Energy band-gap engineering of graphene nanoribbons

We investigate electronic transport in lithographically patterned graphene ribbon structures where the lateral confinement of charge carriers creates an energy gap near the charge neutrality point. Individual graphene layers are contacted with metal electrodes and patterned into ribbons of varying widths and different crystallographic orientations. The temperature dependent conductance measurements show larger energy gaps opening for narrower ribbons. The sizes of these energy gaps are investigated by measuring the conductance in the nonlinear response regime at low temperatures. We find that the energy gap scales inversely with the ribbon width, thus demonstrating the ability to engineer the band gap of graphene nanostructures by lithographic processes.     

Ultrarelativistic electron-hole pairing in graphene bilayer

We consider the ground state of an electron-hole graphene bilayer composed of two independently-doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only the conduction band of the electron-doped layer and the valence band of the hole-doped layer, thus the ground state is similar to an ordinary BCS condensate. At strong coupling, an ultrarelativistic character of the electron dynamics reveals itself and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. Analysis of the instability of the unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. The relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of a separable potential. It is shown that, if the characteristic width of the pairing region is of the order of magnitude of the chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.     

石墨烯纳米带的制备与电学特性调控

石墨烯由于其独特的晶体结构展现出了特殊的电学特性,其导带与价带相交于第一布里渊区的六个顶点处,形成带隙为零的半金属材料,具有优异的电子传输特性的同时也限制了其在电子学器件中的使用.因而科研人员尝试各种方法来打开其带隙并调控其能带特性,主要有利用缺陷、应力、掺杂、表面吸附、结构调控等手段.其中石墨烯纳米带由于量子边界效应和限制效应,存在带隙.本综述主要介绍了制备各类石墨烯纳米带的方法,并通过精确调控其细微结构,从而对其进行精确的能带调控,改变其电学特性,为其在电子学器件中的应用提供一些可行的方向.     

扭转形变对石墨烯吸附O原子电学和光学性质影响的电子理论研究

基于密度泛函理论的第一性原理方法研究了扭转形变对石墨烯吸附O体系结构稳定性、电子结构和光学性质,包括吸附能、带隙、吸收系数及反射率的影响.研究发现,吸附O原子后,距O原子最近的C原子被拔起,导致石墨烯平面发生扭曲.吸附能计算表明,扭转形变使石墨烯吸附O原子体系结构稳定性下降,而扭转程度对结构稳定性影响微弱.能带结构分析发现,O原子的吸附使石墨烯由金属变成半导体,扭转形变发生时,可实现其从半导体到金属、再到半导体特性的转变.扭转角为12°的吸附O原子体系为间接带隙,而其他出现带隙的体系均为直接带隙.与本征石墨烯受扭体系相比,吸附O原子体系的电子结构对扭转形变的敏感度降低,其中扭转角在10°—16°范围内变化时,带隙始终稳定在0.11 eV附近,即在此扭转角范围内始终对应窄带隙半导体.在光学性能中,受扭转形变的吸附体系吸收系数和反射率峰值较未受扭转形变石墨烯吸附O原子体系均减弱,且随着扭转程度的加剧,均出现红移到蓝移的转变.     

锯齿型石墨烯纳米带的能带研究

运用π电子紧束缚模型,具体研究了锯齿型石墨烯纳米带(ZGNRs)的边界结构对能带,特别是费米面附近的导带和价带电子的影响.计算了七种不同边界结构的ZGNRs的能带色散关系及费米面附近价带电子在原胞中各原子上的分布情况.计算结果表明:两边界都无悬挂原子的NN-ZGNRs,只有一边界有悬挂原子的DN-ZGNRs,两边界都有五边形环的SPP-ZGNRs和ASPP-ZGNRs为金属性.两边界都有悬挂原子的DD-ZGNRs,一边界为五边形环另一边界无悬挂原子的PN-ZGNRs和一边界为五边形环另一边界有悬挂原子的P 关键词： 锯齿型石墨烯纳米带 紧束缚模型 电子密度分布 缺陷结构     

铂掺杂扶手椅型石墨烯纳米带的电学特性研究

本文采用基于密度泛函理论(DFT)的第一性原理计算了铂原子填充扶手椅型石墨烯纳米带(AGNR)中双空位结构的电学性能.计算结果表明: 通过控制铂原子的掺杂位置, 可以实现纳米带循环经历小带隙半导体—金属—大带隙半导体的相变过程; 纳米带边缘位置是铂原子掺杂的最稳定位置, 边缘掺杂纳米带的带隙值随宽度的变化与本征AGNR一样可用三簇曲线表示, 但在较大宽度时简并成两条曲线, 一定程度上抑制了带隙值的振荡; 并且铂原子边缘掺杂导致宽度系数N_a = 3p和3p + 1(p是一个整数)的几个较窄纳米带的带隙中出现杂质能级, 有效地降低了其过大的带隙值. 此外, 铂掺杂AGNR的能带结构对掺杂浓度不是很敏感, 从而降低了对实验精度的挑战. 本文的计算有利于推动石墨烯纳米带在纳米电子学方面的应用.     

