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.

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.

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.

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.

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.

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.

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.

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.

Electronic Casimir–Polder Force in a One-dimensional Tight-Binding Nanowire at Finite Temperature

We study the effect of two non-interacting impurity atoms near by a one-dimensional nanowire, which is modeled as a tight-binding hopping model. The virtual single-electron hopping between two impurities will induce an additional energy depending on the distance of two impurities, which gives a electronic Casimir–Polder effect. We find that the Casimir–Polder force between the two impurities decreases with the impurity-impurity distance exponentially.And the effects of nanowire and finite temperature on the Casimir–Polder force are also discussed in detail, respectively.

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.

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.

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.

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.

Spin gapless armchair graphene nanoribbons under magnetic field and uniaxial strain

Using Green＇s function method, we investigate the spin transport properties of armchair graphene nanoribbons （AG- NRs） under magnetic field and uniaxial strain. Our results show that it is very difficult to transform narrow AGNRs directly from semiconductor to spin gapless semiconductors （SGS） by applying magnetic fields. However, as a uniaxial strain is exerted on the nanoribbons, the AGNRs can transform to SGS by a small magnetic field. The combination mode be- tween magnetic field and uniaxial strain displays a nonmonotonic arch-pattern relationship. In addition, we find that the combination mode is associated with the widths of nanoribbons, which exhibits group behaviors.

One-dimensional method of investigating the localized states in armchair graphene-like nanoribbons with defects

In this paper we propose a type of new analytical method to investigate the localized states in the armchair graphene-like nanoribbons. The method is based on the tight-binding model and with a standing wave assumption. The system of armchair graphene-like nanoribbons includes the armchair supercells with arbitrary elongation-type line defects and the semi-infinite nanoribbons. With this method, we analyze many interesting localized states near the line defects in the graphene and boron-nitride nanoribbons. We also derive the analytical expressions and the criteria for the localized states in the semi-infinite nanoribbons.

Electronic band transformation from indirect gap to direct gap in Si-H compound

The electronic band structures of periodic models for S^H compounds are investigated by the density functional theory. Our results show that the Si H compound changes from indirect-gap semiconductor to direct-gap semiconductor with the increase of H content. The density of states, the partial density of states and the atomic charge population are examined in detail to explore the origin of this phenomenon. It is found that the Si-Si bonds are affected by H atoms, which results in the electronic band transformation from indirect gap to direct gap. This is confirmed by the nearest neighbour semi-empirical tight-binding （TB） theory.

Electronic and magnetic properties at rough alloyed interfaces of Fe/Co on Au substrates: An augmented space study

We studied the interface electronic and magnetic properties of Fe/Co deposited on Au substrate and researched the effects of roughness at the interfaces within augmented space formalism （ASF）. The full calculation is carried out by recursion and tight-binding linear muffin tin orbital （TB-LMTO） methods. The amount of roughness is different at different atomic layers. The formalism is also applied to sharp interface, when interdiffusion of atoms is negligible. Our results of one monolayer transition metal agree with other reported results. A realistic rough interface is also modeled with three and four monolayers of transition metals, deposited on Au substrates.

Theoretical Simulations of Irradiation-Induced Sputtering at Tungsten Surface

The irradiation-induced sputtering and the structural damage at tungsten surface are investigated by using molecular dynamics simulations at the level of quantum mechanics. Our simulations indicate that the sputtered atoms appear when the energy of incident primary knock-on atom （PKA） is more than 200 eV and the incident angle of the PKA is larger than 65°. Meanwhile, the irradiation-induced vacancies are less when the incident angle of PKA is in the range of 45°-65°. So, the optimum incident angles of PKA are suggested to reduce the irradiation-induced damage of the W surface. Furthermore, we find that the interstitials contained in the systems accelerate the sputtering whereas the intrinsic vacancies suppress the sputtering when the PKA is near the defects.