Band gap of carbon nanotubes under combined uniaxial–torsional strain

Within tight-binding model, the band gaps of armchair and zigzag carbon nanotubes (CNTs) under both uniaxial tensile and torsional strains have been studied. It is found that the changes in band gaps of CNTs depend strongly on the strain type. The torsional strain can induce a band gap for armchair CNTs, but it has little effect on band gap of the zigzag CNTs. While the tensile strain has great effect on band gap of zigzag CNTs, but it has no effect on that of the armchair CNTs. More importantly, when both the tensile and torsional strains are simultaneously applied to the CNTs, the band gap changes of armchair CNTs are not equal to a simple sum over those induced separately by uniaxial tensile and torsional strains. There exists a cooperative effect between two kinds of strains on band gap changes of armchair CNTs. But for zigzag CNTs, the cooperative effect was not found. Analytical expressions for the band gaps of armchair and zigzag CNTs under combined uniaxial–torsional strains have been derived, which agree well with the numerical results.     

Anisotropic elastic behaviour and one‐dimensional metal in phosphorene

Using first‐principles calculations, we investigate the mechanical and electronic properties of phosphorene nanosheets under tensile strains. It is found that phosphorene possesses a prominent anisotropic elasticity with the large anisotropic factor of 15.5. Along the armchair direction, the phosphorene sheet exhibits a high tensile ductility, characterized by a large elastic strain limit of 0.31. While in the zigzag direction, the critical strain of phosphorene is dictated by the phonon instability and the in‐plane soft mode occurs beyond the 0.22 strain. Under uniaxial strains, the band gaps of phosphorene can be modulated continuously, whose band features are also altered accordingly. A Dirac‐like band structure appears in phosphorene under adequate strains along the zigzag direction. More interestingly, these Dirac cones of phosphorene display evident anisotropy, which have high Fermi velocities up to (6 – 7) × 10⁵ m/s along the armchair direction but drop to zero along the zigzag direction. With such a characteristic, the strained phosphorene sheet acts as an intriguing one‐dimensional metal, which enables the system many potential applications in power‐efficient and ultrafast nanodevices. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Electronic structure of collapsed C,BN, and BC3 nanotubes

The electrical properties of single-wall C, BN, and BC₃ nanotubes in ideally rolled-up forms show a wide spectrum from truly metals to large band gap semiconductors. In the presence of radial deformations that collapse tubes, the electrical properties are severely modified such that metals turn into semiconductors and vice versa. Based on first-principles pseudopotential calculations, we find that metallic C nanotubes have a finite band gap if radial deformations break all mirror symmetries of the tubes, and that original finite gaps (∼0.5 eV) of semiconducting C and BC₃ tubes are closed by collapsing deformations. In BN tubes, band gaps can be tuned in the range 2–5 eV. On the other hand, the band gaps of armchair BN and zigzag BC₃ nanotubes are found to be insensitive to radial deformations. These new findings can be applied to design new types of nanotube-based functional devices using radial deformations.     

形变碳纳米管场效应晶体管的电学性质

在紧束缚理论的基础上,推导出轴向拉伸和扭转形变时碳纳米管（CNT）的能带公式.结果显示拉伸和扭转形变都可以改变CNT的导电性质,在金属型和半导体型之间转变,特别是对于锯齿型CNT,根据n 与3的余数关系,在拉伸和扭转中分别显示出三种不同的变化规律.进一步应用场效应晶体管Natori理论模拟计算形变对CNT场效应晶体管的电流-电压特性的影响,锯齿型CNT根据n 与3的余数关系表现出不同的电流变化趋势,而对于扶手椅型CNT轴向拉伸不改变电流;在扭转形变时,CNT电流急剧升高,特别是扶手椅型CNT.锯齿型CNT和扶手椅型CNT的电流随扭转角度和外电压行为明显不同.在某些特定的扭转角度,电流随扭转角度变化非常显著,显示出锯齿型CNT和扶手椅型CNT发生半导体型与金属型之间的转变. 关键词： 碳纳米管 紧束缚理论 费米能级 能带结构     

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.     