单空位缺陷对石墨纳米带电子结构和输运性质的影响

基于第一性原理电子结构和输运性质计算,研究了单空位缺陷对单层石墨纳米带(包括zigzag型和armchair型带)电子性质的影响.研究发现,单空位缺陷使石墨纳米带在费米面上出现一平直的缺陷态能带;单空位缺陷的引入使zigzag型半导体性的石墨纳米带变为金属性,这在能带工程中有重要的应用价值;奇数宽度的armchair型石墨纳米带表现出金属特性,有着很好的导电性能,同时,偶数宽度的armchair型石墨带虽有金属性的能带结构,但却有类似半导体的伏安特性;单空位缺陷使得奇数宽度的armchair石墨纳米带导电 关键词： 石墨纳米带 单空位缺陷 电子结构 输运性质     

Manipulation of resonant tunneling by substrate-induced inhomogeneous energy band gaps in graphene with square superlattice potentials

We investigate the resonant transmission of Dirac electrons through inhomogeneous band gap graphene with square superlattice potentials by transfer matrix method. The effects of the incident angle of the electrons, Fermi energy and substrate-induced Dirac gaps on the transmission are considered. It is found that the Dirac gap of graphene adds another degree of freedom with respect to the incident angle, the Fermi energy and the parameters of periodic superlattice potentials (i.e., the number, width and height of the barriers) for the transmission. In particular, the inhomogeneous Dirac gap induced by staggered substrates can be used to manipulate the transmission. The properties of the conductance and Fano factor at the resonant peaks are found to be affected by the gaps significantly. The results may be helpful for the practical application of graphene-based electronic devices.     

Temperature effects on the band gaps of Lamb waves in a one-dimensional phononic-crystal plate (L)

This study investigates the temperature-tuned band gaps of Lamb waves in a one-dimensional phononic-crystal plate, which is formed by alternating strips of ferroelectric ceramic Ba(0.7)Sr(0.3)TiO(3) and epoxy. The sensitive and continuous temperature-tunability of Lamb wave band gaps is demonstrated using the analyses of the band structures and the transmission spectra. The width and position of Lamb wave band gaps shift prominently with variation of temperature in the range of 26 °C-50 °C. For example, the width of the second band gap increases from 0.066 to 0.111 MHz as the temperature is increased from 26 °C to 50 °C. The strong shift promises that the structure could be suitable for temperature-tuned multi-frequency Lamb wave filters.     

Graphene based photonic crystal optical filter: Design and exploration of the tunability

Optical characteristics of two new graphene based photonic crystals are studied in detail. A structure containing alternating layers of graphene and SiO₂ slabs is considered as the ideal crystal. The dependency of the photonic band gaps (PBGs) to the dielectric layer thickness and the period number is explored at first step. Potential of the proposed crystal to be used as an optical filter is then investigated. Adding a nonlinear electro-optic polymer as a defect layer, the alterations of the optical features are inspected. Results show that the defect layer insertion causes a resonant mode inside the PBGs. However, the location of the defect layer inside the crystal is very effective on both the frequency and width of the resonant mode. Tunability of the optical features is probed by taking into account of the dependencies to the wave incident angle, graphene chemical potential and the applied external voltage to the defect layer.     

双空位缺陷石墨纳米带的电子结构和输运性质研究

基于第一原理电子结构和输运性质计算,研究了585双空位拓扑缺陷对锯齿（zigzag）型石墨纳米带（具有椅型（armchair）边）电子结构和输运性质的影响.研究发现,585双空位缺陷的存在使得锯齿型石墨纳米带的能隙增大,并在能隙中出现了一条局域于缺陷处的缺陷态能带,双空位缺陷的取向也影响其能带结构.另外,585双空位缺陷对能隙较小的锯齿型石墨纳米带输运性质的影响较大,而对能隙较大的锯齿型石墨纳米带影响很小,缺陷取向并不显著影响纳米带的输运性质. 关键词： 石墨纳米带 585空位缺陷 电子结构 输运性质     

双色光晶格势阱中玻色-爱因斯坦凝聚体的Landau-Zener隧穿行为

考虑玻色-爱因斯坦凝聚体局限于周期性的双色光晶格势阱中,研究其中的Bloch能带结构、第一能隙和第二能隙的Landau-Zener隧穿行为.结果表明,随着双色光晶格势阱的主、次晶格相位差从0增加到π,Bloch能带中第一能隙宽度逐渐增加,而第二能隙宽度逐渐减小.同时发现,双色光晶格势阱的主、次晶格深度及其相位差对第一能隙和第二能隙的Landau-Zener隧穿性质有重要的影响.     

