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.     

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.     

Energy gap modulation of graphene nanoribbons by F termination

Under the generalized gradient approximation (GGA), the electronic properties are studied for the F-terminated graphene nanoribbons (GNRs) with either zigzag edge (ZGNRs) or armchair edge (AGNRs) by using the first-principles projector augmented wave potential within the density function theory (DFT) framework. The results show that an edge state appears at the Fermi level E_F in the broader F-terminated ZGNRs, but does not appear in all the F-terminated AGNRs due to their dimerized C-C bonds at edge. The density of states (DOS) and projected DOS (PDOS) analyses show that the F-terminated ZGNRs are metallic and have a sharp peak at the Fermi level when the width is large enough. In contrast, the AGNRs are always semiconductors independent of their width. The charge density contours analyses shows that the C-F bond is an ionic bond due to a much stronger electronegativity of the F atom than that of the C atom. However, all kinds of the C-C bonds display a typical nonpolar covalent bonding feature.     

Magnetoconductivity of band-gap graphene

The effect of a magnetic field on the conductivity of band-gap graphene has been investigated. In the case of a non-quantizing field, the magnetic-field dependences of the conductivity and Hall conductivity have been found on the basis of the Boltzmann equation. The formula for the conductivity of graphene in a quantizing magnetic field at low temperatures has been derived within the Born approximation in the scattering potential. It has been shown that the magnetic-field dependence of the conductivity is oscillatory in this case.     

Strain engineering of graphene nanoribbons: pseudomagnetic versus external magnetic fields

Bandgap opening due to strain engineering is a key architect for making graphene’s optoelectronic, straintronic, and spintronic devices. We study the bandgap opening due to strain induced ripple waves and investigate the interplay between pseudomagnetic fields and externally applied magnetic fields on the band structures and spin relaxation in graphene nanoribbons (GNRs). We show that electron-hole bands of GNRs are highly influenced (i.e. level crossing of the bands are possible) by coupling two combined effects: pseudomagnetic fields (PMF) originating from strain tensor and external magnetic fields. In particular, we show that the tuning of the spin-splitting band extends to large externally applied magnetic fields with increasing values of pseudomagnetic fields. Level crossings of the bands in strained GNRs can also be observed due to the interplay between pseudomagnetic fields and externally applied magnetic fields. We also investigate the influence of this interplay on the electromagnetic field mediated spin relaxation mechanism in GNRs. In particular, we show that the spin hot spot can be observed at approximately B = 65 T (the externally applied magnetic field) and B₀ = 53 T (the magnitude of induced pseudomagnetic field due to ripple waves) which may not be considered as an ideal location for the design of straintronic devices. Our analysis might be used for tuning the bandgaps in strained GNRs and utilized to design the optoelectronic devices for straintronic applications.     

Magnetoconductance of graphene nanoribbons

The electronic and transport properties of monolayer and AB-stacked bilayer zigzag graphene nanoribbons subject to the influences of a magnetic field are investigated theoretically. We demonstrate that the magnetic confinement and the size effect affect the electronic properties competitively. In the limit of a strong magnetic field, the magnetic length is much smaller than the ribbon width, and the bulk electrons are confined solely by the magnetic potential. Their properties are independent of the width, and the Landau levels appear. On the other hand, the size effect dominates in the case of narrow ribbons. In addition, the dispersion relations rely sensitively on the interlayer interactions. Such interactions will modify the subband curvature, create additional band-edge states, change the subband spacing or the energy gap, and separate the partial flat bands. The band structures are symmetric or asymmetric about the Fermi energy for monolayer or bilayer nanoribbons, respectively. The chemical-potential-dependent electrical and thermal conductance exhibits a stepwise increase behaviour. The competition between the magnetic confinement and the size effect will also be reflected in the transport properties. The features of the conductance are found to be strongly dependent on the field strength, number of layers, interlayer interactions, and temperature.     

Specific heat of graphene nanoribbons

We studied the specific heat of graphene nanoribbons (GNRs) using an extended force constant model. We found that at low temperature, the specific heat decreases, and its variation with temperature increases with increasing GNR width. However, the specific heat increases with increasing GNR width after crossing a chaotic region. Free boundary conditions, -CHOH-terminated and armchair-edge-induced phonon nondegeneracy, shift and distortion and localized vibrational modes significantly influence GNR specific heat compared with periodic boundary conditions and bare and zigzag edges in GNRs. Finally, we found a uniform expression for specific heat vs. width at every temperature except for the chaotic region.     

Coulomb blockade in graphene nanoribbons

We propose that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of Coulomb blockade. Electron interactions play a decisive role at the quantum dots which form due to the presence of necks arising from the roughness of the graphene edge. With the average transmission as the only fitting parameter, our theory shows good agreement with the experimental data.     

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     

Zigzag型边界石墨烯纳米带的电子态

在紧束缚近似下, 提出有限系统的Bloch定理方法, 解析计算了Zigzag型石墨烯纳米带的电子态和能带.研究发现, 其电子态有两类, 分别是驻波态和边缘态; 驻波态的波矢为实数, 波函数是正弦函数形式; 边缘态的波矢主要是虚数, 实数部分为零或者π/2, 波函数是双曲正弦函数形式. Zigzag型石墨烯纳米带的能带由驻波态能量和边缘态能量组成, 我们推导了边缘态的关于无限长方向波矢和能量的精确取值范围. 讨论了边缘态和驻波态的过渡点, 发现两种电子态通过不同的方式在受限波矢趋于零时关于格点位置逼近线性关系. 当受限方向也变成无限长时, 可以得到与无限大石墨烯相同的能带关系. 关键词： 紧束缚模型 Zigzag型石墨烯纳米带 边缘态     

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.     

