From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials

In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.

Fifth-Nearest-Neighbor Tight-Binding Description of Electronic Structure of Graphene

An analytic expression for π and π＊ electronic structure of graphene is derived within the tight-binding approximation. Including up to fifth-nearest neighbors, the tight-binding description of electronic dispersion quite accurately reproduces the first-principle calculation result over the entire Brillouin zone. The maximal deviation of the fifth-nearest tight-binding result from the first-principle result is only 6 meV for π band, and 25 meV for π＊ band. This 25 meV deviation is only one-tenth of the maximal deviation of the third-nearest tight-binding result. It is more important that the fitted parameters exponentially approach to zero as the distance between interacting atoms increases.

Dirac states from p_(x,y)orbitals in the buckled honeycomb structures:A tight-binding model and first-principles combined study

Dirac states composed of Px,y orbitals have been reported in many two-dimensional （2D） systems with honeycomb lattices recently. Their potential importance has aroused strong interest in a comprehensive understanding of such states. Here, we construct a four-band tight-binding model for the Px,y-orbital Dirac states considering both the nearest neighbor hopping interactions and the lattice-buckling effect. We find that Px,y-orbital Dirac states are accompanied with two addi- tional narrow bands that are flat in the limit of vanishing n bonding, which is in agreement with previous studies. Most importantly, we analytically obtain the linear dispersion relationship between energy and momentum vector near the Dirac cone. We find that the Fermi velocity is determined not only by the hopping through n bonding but also by the hopping through ~ bonding of Px,y orbitals, which is in contrast to the case of pz-orbital Dirac states. Consequently, Px,y-orbital Dirac states offer more flexible engineering, with the Fermi velocity being more sensitive to the changes of lattice constants and buckling angles, if strain is exerted. We further validate our tight-binding scheme by direct first-principles calcula- tions of model-materials including hydrogenated monolayer Bi and Sb honeycomb lattices. Our work provides a more in-depth understanding of Px,y-orbital Dirac states in honeycomb lattices, which is useful for the applications of this family of materials in nanoelectronics.

Next-Nearest-Neighbor Tight-Binding Model of Plasmons in Graphene

In this paper we investigate the influence of the next-nearest-neighbor coupling on the spectrum of plasmon excitations in graphene. The nearest-neighbor tight-binding model was previously considered to calculate the plasmon spectrum in graphene [1]. We extend these results to the next-nearest-neighbor tight-binding model. As in the calculation of the nearest-neighbor model, our approach is based on the numerical calculation of the dielectric function and the loss function. We compare the plasmon spectrum of the two models and discuss the differences in the dispersion.

Time-dependent Density Functional-based Tight-bind Method Efficiently Implemented with OpenMP Parallel and GPU Acceleration

The time-dependent density functional-based tight-bind （TD-DFTB） method is implemented on the multi-core and the graphical processing unit （GPU） system for excited state calcu-lations of large system with hundreds or thousands of atoms. Sparse matrix and OpenMP multithreaded are used for building the Hamiltonian matrix. The diagonal of the eigenvalue problem in the ground state is implemented on the GPUs with double precision. The GPU- based acceleration fully preserves all the properties, and a considerable total speedup of 8.73 can be achieved. A Krylov-space-based algorithm with the OpenMP parallel and CPU acceleration is used for finding the lowest eigenvalue and eigenvector of the large TDDFT matrix, which greatly reduces the iterations taken and the time spent on the excited states eigenvalue problem. The Krylov solver with the GPU acceleration of matrix-vector product can converge quickly to obtain the final result and a notable speed-up of 206 times can be observed for system size of 812 atoms. The calculations on serials of small and large systems show that the fast TD-DFTB code can obtain reasonable result with a much cheaper computational requirement compared with the first-principle results of CIS and full TDDFT calculation.

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.

Topological properties of tetratomic Su-Schrieffer-Heeger chains with hierarchical long-range hopping

We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening(closure) of an energy bandgap at the center(boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.

环状共聚物的电子特性研究

针对由小带隙的聚乙炔和大带隙的苯作为聚合物单体的聚合物的几种简单环状模型,采用紧束缚近似计算方法,研究了它们的电子能谱和态密度特征,并考虑到环状结构的特点,同时在计算过程中也考虑了聚乙炔链中的最近邻和次近邻跃迁.结果表明:由于考虑了次近邻跃迁,导带和价带的对称性被破坏了,有着明显的不对称特征,能隙稍变窄.随着环状聚乙炔链中的苯环数的增多,电子能谱和态密度均有显著的变化,能谱分布逐渐不均匀,呈现出较明显的4条能带,态密度分布也相应地出现4个峰.