Electronic structure and optic absorption of phosphorene under strain

We studied the electronic structure and optic absorption of phosphorene (monolayer of black phosphorus) under strain. Strain was found to be a powerful tool for the band structure engineering. The in-plane strain in armchair or zigzag direction changes the effective mass components along both directions, while the vertical strain only has significant effect on the effective mass in the armchair direction. The band gap is narrowed by compressive in-plane strain and tensile vertical strain. Under certain strain configurations, the gap is closed and the energy band evolves to the semi-Dirac type: the dispersion is linear in the armchair direction and is gapless quadratic in the zigzag direction. The band-edge optic absorption is completely polarized along the armchair direction, and the polarization rate is reduced when the photon energy increases. Strain not only changes the absorption edge (the smallest photon energy for electron transition), but also the absorption polarization.     

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.     

Effects of temperature and vacancy defects on tensile deformation of single-walled carbon nanotubes

This study adopts the Tersoff-Brenner interaction potential function in a series of molecular dynamic (MD) simulations which investigate the mechanical properties under tensile loading of (10,0) zigzag, (8,3) chiral and (6,6) armchair single-walled carbon nanotubes (SWCNTs) of similar radii. The Young's modulus values of the (10,0), (8,3) and (6,6) nanotubes are determined to be approximately 0.92, 0.95, and 1.03 TPa, respectively. Of these nanotubes, the results reveal that the (6,6) nanotube possesses the best tensile strength and toughness properties under tension. Although it is noted that under small tensions, the mechanical properties such as Young's modulus are essentially insensitive to helicity, under larger plastic deformations, they may be influenced by helicity effects. Finally, the simulations demonstrate that the values of the majority of the considered mechanical properties decrease with increasing temperature and increasing vacancy percentage.     

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.     

拉伸作用对单层石墨片电子能隙的影响

基于紧束缚方法,在考虑最近邻相互作用的情况下,研究了拉伸锯齿型边和扶手型边单层石墨的能带结构,得到了两种类型单层石墨片的π电子能带及带隙与拉力的解析关系式.通过数值计算能够发现：拉力不但使单层石墨产生带隙,而且带隙随着拉力的增大而变宽,并且锯齿型比扶手型的带隙更易变宽. 关键词： 单层石墨片 拉伸形变 电子能隙     

Ab initio study of the electronic and transport properties of waved graphene nanoribbons

We apply the nonequilibrium Green's function method based on density functional theory to investigate the electronic and transport properties of waved zigzag and armchair graphene nanoribbons. Our calculations show that out-of-plane mechanical deformations have a strong influence on the band structures and transport characteristics of graphene nanoribbons. The computed I-V curves demonstrate that the electrical conductance of graphene nanoribbons is significantly affected by deformations. The relationship between the conductance and the compression ratio is found to be sensitive to the type of the nanoribbon. The results of our study indicate the possibility of mechanical control of the electronic and transport properties of graphene nanoribbons.     

Electronic structures for armchair-edge graphene nanoribbons under a small uniaxial strain

We theoretically investigate the electronic structures for armchair-edge graphene nanoribbons (AGNRs) under a small in-plane uniaxial strain along armchair (longitudinal) and zigzag (transversal) direction, respectively. We demonstrate that, by both the tight-binding calculation and first-principles study, the applying of a small asymmetrical strain results in variation of energy subband spacing, which opens a band gap for metallic AGNRs and modifies the band gaps for semiconducting AGNRs near the Fermi level. It is believed that these results are of importance in the band gap engineering and electromechanical applications of graphene-nanoribbon-based devices.     

First principles prediction of the third conformer of hydrogenated BN sheet

We report, using first principles density functional calculations, the relative stabilities, structural and electronic properties of various conformers of hydrogenated BN sheet (BHNH). The already known chair and boat BHNH conformers are structurally similar to those of graphane. We propose a third BHNH conformer called ‘stirrup’ which turns out to be the most stable one, as also verified by frequency analysis. In this conformer, the B–H and N–H bonds of a hexagon alternate in 3‐up and 3‐down fashion on either side of the sheet. We also explore that any other alternative hydrogenation of the BN sheet disrupts its periodic puckered geometry and turns out to be energetically less stable. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

曲率效应对超小碳纳米管电子性质的影响

在考虑曲率效应的情况下,在螺旋坐标系下解析地推导了非手性的碳纳米管(SWNTs)(包括扶手椅型和锯齿型)的能量色散关系,并分析了曲率效应对超小扶手椅型SWNTs的能带、能隙和导电能力及其对超小锯齿型SWNTs(包括扶手椅型和锯齿型)的能隙的影响.     