Magnetic anisotropy and engineering of magnetic behavior of the edges in Co embedded graphene nanoribbons

Using first-principles calculations, we demonstrate the existence of anisotropic ferromagnetic interactions in Co embedded graphene nanoribbons (GNRs). Spin polarization of the edge states is found to alter significantly compared to the metal-free cases. Our findings can all be well-justified as the output of the interplay between the development of an induced spin polarization in the neighborhood of the Co atoms and the maintaining of the polarization picture of the Co-free GNR. Based on our results, we propose an efficient pathway for graphene-based spintronics applications.     

Exciton effects in armchair graphene nanoribbons

We have studied the exciton effects in armchair graphene nanoribbons systematically, using the nonorthogonal tight-binding model supplement by the long-range Coulomb interactions. It is found from our calculations that the excitation energies, the exciton binding energies and the exciton wave function sizes of the E ₁₁ and E ₂₂ excitons all exhibit oscillation as a function of the ribbon width. And there is a phase shift of π between the oscillation of the E ₁₁ and E ₂₂ excitons.     

Plasmon resonance in multilayer graphene nanoribbons

Plasmon resonances in nanopatterned single‐layer graphene nanoribbons (SL‐GNRs), double‐layer graphene nanoribbons (DL‐GNRs) and triple‐layer graphene nanoribbons (TL‐GNRs) are studied experimentally using ‘realistic’ graphene samples. The existence of electrically tunable plasmons in stacked multilayer graphene nanoribbons was first experimentally verified by infrared microscopy. We find that the strength of the plasmonic resonance increases in DL‐GNRs when compared to SL‐GNRs. However, further increase was not observed in TL‐GNRs when compared to DL‐GNRs. We carried out systematic full‐wave simulations using a finite‐element technique to validate and fit experimental results, and extract the carrier‐scattering rate as a fitting parameter. The numerical simulations show remarkable agreement with experiments for an unpatterned SLG sheet, and a qualitative agreement for a patterned graphene sheet. We conclude with our perspective of the key bottlenecks in both experiments and theoretical models.

     

Curved graphene nanoribbons and tunneling current

The density of states and the electronic spectrum of long-wave electrons in a curved graphene nanoribbon is calculated on the basis of the Dirac equation in curved space-time. Using this density of states, we obtain the current-voltage characteristics of tunnel junctions of nanoribbons with metal and quantum dots. The dependence of the curved nanoribbon on the geometric parameters is found.     

Lithium adsorption on armchair graphene nanoribbons

Lithium adsorption on two dimensional graphene and armchair graphene nanoribbons is studied using advanced density functional theory calculations. The relative stability of different adsorption sites is investigated taking into account different ribbon widths, adsorbate densities, and spin states. We find the singlet spin state to be the true ground state of the systems considered. For this spin state, the binding energy increases with decreasing adatom density due to lower Coulomb repulsion between the partially charged Li atoms. At low adsorbate densities the favorable adsorption sites on the nanoribbons are found to be the hollow sites near the edges of the ribbon, whereas at higher densities, Li atoms tend to couple on next-nearest neighboring hexagons close to the ribbon's edge. Adsorption of the metal atoms is found to significantly decrease the bandgaps of all systems studied, turning them metallic for sufficiently large adatom densities. This suggests lithium doping as a possible route for bandgap engineering of graphitic systems.     

Electronic properties of Li-doped zigzag graphene nanoribbons

Zigzag graphene nanoribbons (ZGNRs) are known to exhibit metallic behavior. Depending on structural properties such as edge status, doping and width of nanoribbons, the electronic properties of these structures may vary. In this study, changes in electronic properties of crystal by doping Lithium (Li) atom to ZGNR structure are analyzed. In spin polarized calculations are made using Density Functional Theory (DFT) with generalized gradient approximation (GGA) as exchange correlation. As a result of calculations, it has been determined that Li atom affects electronic properties of ZGNR structure significantly. It is observed that ZGNR structure exhibiting metallic behavior in pure state shows half-metal and semiconductor behavior with Li atom.     

Resonant states in heterostructures of graphene nanoribbons

We study the transport properties of heterostructures of armchair graphene nanoribbons (AGNR) forming a double symmetrical barrier configuration. The systems are described by a single-band tight-binding Hamiltonian and Green's functions formalism, based on real-space renormalization techniques. We present results for the quantum conductance and the current for distinct configurations, focusing our analysis on the dependence of the transport with geometrical effects such as separation, width and transverse dimension of the barriers. Our results show the apparition of a series of resonant peaks in the conductance, showing a clear evidence of the presence of resonant states in the conductor. Changes in the barrier dimensions allow the modulation of the resonances in the conductance, making possible to obtain a complete suppression of electron transmission for determined values of the Fermi energy. The current–voltage curves show the presence of a negative differential resistance effect with a threshold voltage that can be controlled by varying the separation between the barriers and by modulating its confinement potential.     

Diverse nanowires activated self-scrolling of graphene nanoribbons

Diverse nanowires (NWs) activating the self-scrolling of planar graphene (GN) nanoribbons have been studied by using molecular dynamics (MD) simulations. Once the NWs’ radiuses reach a threshold, all the seven NWs, acting as an external force, can initiate the conformational change of the GN nanoribbons, and finally form the core/shell composite NWs. Our simulation found that van der Waals (vdW) force plays an important role in the process of forming core/shell composite NWs. This preparation method of the core/shell composite NWs will open a further development of a broad new class of metal/GN core/shell composite NWs with enhanced properties. And these core/shell structures can be the building blocks of functional nanodevices with unique mechanical, electrical, or optical properties.