双圆弧逼近空间曲线的误差分析

本文讨论的是用双圆弧逼近空间曲线 ,及所产生的误差 ,包括线误差和角误差 ,以确定用双弧逼近空间曲线时是否要对样条分段。

基于MO-RAMP插值模型的阻尼板GCMOC法拓扑减振优化

为了有效实现板件的抗振性动力学设计,研究约束阻尼板拓扑动力学优化方法。建立约束阻尼板有限元动力学分析模型,推导出模态损耗因子计算公式;建立了基于模态损耗因子最大化目标,以阻尼层单元相对密度为拓扑变量,以阻尼材料使用量及结构频率作为控制的阻尼板优化数学模型;利用序列凸规划理论而对传统优化准则法进行改进,采用改进准则法GCMOC(global extreme point converged by method of optimization criterion)解算优化模型以求取全域性优化解,推导出面向GCMOC的拓扑变量迭代式;考虑到多阶次RAMP(rational approxination of material properties)函数的形状具有较理想的可控下凹几何特征,提出在优化迭代中采用多阶次RAMP材料插值模型(MO-RAMP)对拓扑变量集合进行惩罚以实现其快速的0,1二值化,并尽量减少处于0.3~0.7的中间拓扑变量值出现;编制了面向约束阻尼板的拓扑动力学优化程序,实现了基于MO-RAMP的约束阻尼板GCMOC法变密度式减振拓扑动力学优化过程。算例分析表明,MO-RAMP与GCMOC复合的算法用于阻尼板拓扑迭代时,可将阻尼单元密度值快速地推向逼近0或1的值。它能得到清晰的阻尼单元优化密度云并有利于优化构型的实现;能在大幅减少阻尼材料用量条件下充分发挥其黏弹耗能效应,能在保证阻尼板动力学特性基本稳定的前提下使结构获得更好的减振效果。

Analytical formulas for carrier density and Fermi energy in semiconductors with a tight-binding band

Analytical formulas for evaluating the relation of carrier density and Fermi energy for semiconductors with a tight-binding band have been proposed. The series expansions for a carrier density with fast convergency have been obtained by means of a Bessel function. A simple and analytical formula for Fermi energy has been derived with the help of the Gauss integration method. The results of the proposed formulas are in good agreement with accurate numerical solutions. The formulas have been successfully used in the calculation of carrier density and Fermi energy in a miniband superlattice system. Their accuracy is in the order of 10-5.

Molecular Simulations in Materials Science

Molecular simulation finds application in a wide range of research fields based on life and materials sciences.It helps comprehend and predict the chemical and physical properties of substances;thus,it is useful in directing R&D and industrial production.In this special issue,we focus on molecular simulations in material sciences.Molecular simulation employs computational models from microscopic to mesoscopic levels,which is reflected in this special issue.For example,Liu et al.1 reported modulation of catalytic activity for CO2 hydrogenation using quantum density functional theory(DFT).Yin et al.2 parameterized a semiempirical density functional tight-binding(DFTB)model to study deposition of carbon on copper surface.At the atomic level,Ren et al.

Quantum dynamics of charge transfer on the one-dimensional lattice:Wave packet spreading and recurrence

The wave function temporal evolution on the one-dimensional （ID） lattice is considered in the tight-binding approxi- mation. The lattice consists of N equal sites and one impurity site （donor）. The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time -t1/3 and its amplitude decreases ,- t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

Curvature and Zeeman effects on persistent currents in a multi-walled carbon nanotorus

Taking into account both the intrinsic curvature and Zeeman effects, persistent currents in a multi-walled carbon nanotorus are explored by using a supercell method, within the tight-binding formalism. It is shown that in the absence of the Zeeman effect, the intrinsic curvature induces some dramatic changes in energy spectra and thus changes in the shape of the flux-dependent current. A paramagnetism diamagnetism transition is observed. With consideration of the Zeeman splitting energy, the period of persistent current is destroyed, and a diamagnetism-paramagnetism transition is obtained at high magnetic field. In addition, we further explore the effect of external electric field energy （Eef） on persistent current, indicating that it changes unmonotonously with Eef.

特殊节点的Lagrange多项式对光滑函数的逼近阶

本文讨论以Ｃｈｅｂｙｓｈｅｖ多项式的零点为节点的Ｌａｇｒａｎｇｅ型多项式来逼近光滑函数的逼近阶。

A new many-body potential with the second-moment approximation of tight-binding scheme for Hafnium

In this work,we develop a new many-body potential for alpha-hafnium(α-Hf)based on the second moment approximation of tight-binding(TB-SMA)theory by introducing an additional Heaviside step function into the potential model and a new analytical scheme of density function.All the parameters of the new potential have been systematically evaluated by fitting to ground-state properties including cohesive energy,lattice constants,elastic constants,vacancy formation energy,structure stability and equation of state.By using the present model,the melting point,melt heat,thermal expansion coefficient,point defects,and low-index surface energies ofα-Hf were calculated through molecular dynamics simulations.Comparing with experiment observations from others,it is shown that these properties can be reproduced reasonably by the present model,some results being more consistent to the experimental data than those by previous suggested models.This indicates that this work is sutiable in TB-SMA potential for hexagonal close packed metals.

一类变分问题的数值解法

本文研究与板壳几何非线性弯曲问题相联的一类变分问题的数值解法。首先给出区域和泛函的变换公式;继而提出变分问题的数值解法,并给出了统一计算格式。最后,研究了具体算例。本文的解法,适合工程应用。

Tight-binding models for ultracold atoms in optical lattices：general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

关于积分中值定理中间值的探讨

本文针对被积函数是对数lnx或f(x)-blnx→k(x→+∞)时,当积分区间趋于无穷大时,积分中值定理中间值的逼近情形。

Adsorption and diffusion of Si adatom near single-layer steps on Si surface

By use of the empirical tight-binding （ETB） method, the adsorption and diffusion behaviours ot single sllmon adatom on the reconstructed Si（100） surface with single-layer steps are simulated. The adsorption energies around the SA step, nonrebonded SB step, rebonded SB step, and rough SB step with a kink structure are specially mapped out in this paper, from which the favourable binding sites and several possible diffusion paths are achieved. Because of the rebonded and kink structures, the SB step is more ~uitable for the attachment of Si adatom than the SA step or defective surface.