Consideration of mechanical properties of single-walled carbon nanotubes under various loading conditions

In this article, mechanical properties of single-walled carbon nanotubes (SWCNTs) with various radiuses under tensile, compressive and lateral loads are considered. Stress–strain curve, elastic modulus, tensile, compressive and rotational stiffness, buckling behaviour, and critical axial compressive load and pressure of eight different zigzag and armchair SWCNTs are investigated to figure out the effect of radius and chirality on mechanical properties of nanotubes. Using molecular dynamic simulation (MDS) method, it can be explained that SWCNTs have higher Young’s modulus and tensile stiffness than compressive elastic modulus and compressive stiffness. Critical axial force of zigzag SWCNT is independent from the radius, but that of armchair type rises by increasing of radius, also these two types show different buckling modes.     

Strain-induced changes in the band gap of doped carbon nanotubes

The results of a theoretical research into the band gap of strained doped carbon nanotubes of two structural modifications of the “armchair” and “zigzag” types are described. The electronic states in the doped nanotubes are considered in terms of the periodic Anderson model. Nitrogen and boron atoms are selected as donor and acceptor substitutional defects, respectively. The dependences of the band gap of the carbon nanotubes on impurity concentration and compressive and tensile strain are studied.     

A first-principles investigation on the effect of the divacancy defect on the band structures of boron nitride (BN) nanoribbons

On the basis of the comprehensive first-principles computations, we investigated the geometries, electronic and magnetic properties of zigzag and armchair boron nitride nanoribbons (BNNRs) with the divacancy defect of 5–8–5 ring fusions formed by removing B–N pair, where the defect orientation and position are considered. Our computed results reveal that all of the defective BNNRs systems can uniformly exhibit nonmagnetic semiconducting behavior, and the formation of the divacancy 5–8–5 defect can significantly impact the band structures of BNNRs with not only the zigzag but also armchair edges, where their wide band gaps are reduced and the defect orientation and position play an important role. Clearly, introducing divacancy defect can be a promising and effective approach to engineer the band structures of BNNRs, and the present computed results can provide some valuable insights for promoting the practical applications of excellent BN-based nanomaterials in the nanodevices.     

Mechanical properties of kirigami phosphorene via molecular dynamics simulation

The newly discovered two-dimensional phosphorene suffers low stretchability which limits its application in flexible devices. Herein we employ kirigami technique to overcome this limitation. Molecular dynamics simulation is employed to investigate the mechanical properties of kirigami-phosphorene under shear and tensile loadings. Our simulation results show that loading type, intrinsic structural anisotropy, and the height of middle cuts are three key factors that govern the mechanical response of kirigami-phosphorene. Under the tensile loading along the armchair direction, phosphorene exhibits a considerable increase in its tensile strain. By contrast, phosphorene is too weak to stand any structural modification induced by kirigami in the zigzag direction. Under shear loading, there is merely no improvement in the shear properties of kirigami-phosphorene. Our results demonstrate the prospective applications of kirigami-phosphorene along the armchair direction in modern wearable, and stretchable electronics and optoelectronics devices.     

Band-gap modulation of graphane-like SiC nanoribbons under uniaxial elastic strain

The band-gap modulation of zigzag and armchair graphane-like SiC nanoribbons (GSiCNs) under uniaxial elastic strain is investigated using the density functional theory. The results show that band gap of both structures all decreases when being compressed or tensed. In compression, both zigzag and armchair GSiCNs are semiconductors with a direct band gap. However, in tension, the armchair GSiCNs undergo a direct-to-indirect band-gap transition but the zigzag GSiCNs still have a direct band gap. These results are also proved by HSE06 method. This implies a potential application of the graphane-like SiC nanoribbons in the future pressure sensor and optical electronics nanodevices.     

Stability and electronic structure of InN nanotubes from first-principles study

The stability and electronic structure of hypothetical InN nanotubes were studied by first-principles density functional theory. It was found that the strain energies of InN nanotubes are smaller than those of carbon nanotubes of the same radius. Single-wall zigzag InN nanotubes were found to be semiconductors with a direct band gap while the armchair counterparts have an indirect band gap. The band gaps of nanotubes decrease with increasing diameter, similar to the case of carbon nanotubes.