非近邻跳跃对扶手椅型石墨烯纳米带电子结构的影响

根据π电子的紧束缚模型,将电子的次近邻和第三近邻跳跃能考虑在内,得到扶手椅型石墨烯纳米带（AGRNs）能带结构的解析解.讨论了由次近邻和第三近邻电子跳跃引起的能带和能隙变化,发现次近邻和第三近邻跳跃分别对带隙产生增大和减小的影响. 比较了边界弛豫与非近邻跳跃之间的互相竞争关系. 当纳米带的宽度n为奇数时,二维石墨面的紧束缚模型中所固有的van Hove奇异性表现为AGRNs中的无色散带. 当AGRNs宽度增加时,能谱趋向于二维石墨烯时的能谱结构. 关键词： 扶手椅型石墨烯纳米带 非近邻跳跃 边界弛豫 电子结构     

旋转双层石墨烯的电子结构

本文将第一性原理和紧束缚方法结合起来, 研究了层间不同旋转角度对双层石墨烯的电子能带结构和态密度的影响. 分析发现, 旋转双层石墨烯具有线性的电子能量色散关系, 但其费米速度随着旋转角度的减小而降低. 进一步研究其电子能带结构发现, 不同旋转角度的双层石墨烯在M点可能会出现大小不同的的带隙, 而这些能隙会增强双层石墨烯的拉曼模强度, 并由拉曼光谱实验所证实. 通过对比双层石墨烯的晶体结构和电子态密度, 发现M点处带隙来自于晶体结构中的“类AB堆垛区”. 关键词： 旋转双层石墨烯 第一性原理 紧束缚 电子结构     

Electronic properties of bearded graphene nanoribbons

We investigate the electronic properties of graphene nanoribbons with attachment of bearded bonds as a model of edge modification. The main effect of the addition of the beards is the appearance of additional energy subbands. The originally gapless armchair graphene nanoribbons become semiconducting. On the other hand, the originally semiconducting armchair graphene nanoribbons may or may not change to gapless systems depending on the width. With the inclusion of a transverse electric field, the band structures of bearded graphene nanoribbons are further altered. An electric field creates additional band-edge states, and changes the subband curvatures and spacings. Furthermore, the energy band symmetry about the chemical potential is lifted by the field. With varying width, the bandgap demonstrates a declining zigzag behavior, and touches the zero value regularly. Modifications in the electronic structure are reflected in the density of states. The numbers and energies of the density of state divergent peaks are found to be strongly dependent on the geometry and the electric field strength. The beard also causes electron transfer among different atoms, and alters the probability distributions. In addition, the electron transfers are modified by the electric field. Finally, the field introduces more zero values in the probability distributions, and removes their left–right symmetry.     

Quasiparticle energies and band gaps in graphene nanoribbons

We present calculations of the quasiparticle energies and band gaps of graphene nanoribbons (GNRs) carried out using a first-principles many-electron Green's function approach within the GW approximation. Because of the quasi-one-dimensional nature of a GNR, electron-electron interaction effects due to the enhanced screened Coulomb interaction and confinement geometry greatly influence the quasiparticle band gap. Compared with previous tight-binding and density functional theory studies, our calculated quasiparticle band gaps show significant self-energy corrections for both armchair and zigzag GNRs, in the range of 0.5-3.0 eV for ribbons of width 2.4-0.4 nm. The quasiparticle band gaps found here suggest that use of GNRs for electronic device components in ambient conditions may be viable.     

Power flow analysis in a hybrid phononic crystal structure

To reveal the energy transmission through a hybrid phononic crystal structure, power flow analysis is carried out in this paper. Hysteretic damping having significant relationship with power flow is added and corresponding theoretical formulas of the dispersion relation are derived. Besides, the power flow in the hybrid structure is calculated by using the finite element method. The results show that as the damping increases, the boundaries of the band gaps become smoother and dimmer, i.e., broader width. With the increase of damping, the power flow is lowered at the resonance frequencies,while slightly increases near the resonance frequencies. The power flow maps manifest energy distribution in the hybrid structure within and out of the band gaps, which can be exploited in the optimization of the structure design.     

带状碳单层与石墨基底之间相互作用的第一性原理计算

利用基于密度泛函理论的第一性原理计算,研究边缘为Armchair型带状碳单层与石墨基底的相互作用,结果发现,其间的相互作用导致双方发生变形,带状碳单层的禁带宽度较其独立存在时有所减小,但石墨基底的作用并不改变其能带结构的基本特征. 关键词： 带状碳单层 第一性原理计算 能带结构     

Carrier generation and recombination rate in armchair graphene nanoribbons

Armchair graphene nanoribbons (A-GNRs), with a tunable energy gap, are an alternative structure for use in optoelectronic devices. The performance of these optoelectronic devices critically depends on the carrier generation and recombination rates, which have been calculated in this paper. Because of the 1D band structure of A-GNRs, carrier scattering, generation and recombination rates in these structures would be completely different from those in 2D graphene sheets. In this paper, using the tight binding model, and by considering the edge deformation and Fermi golden rule, we find the band structure, and the carrier generation and recombination rates for pure A-GNR due to optical and acoustic phonons, as well as Line Edge Roughness (LER) scatterings. The obtained results show that the total generation and recombination rates increase with increasing A-GNR width and eventually saturate for wide ribbons. These rates increase as the carrier concentration is increased (which has been considered homogenous along ribbon width) and temperature. Also, despite the large LER scattering in narrow ribbons, the generation and recombination rates are less for A-GNRs than for graphene sheets. Using this theoretical model, one can find the suitable A-GNR structure for the design of optoelectronic devices.     

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.