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.

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.

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.

Persistent currents in three-dimensional shell-doped nanorings

The persistent current in three-dimensional （P × N2） nanorings as a function of the unit cell number （P）, the channel number （M =N2）, surface disorder （ζ）, and temperature （T） is theoretically investigated in terms of rotational symmetry. On the whole, the typical current increases linearly with √M but decreases exponentially with P, while wide fluctuations exist therein. In the presence of surface disorder, the persistent current decreases with ζ in the regime of weak disorder but increases in the regime of strong disorder. In addition, it is found that the persistent current in perfect rings decreases exponentially with temperature even at T 〈 T＊, while in most disorder rings, the typical current decreases slightly with temperature at T 〈 T＊.

An easy and efficient way to treat Green's function for nano-devices with arbitrary shapes and multi-terminal configurations

The efficiency of the calculation of Green＇s function （GF） for nano-devices is very important because the calculation is often needed to be repeated countlessly. We present a set of efficient algorithms for the numerical calculation of GF for devices with arbitrary shapes and multi-terminal configurations. These algorithms can be used to calculate the specified blocks related to the transmission, the diagonals needed by the local density of states calculation, and the full matrix of GF, to meet different calculation levels. In addition, the algorithms for the non-equilibrium occupation and current flow are also given. All these algorithms are described using the basic theory of GF, based on a new partition strategy of the computational area. We apply these algorithms to the tight-binding graphene lattice to manifest their stability and efficiency. We also discuss the physics of the calculation results.

Resonant tunneling through double-barrier structures on graphene

Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tightbinding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schro¨dinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.

Projective representation of D_(6)group in twisted bilayer graphene

Within the framework of continuum model,we study the projective representation of emergent D_(6)point group in twisted bilayer graphene.We then construct tight-binding models of the lowest bands without and with external electromagnetic fields,based on the projective representation.

Spin–orbit stable dirac nodal line in monolayer B_(6)O

The two-dimensional(2D) materials with nodal line band crossing have been attracting great research interest. However, it remains a challenge to find high-stable nodal line structure in 2D systems. Herein, based on the first-principles calculations and theoretical analysis, we propose that monolayer B_(6)O possesses symmetry protected Dirac nodal line(DNL)state, with its Fermi velocity of 10^(6)m/s in the same order of magnitude as that of graphene. The origin of DNL fermions is induced by coexistence of time-reversal symmetry and inversion symmetry. A two-band tight-binding model is further given to understand the mechanism of DNL. Considering its robustness against spin–orbit coupling(SOC) and high structural stability, these results suggest monolayer B_(6)O as a new platform for realizing future high-speed low-dissipation devices.

Theoretical Research on Thermoelectric Properties of Graphene Nanorings

Based on the tight-binding approach and the nonequilibrium Green's function method,the thermoelectric performance of graphene nanoribbons(GNRs) and graphene rings are investigated systematically.Thermoelectric properties show substantial dependence on graphene structure.The maximum value of thermoelectric figure of merit(ZT) in perfect GNRs declines exponentially with the increase of width JV except for metallic armchair GNRs with JV = 3/ + 2(i is an integer).In graphene rings,the ZT value is enhanced dramatically at room temperature,which oscillates with perpendicular magnetic field due to Aharonov-Bohm effect.The significantly enhanced ZT value makes graphene ring a promising candidate for thermoelectric applications.