Electronic specific heat of nanographite ribbons

The electronic specific heat of nanographite ribbons exhibits rich temperature dependence, mainly owing to the special band structures. The thermal property strongly depends on the geometric structures, the edge structure and the width. There is a simple relation between the ribbon width and the electronic specific heat for the metallic or semiconducting armchair ribbons. However, it is absent for the zigzag ribbons. The metallic armchair ribbons exhibit linear temperature dependence. The semiconducting armchair ribbons exhibit composite behavior of power and exponential functions. As for the zigzag ribbons, the temperature dependence of the specific heat is proportional to T^1−p. The value of p quickly increases from to 1 as the ribbon width gradually grows. The zigzag ribbons might be the first system which exhibits the novel temperature dependence. The nanographite ribbons differ from an infinite graphite sheet, which illustrates that the finite-size effects are significant.     

Electronic structures of the F-terminated AlN nanoribbons

Using the first-principles calculations, electronic properties for the F-terminated AlN nanoribbons with both zigzag and armchair edges are studied. The results show that both the zigzag and armchair AlN nanoribbons are semiconducting and nonmagnetic, and the indirect band gap of the zigzag AlN nanoribbons and the direct band gap of the armchair ones decrease monotonically with increasing ribbon width. In contrast, the F-terminated AlN nanoribbons have narrower band gaps than those of the H-terminated ones when the ribbons have the same bandwidth. The density-of-states (DOS) and local density-of-states (LDOS) analyses show that the top of the valence band for the F-terminated ribbons is mainly contributed by N atoms, while at the side of the conduction band, the total DOS is mainly contributed by Al atoms. The charge density contour analyses show that Al–F bond is ionic because the electronegativity of F atom is much stronger for F atom than for Al atom, while N–F bond is covalent because of the combined action of the stronger electronegativity and the smaller covalent radius.     

Electronic properties of α-graphyne nanoribbons under the electric field effect

In this paper, we investigate the electronic structure of both armchair and zigzag α-graphyne nanoribbons. We use a simple tight binding model to study the variation of the electronic band gap in α-graphyne nanoribbon. The effects of ribbon width, transverse electric field and edge shape on the electronic structure have been studied. Our results show that in the absence of external electric field, zigzag α-graphyne nanoribbons are semimetal and the electronic band gap in armchair α-graphyne nanoribbon oscillates and decreases with ribbon's width. By applying an external electric field the band gap in the electronic structure of zigzag α-graphyne nanoribbon opens and oscillates with ribbon width and electric field magnitude. Also the band gap of armchair α-graphyne nanoribbon decreases in low electric field, but it has an oscillatory growth behavior for high strength of external electric field.     

Energy gaps in graphene nanoribbons

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our ab initio calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our ab initio calculation results very well.     

Effect of oxidation of graphene nanoribbons on electronic and magnetic properties

The electronic properties, band gap and ionization potential as well as the energies of the singlet and triplet states of zigzag and armchair graphene nanoribbons are calculated as a function of the number of oxygen atoms on the ribbon employing density functional theory at B3LYP/6-31G* level. The calculated band gaps indicate that both structures are semiconducting. The band gap of the armchair ribbons initially decreases followed by an increase with oxygen number. For zigzag ribbons the band gap decreases with increasing oxygen number whereas the ionization potential increases with oxygen content. In both armchair and zigzag ribbons the ionization potential shows a gradual increase with the number of oxygen atoms. Some of the oxygenated ribbons calculated have triplet ground states and have the density of states at the Fermi level for spin down greater than spin up suggesting the possibility they may be ferromagnetic semiconductors.     

Decay and the double-decay properties of edge bands of phosphorene ribbons

Phosphorene (a monolayer of black phosphorus) recently spurred much attention due to its potential for application. We notice there are two types of zigzag edge and two types of armchair edge for phosphorene lattice. We study the winding number of various types of edge of phosphorene ribbons and conclude that, besides on the typical zigzag edge, the flat zero-energy edge band can be found in the ribbon of another nontypical armchair edge. The localization of these edge bands is investigated analytically. We find every single edge state of the atypical armchair edge decays to the bulk at two different decay rates.     

Carbon nanoribbons and nanotubes based on δ-graphyne: A first-principles study

As a stable allotropy of two-dimensional (2D) carbon materials, δ-graphyne has been predicted to be superior to graphene in many aspects. Using first-principles calculations, we investigated the electronic properties of carbon nanoribbons (CNRs) and nanotubes (CNTs) formed by δ-graphyne. It is found that the electronic band structures of CNRs depend on the edge structure and the ribbon width. The CNRs with zigzag edges (Z-CNRs) have spin-polarized edge states with ferromagnetic (FM) ordering along each edge and anti-ferromagnetic (AFM) ordering between two edges. The CNRs with armchair edges (A-CNRs), however, are semiconductors with the band gap oscillating with the ribbon width. For the CNTs built by rolling up δ-graphyne with different chirality, the electronic properties are closely related to the chirality of the CNTs. Armchair (n, n) CNTs are metallic while zigzag (n, 0) CNTs are semiconducting or metallic. These interesting properties are quite crucial for applications in δ-graphyne-based nanoscale devices.     

