Double band-inversions of bilayer phosphorene under strain and their effects on optical absorption

Strain is a powerful tool to engineer the band structure of bilayer phosphorene.The band gap can be decreased by vertical tensile strain or in-plane compressive strain.At a critical strain,the gap is closed and the bilayer phosphorene is turn to be a semi-Dirac semimetal material.If the strain is stronger than the criterion,a band-inversion occurs and it re-happens when the strain is larger than another certain value.For the zigzag bilayer phosphorene ribbon,there are two edge band dispersions and each dispersion curve represents two degenerate edge bands.When the first band-inversion happens,one of the edge band dispersion disappears between the band-cross points while the other survives,and the latter will be eliminated between another pair of band-cross points of the second band-inversion.The optical absorption of bilayer phosphorene is highly polarized along armchair direction.When the strain is turn on,the optical absorption edge changes.The absorption rate for armchair polarized light is decreased by gap shrinking,while that for zigzag polarized light increases.The bandtouch and band-inversion respectively result in the sublinear and linear of absorption curve versus light frequency in low frequency limit.     

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.     

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.     

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。     

Strain- and twist-engineered optical absorption of few-layer black phosphorus

Density functional and many-body perturbation theories calculations were carried out to investigate fundamental and optical bandgap, exciton binding energy and optical absorption property of normal and strain- and twist-engineered few-layer black phosphorus (BP). We found that the fundamental bandgaps of few layer BP can be engineered by layer stacking and in-plane strain, with linear relationships to their associated exciton binding energies. The strain-dependent optical absorption behaviors are also anisotropic that the position of the first absorption peak monotonically blue-shifts as the strain applies to either direction for incident light polarized along the armchair direction, but this is not the case for that along the zigzag direction. Given those striking properties, we proposed two prototype devices for building potentially more balanced light absorbers and light filter passes, which promotes further applications and investigations of BP in nanoelectronics and optoelectronics.     

Polarization dependence of two-photon transitions in quantum wells

Summary We give explicitly the polarization dependence of two-photon subband-subband transitions in semiconductor quantum wells. We consider transitions from heavy-hole subbands as well as from light-hole subbands. We study the polarization dependence in the case of absorption of one photon having an energy of the order of the band gap and one having an energy of the order of the subband separation. We show that the absorption structure depends on the polarization of the low-energy photon. We also give, in the case of equal photons with in-plane linear polarizations, the dependence of the transition rate on the angle between the polarizations.     

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)     

Strain Effects on Properties of Phosphorene and Phosphorene Nanoribbons: a DFT and Tight Binding Study

We perform comprehensive density functional theory calculations of strain effect on electronic structure of black phosphorus(BP) and on BP nanoribbons. Both uniaxial and biaxial strain are applied, and the dramatic change of BP's band structure is observed. Under 0-8% uniaxial strain, the band gap can be modulated in the range of 0.55-1.06 eV, and a direct-indirect band gap transition causes strain over 4% in the y direction. Under 0-8% biaxial strain, the band gap can be modulated in the range of 0.35-1.09 eV, and the band gap maintains directly.Applying strain to BP nanoribbon, the band gap value reduces or enlarges markedly either zigzag nanoribbon or armchair nanoribbon. Analyzing the orbital composition and using a tight-binding model we ascribe this band gap behavior to the competition between effects of different bond lengths on band gap. These results would enhance our understanding on strain effects on properties of BP and phosphorene nanoribbon.     

Anomalous strain effect on the thermal conductivity of borophene: a reactive molecular dynamics study

Borophene, an atomically thin, corrugated, crystalline two-dimensional boron sheet, has been recently synthesized. Here we investigate mechanical properties and lattice thermal conductivity of borophene using reactive molecular dynamics simulations. We performed uniaxial tensile strain simulations at room temperature along in-plane directions, and found 2D elastic moduli of 188 N m⁻¹ and 403 N m⁻¹ along zigzag and armchair directions, respectively. This anisotropy is attributed to the buckling of the borophene structure along the zigzag direction. We also performed non-equilibrium molecular dynamics to calculate the lattice thermal conductivity. Considering its size-dependence, we predict room-temperature lattice thermal conductivities of 75.9 ± 5.0 W m⁻¹ K⁻¹ and 147 ± 7.3 W m⁻¹ K⁻¹, respectively, and estimate effective phonon mean free paths of 16.7 ± 1.7 nm and 21.4 ± 1.0 nm for the zigzag and armchair directions. In this case, the anisotropy is attributed to differences in the density of states of low-frequency phonons, with lower group velocities and possibly shorten phonon lifetimes along the zigzag direction. We also observe that when borophene is strained along the armchair direction there is a significant increase in thermal conductivity along that direction. Meanwhile, when the sample is strained along the zigzag direction there is a much smaller increase in thermal conductivity along that direction. For a strain of 8% along the armchair direction the thermal conductivity increases by a factor of 3.5 (250%), whereas for the same amount of strain along the zigzag direction the increase is only by a factor of 1.2 (20%). Our predictions are in agreement with recent first principles results, at a fraction of the computational cost. The simulations shall serve as a guide for experiments concerning mechanical and thermal properties of borophene and related 2D materials.     

