Optical Conductivity Spectrum

The electronic structure of YbB6 crystal was studied by means of density functional （GGA ＋ U） method. The calculations were performed by FLAPW method. The high accurate band structure was achieved. The correlation between the feature of the band structure and the Yb-B6 bonding in YbB6 was analyzed. On this basis, some optical constants of YbB6 such as reflectivity, dielectric function, optical conductivity, and energy-loss function were calculated. The results are in good agreement with the experiments. The real part of the optical conductivity spectrum and the energy-loss function spectrum were analyzed in detail. The assignments of the spectra were carried out to correlate the spectral peaks with the interband electronic transitions, which justify the reasonable part of previous empirical assignments and renew the missed or incorrect ones.

Quasiparticle Band Structures of Defects in Anatase TiO2 Bulk

Quasiparticle band structures of the defective anatase TiO2 bulk with O vacancy, Ti interstitial and H interstitial are investigated by the GW method within many-body Green＇s function theory. The computed direct band gap of the perfect anatase bulk is 4.3 eV, far larger than the experimental optical absorption edge （3.2 eV）. We found that this can be ascribed to the inherent defects in anatase which drag the conduction band （CB） edge down. The occupied band-gap states induced by these defects locate close to the CB edge, exclud- ing the possible contribution of these bulk defects to the deep band-gap state below CB as observed in experiments.

The complex band structure for armchair graphene nanoribbons

Using a tight binding transfer matrix method, we calculate the complex band structure of armchair graphene nanoribbons. The real part of the complex band structure calculated by the transfer matrix method fits well with the bulk band structure calculated by a Hermitian matrix. The complex band structure gives extra information on carrier＇s decay behaviour. The imaginary loop connects the conduction and valence band, and can profoundly affect the characteristics of nanoscale electronic device made with graphene nanoribbons. In this work, the complex band structure calculation includes not only the first nearest neighbour interaction, but also the effects of edge bond relaxation and the third nearest neighbour interaction. The band gap is classified into three classes. Due to the edge bond relaxation and the third nearest neighbour interaction term, it opens a band gap for N = 3M- 1. The band gap is almost unchanged for N =3M ＋ 1, but decreased for N = 3M. The maximum imaginary wave vector length provides additional information about the electrical characteristics of graphene nanoribbons, and is also classified into three classes.

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.

Synthesis,Crystal Structure and Band Structure of Tb_3Co_4Sn_(13)

A new intermetallic compound,Tb3Co4Sn13,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.Tb3Co4Sn13 crystallizes in cubic,space group Pm3n（No.223） with a = 9.5072（2） ,V = 859.33（3） 3,Z = 2,Mr = 2255.45,Dc = 8.717 g/cm3,μ = 34.369 mm-1,F（000） = 1906,and the final R = 0.0140 and wR = 0.0312 for 199 observed reflections with I〉 2σ（I）.The structure of Tb3Co4Sn13 belongs to the Yb3Rh4Sn13 type.It is isostructural with RE3Co4Sn13（RE = La,Ce）,featuring a 3D [Co4Sn12] framework based on [CoSn6] trigonal prisms.The [CoSn6] trigonal prisms are interconnected via corner-sharing and Sn-Sn bonds to form a 3D [Co4Sn12] framework.The other Sn and Tb atoms are located in the spacers of the 3D framework.Band structure calculations indicate that Tb3Co4Sn13 is metallic.

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.

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.

Band Structure： A Solid-State Physics Model with Cosmological Implications

This work is aimed at showing that the ＂band structure＂ of the energy distribution in solids which is a well-known model for electronic engineers and solid-state physics scientists is an efficacious description also for phenomena not tied to energy neither related to microcosm. In particular, it is displayed that how the elements of the consolidated physical theories, arranged together using the ＂band structure＂, lead to a model for the distribution of speed in the universe that is essentially analogous to the distribution of energy in solids. The description is accompanied by references to the experimental data that sustain it, together with an overview of the possible development opportunities.

Energy Band Structure of Alq_3/TCAQ Heterostructure Complex Film Determined by Surface Photovoltage Spectroscopy(SPS)

8-Hydroxyquinoling aluminum (Alq3) and 11, 11, 12, 12-tetracyano-9, 10-anthraquino dimethane(TCAQ) monolayer films and their heterostructure complex films were prepared by a vacuum deposition method. By means of surface photovoltage spectroscopy (SPS) and electric field-induced surface photovoltage spectroscopy (EFISPS), the band gaps of TCAQ and Alq3 monolayer films and the properties of the Alq3/TCAQ bilayer film were investigated. By analysing the mechanism and the results of the SPS and the EFISPS, a reasonable energy band structure of the Alq3/TCAQ complex film was roughly determined.