Detection of valley currents in graphene nanoribbons

There are two valleys in the band structure of graphene zigzag ribbons, which can be used to construct valleytronic devices. We studied the use of a T junction formed by an armchair ribbon and a zigzag ribbon to detect the valley-dependent currents in a zigzag graphene ribbon. A current flowing in a zigzag ribbon is divided by the T junction into the zigzag and armchair leads and this separation process is valley dependent. By measuring the currents in the two outgoing leads, the valley-dependent currents in the incoming lead can be determined. The method does not require superconducting or magnetic elements as in other approaches and thus will be useful in the development of valleytronic devices.     

Resonance Transport of Graphene Nanoribbon T-Shaped Junctions

We investigate the transport properties of T-shaped junctions composed of armchair graphene nanoribbons of different widths. Three types of junction geometries are considered. The junction conductance strongly depends on the atomic features of the junction geometry. When the shoulders of the junction have zigzag type edges, sharp conductance resonances usually appear in the low energy region around the Dirac point, and a conductance gap emerges. When the shoulders of the junction have armchair type edges, the conductance resonance behavior is weakened significantly, and the metal-metal-metal junction structures show semimetallic behaviors. The contact resistance also changes notably due to the various interface geometries of the junction.     

Localized electronic states on graphite edge

Examining the band structure of graphite ribbons with a typical edge shapes of armchair or zigzag, we find that minute graphite in a nanometer scale shows a striking contrast in the π electronic states depending on the edge shape. A wide armchair ribbon can reproduces the electronic state of graphite, but a zigzag ribbon shows a pair of partly flat bands which gives a remarkable peak of density of states at the Fermi level. We derive the analytic solution of this peculiar Edge State, disclosing the puzzle of its emergence.     

应变对二维蜂巢晶格光子晶体能带结构的影响

基于平面波法,本论文对应变引起的二维蜂巢晶格光子晶体的能带结构进行了数值计算。选取的两个方向分别是锯齿型边界(zigzag)方向和扶手椅型边界(armchair)方向,在这两个典型方向上对二维蜂巢晶格进行了正负各20%的单轴应变。由于应变导致的对称性破缺,能带结构会有显著的变化。在沿锯齿型边界方向上,TE模带隙随着晶格被拉伸逐渐减小,TM模带隙在应变量大于16%时消失。对于沿扶手椅型边界方向,TE模带隙在压缩15%以上时逐渐减小,在其他应变量的情况下几乎保持不变;TM模带隙在应变量大于18%时消失。这些结果对于完善应力工程和设计二维光子晶体器件有重要的指导意义。     

Quantum transport in armchair graphene ribbons: analytical tight-binding solutions for propagation through step-like and barrier-like potentials

Based on the nearest-neighbor tight-binding approximation, we present exact analytical expressions for transmission coefficients through piecewise constant step-like and barrier-like electrostatic potentials. In the case of single mode propagation through semiconducting ribbon families our analytical solutions predict a new kind of resonances. Its features substantially change the behavior of the transmission coefficients in the range of moderate potentials, which become family-dependent. For semimetal ribbons our approach predicts no unit propagation. The non-zero backscattering is derived to be proportional as the square of the potential amplitude applied.     

Uniaxial-stress effects on electronic structures of nanographite ribbons

The uniaxial-stress effects on the low-energy electronic properties of nanographite ribbons are studied by the tight-binding model. The dependence on the strain, the edge structure, the ribbon width, and the stacking sequence is strong. The strain could induce the alternation of energy dispersions, the destruction of state degeneracy, the variation of energy gap, the semiconductor–metal transition, and the change of special structures in density of states. The effects of strain are important for the AB- and AA-stacked armchair ribbons. However, they are negligible for the AB- and AA-stacked zigzag ribbons. Armchair ribbons could exhibit the semiconductor–metal transition. Such transition is mainly determined by the strain and the ribbon–ribbon interactions.     

Calculations of electric capacitance in carbon and BN nanotubes, and zigzag nanographite (BN, BCN) ribbons

Electronic states in nanographite ribbons with zigzag edges are studied using the extended Hubbard model with nearest neighbor Coulomb interactions. The electronic states with the opposite electric charges separated along both edges are analogous as nanocondensers. Therefore, electric capacitance, defined using a relation of polarizability, is calculated to examine nano-functionalities. We find that the behavior of the capacitance is widely different depending on whether the system is in the magnetic or charge polarized phases. In the magnetic phase, the capacitance is dominated by the presence of the edge states while the ribbon width is small. As the ribbon becomes wider, the capacitance remains with large magnitudes as the system develops into metallic zigzag nanotubes. It is proportional to the inverse of the width, when the system corresponds to the semiconducting nanotubes and the system is in the charge polarized phase also. The latter behavior could be understood by the presence of an energy gap for charge excitations. In the BN (BCN) nanotubes and ribbons, the electronic structure is always like that of semiconductors. The calculated capacitance is inversely proportional to the distance between the positive and negative electrodes.     