Strain-induced structural and direct-to-indirect band gap transition in ZnO nanotubes

First-principles calculations have been employed to investigate the structural transformation and direct to indirect band gap transition of ZnO nanotubes under uniaxial strain. The results show that armchair and zigzag nanotubes can be transformed to each other via unusual fourfold-coordinated structures under the applied strain. Both the armchair and zigzag nanotubes exhibit direct band gap while the unusual fourfold-coordinated ones display indirect band gap. The origin of such a direct-to-indirect band gap transition is explained based on the analyses of atomic orbital contributions.     

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.     

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     

Doping effects on metallic and semiconductor single-wall carbon nanotubes

In this paper we investigate nitrogen- and boron-doped zigzag and armchair single-wall carbon nanotubes (SWNTs) with theoretical models based on the density functional theory. We take into account nitrogen and boron doping for two isomers in which substitutive atoms are on opposite sides of the tube, but only in one isomer the impurity sites are symmetrical with respect to the diameter. The band structures show a strong hybridization with impurity orbitals that change the original band structure. Although the two isomers of armchair SWNT exhibit the same formation energy, their band structures are different. Indeed asymmetrical isomers are gapless and exhibit a crossing of valence and conduction bands at k?=?π/c, leading to metallic SWNTs. Band structures of symmetrical isomers, on the other hand, exhibit an energy gap of 0.4?eV between completely filled valence and empty conduction bands. We use density of charge in order to understand this difference. In zigzag SWNT an impurity band is introduced in the energy gap and for N doping this band is just partially occupied in such a way that the electronic behaviour is reversed from semiconductor to metallic. Whereas for a given isomer armchair SWNT shows similar behaviours of N- and B-doped structures, B-doped zigzag SWNTs present different band structure and occupation compared to the N-doped case.     

第一性原理研究电场对BN纳米管电子结构的影响

采用基于密度泛函理论的第一性原理计算研究了电场对BN纳米管的电子结构的影响.首先对在不同电场强度下的纳米管几何结构进行了优化,可以看出纳米管沿轴方向层间距出现了不规则的变化.电子能带结构显示,在电场作用下,zigzag型和armchair型两种结构纳米管的能带向低能方向移动,并且导致纳米管的带隙有显著的减小.电场使得armchair型纳米管的带隙发生了从间接带隙向直接带隙的转变.在电场作用下,纳米管的两端态密度呈现出明显的差异,正负电荷沿轴向出现了沿轴向的空间分离,Mulliken电荷分布图揭示出最高占据轨道和最低未占据轨道分居在纳米管的两端.     

锯齿型与扶手椅型碳化硅纳米管光电性质第一性原理研究

本文基于密度泛函理论计算分析了手性参数为(17,0)、(20,0)、(26,0) (10,10)、(12,12)、(15,15)的碳化硅纳米管的能带图,态密度及主要光学性质。结果表明：锯齿型与扶手椅型碳化硅纳米管均具有明显的半导体性质;在相近直径下,扶手椅型碳化硅纳米管带隙宽度要大于锯齿型碳化硅纳米管的带隙宽度;碳化硅纳米管的光吸收峰在100nm~200nm之间,可用于制作紫外线探测器件。     

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.     

New class of non-carbon AlP nanotubes: Structure and electronic properties

A new class of non-carbon nanotubes based on Group III and Group V elements (aluminum and phosphorus, respectively) is considered. The equilibrium geometry, energy characteristics, and electronic structure of the AlP nanotubes were calculated using the density functional theory. These calculations demonstrated that the AlP nanotubes are energetically stable structures. It was found that a low strain energy (approximately 0.01–0.07 eV) is required for rolling a two-dimensional hexagonal AlP structure into a tube. The AlP nanotubes are found to be wide-band-gap semiconductors with a band gap of 2.05–3.73 eV with direct (for the zigzag type) or indirect (for the armchair type) transitions between the top of the valence band and the bottom of the conduction band. The band gap of these nanotubes increases with the tube diameter, approaching the band gap of a two-dimensional hexagonal AlP layer.     

电场调控双层石墨烯纳米带的电子结构和光学性质

利用基于密度泛函理论的第一性原理方法,研究了外加电场作用下双层AA堆垛的Armchair边缘石墨烯纳米带(BAGNRs)的电子结构和光学性质. BAGNRs具有半导体特性,其带隙随带宽(宽度为4～12个碳原子)的增加而振荡性减小.当施加电场后,BAGNRs的带隙随着电场强度的增加而逐渐减小,带隙越大对电场值的变化越敏感.当电场值为0.5 V/?时,所有BAGNRs的带隙都为零. BAGNRs具有各向异性的光学性质,其介电函数在垂直极化方向为半导体特性,而在平行极化方向为金属特性.在外加电场的作用下,BAGNRs的介电函数、吸收系数、折射系数、反射系数、电子能量损失系数和光电导率,其峰值向低能量区域移动,即产生红移现象.电场增强了能带间的跃迁几率.纳米带宽度对这些光学性质参数具有不同程度的影响.研究结果解释了电场调控BAGNRs光学性质的规律和微观机理.     

Band structure of deformed armchair nanoribbon with bond alternation

Electronic energy band structure of deformed armchair graphene nanoribbons with bond alternation is studied by the tight-binding approximation. In the presence of bond alternation, all armchair graphene nanoribbons become semiconducting with small band gap opened at center of the Brillouin zone. Under tensional strain, armchair graphene nanoribbons can become metallic at the critical values of deformation and we can control the band gap of nanoribbon by its strain.     

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.