Electronic properties of graphene nanoribbon doped by boron/nitrogen pair: a first-principles study

By using the first-principles calculations, the electronic properties of graphene nanoribbon (GNR) doped by boron/nitrogen (B/N) bonded pair are investigated. It is found that B/N bonded pair tends to be doped at the edges of GNR and B/N pair doping in GNR is easier to carry out than single B doping and unbonded B/N co-doping in GNR. The electronic structure of GNR doped by B/N pair is very sensitive to doping site besides the ribbon width and chirality. Moreover, B/N pair doping can selectively adjust the energy gap of armchair GNR and can induce the semimetal-semiconductor transmission for zigzag GNR. This fact may lead to a possible method for energy band engineering of GNRs and benefit the design of graphene electronic device.     

First-principles investigation of armchair stanene nanoribbons

In this study, we systematically investigated the structural, electronic and optical properties of armchair stanene nanoribbons (ASNRs) by using the first-principles calculations. First, we performed full geometry optimization calculations on various finite width ASNRs where all the edge Sn atoms are saturated by hydrogen atoms. The buckled honeycomb structure of two dimensional (2D) stanene is preserved, however the bond length between the edge Sn atoms is shortened to 2.77 Å compared to the remaining bonds with 2.82 Å length. The electronic properties of these nanoribbons strongly depend on their ribbon width. In general, band gap opens and increases with decreasing nanoribbon width indicating the quantum confinement effect. Consequently, the band gap values vary from a few meV exhibiting low-gap semiconductor (quasi-metallic) behavior to ～0.4–0.5 eV showing moderate semiconductor character. Furthermore, the band gap values are categorized into three groups according to modulo 3 of integer ribbon width N which is the number of Sn atoms along the width. In order to investigate the optical properties, we calculated the complex dielectric function and absorption spectra of ASNRs, they are similar to the one of 2D stanene. For light polarized along ASNRs, in general, largest peaks appear around 0.5 eV and 4.0 eV in the imaginary part of dielectric functions, and there are several smaller peaks between them. These major peaks redshifts, slightly to the lower energies of incident light with increasing nanoribbon width. On the other hand, for light polarized perpendicular to the ribbon, there is a small peak around 1.6 eV, then, there is a band formed from several peaks from 5 eV to ～7.5 eV, and the second one from 8 eV to ～9.5 eV. Moreover, the peak positions hardly move with varying nanoribbon width, which indicates that quantum confinement effect is not playing an essential role on the optical properties of armchair stanene nanoribbons. In addition, our calculations of the optical properties indicate the anisotropy with respect to the type of light polarization. This anisotropy is due to the quasi-2D nature of the nanoribbons.     

石墨带的晶格动力学研究

基于晶格动力学理论,采用力常数模型,计算了石墨带的声子色散关系、振动模式密度和比热.计算结果表明,石墨带的声子谱特征介于一维碳纳米管和二维石墨片之间.扶手椅型和锯齿型石墨带的中、高频声子支分别与锯齿型和扶手椅型碳纳米管的类似.由于声子限域效应,低频声子支随着石墨带带宽的改变出现明显的频移现象.振动模式密度在高频区几乎不敏感于带宽,而低频区的峰位随着带宽的增加而逐渐向低频移动.此外,无论是在低温还是高温,比热都随着带宽的增加而逐渐降低,呈现量子尺寸效应.在300K时,比热可以拟合成C_V=C_Vg+A/n,其中C_Vg为石墨片的热容,而A/n项反映了石墨带中边缘效应对比热的影响. 关键词： 石墨带 声子色散关系 比热     

Effects of the spin–orbit coupling on the vacancy-induced magnetism on the honeycomb lattice

The local magnetism induced by vacancies in the presence of the spin–orbit interaction is investigated based on the half-filled Kane–Mele–Hubbard model on the honeycomb lattice. Using a self-consistent mean-field theory, we find that the spin–orbit coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. We find that the spin–orbit coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin–orbit gap. As a result, in the case of the balance number of sublattices, it will suppress completely this kind of ferrimagnetic order. But, for the imbalance case, a ferrimagnetic order along both edges exists because additional zero modes will not be affected by the spin–orbit coupling.     

Electronic shell and supershell structure in graphene flakes

We use a simple tight-binding (TB) model to study electronic properties of free graphene flakes. Valence electrons of triangular graphene flakes show a shell and supershell structure which follows an analytical expression derived from the solution of the wave equation for triangular cavity. However, the solution has different selection rules for triangles with armchair and zigzag edges, and roughly 40?000 atoms are needed to see clearly the first supershell oscillation. In the case of spherical flakes, the edge states of the zigzag regions dominate the shell structure which is thus sensitive to the flake diameter and center. A potential well that is made with external gates cannot have true bound states in graphene due to the zero energy band gap. However, it can cause strong resonances in the conduction band.