Chirality effect in disordered graphene ribbon junctions

We investigate the influence of edge chirality on the electronic transport in clean or disordered graphene ribbon junctions. By using the tight-binding model and the Landauer-Büttiker formalism, the junction conductance is obtained. In the clean sample, the zero-magnetic-field junction conductance is strongly chirality-dependent in both unipolar and bipolar ribbons, whereas the high-magnetic-field conductance is either chirality-independent in the unipolar or chirality-dependent in the bipolar ribbon. Furthermore, we study the disordered sample in the presence of magnetic field and find that the junction conductance is always chirality-insensitive for both unipolar and bipolar ribbons with adequate disorders. In addition, the disorder-induced conductance plateaus can exist in all chiral bipolar ribbons provided the disorder strength is moderate. These results suggest that we can neglect the effect of edge chirality in fabricating electronic devices based on the magnetotransport in a disordered graphene ribbon.     

Conductance of bilayer graphene nanoribbons with different widths

The electronic and transport properties of bilayer graphene nanoribbons with different width are investigated theoretically by using the tight-binding model. The energy dispersion relations are found to exhibit significant dependence on the interlayer interactions and the geometry of the bilayer graphene nanoribbons. The energy gaps are oscillatory with the upper ribbon displacement. For all four types of bilayer graphene nanoribbons, the bandgaps touch the zero value and exhibit semiconductor–metal transitions. Variations in the electronic structures with the upper ribbon displacement will be reflected in the electrical and thermal conductance. The chemical-potential-dependent electrical and thermal conductances exhibit a stepwise increase and spike behavior. These conductances can be tuned by varying the upper ribbon displacement. The peak and trench structures of the conductance will be stretched out as the temperature rises. In addition, quantum conductance behavior in bilayer graphene nanoribbons can be observed experimentally at temperature below 10 K.     

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.     

Quantum transport in honeycomb lattice ribbons with armchair and zigzag edges coupled to semi-infinite linear chain leads

We study quantum transport in honeycomb lattice ribbons with either armchair or zigzag edges. The ribbons are coupled to semi-infinite linear chains serving as the input and output leads and we use a tight-binding Hamiltonian with nearest-neighbor hops. The input and output leads are coupled to the ribbons through bar contacts. In narrow ribbons we find transmission gaps for both types of edges. The appearance of this gap is due to the enhanced quantum interference coming from the multiple channels in bar contacts. The center of the gap is at the middle of the band in ribbons with armchair edges. This particle-hole symmetry is because bar contacts do not mix the two sublattices of the underlying bipartite honeycomb lattice when the ribbon has armchair edges. In ribbons with zigzag edges the gap center is displaced to the right of the band center. This breakdown of particle-hole symmetry is the result of bar contacts now mixing the two sublattices. We also find transmission oscillations and resonances within the transmitting region of the band for both types of edges. Extending the length of a ribbon does not affect the width of the transmission gap, as long as the ribbon’s length is longer than a critical value when the gap can form. Increasing the width of the ribbon, however, changes the width of the gap. In ribbons with zigzag edges the gap width systematically shrinks as the width of the ribbon is increased. In ribbons with armchair edges the gap is not well-defined because of the appearance of transmission resonances. We also find only evanescent waves within the gap and both evanescent and propagating waves in the transmitting regions.     

Ab initio study of gold-doped zigzag graphene nanoribbons

The electronic transport properties of zigzag graphene nanoribbons (ZGNRs) through covalent functionalization of gold (Au) atoms is investigated by using non-equilibrium Green’s function combined with density functional theory. It is revealed that the electronic properties of Au-doped ZGNRs vary significantly due to spin and its non-inclusion. We find that the DOS profiles of Au-adsorbed ZGNR due to spin reveal very less number of states available for conduction, whereas non-inclusion of spin results in higher DOS across the Fermi level. Edge Au-doped ribbons exhibit stable structure and are energetically more favorable than the center Au-doped ZGNRs. Though the chemical interaction at the ZGNR–Au interface modifies the Fermi level, Au-adsorbed ZGNR reveals semimetallic properties. A prominent qualitative change of the I–V curve from linear to nonlinear is observed as the Au atom shifts from center toward the edges of the ribbon. Number of peaks present near the Fermi level ensures conductance channels available for charge transport in case of Au-center-substituted ZGNR. We predict semimetallic nature of the Au-adsorbed ZGNR with a high DOS peak distributed over a narrow energy region at the Fermi level and fewer conductance channels. Our calculations for the magnetic properties predict that Au functionalization leads to semiconducting nature with different band gaps for spin up and spin down. The outcomes are compared with the experimental and theoretical results available for other materials.     

Transverse field effect in graphene ribbons

It is shown that a graphene ribbon, a ballistic strip of carbon monolayer, may serve as a quantum wire whose electronic properties can be continuously and reversibly controlled by an externally applied transverse voltage. The electron bands of armchair-edge ribbons undergo dramatic transformations: The Fermi surface fractures, Fermi velocity and effective mass change sign, and excitation gaps are reduced by the transverse field. These effects are manifest in the conductance plateaus, van Hove singularities, thermopower, and activated transport. The control over one-dimensional bands may help enhance effects of electron correlations, and be utilized in device 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.     

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.     

First-principle study of energy band structure of armchair graphene nanoribbons

First-principle calculation is carried out to study the energy band structure of armchair graphene nanoribbons (AGNRs). Hydrogen passivation is found to be crucial to convert the indirect band gaps into direct ones as a result of enhanced interactions between electrons and nuclei at the edge boundaries, as evidenced from the shortened bond length as well as the increased differential charge density. Ribbon width usually leads to the oscillatory variation of band gaps due to quantum confinement no matter hydrogen passivated or not. Mechanical strain may change the crystal symmetry, reduce the overlapping integral of C–C atoms, and hence modify the band gap further, which depends on the specific ribbon width sensitively. In practical applications, those effects will be hybridized to determine the energy band structure and subsequently the electronic properties of graphene. The results can provide insights into the design of carbon-based devices.     

First principles calculations of armchair graphene nanoribbons interacting with Cu atoms

We have investigated the electronic properties of bare, H-terminated, Cu-terminated and Cu-doped armchair graphene nanoribbons (AGNRs) using ab-initio approach. We found that H-termination enhances the stability and band gap whereas H extraction introduces dangling bands and lowers the band gap making bare ribbons indirect band gap semiconductors. The calculations revealed that strong hybridization between Cu atoms and AGNRs, lessen the band gap for Cu-terminated ribbons and gives rise to metallicity in Cu-doped AGNRs irrespective of their widths. Formation energy of considered ribbons yield that H-terminated AGNRs with lowest formation energy are most energetically favored, next are one edge Cu-terminated ribbons followed by bare ones whereas both edges Cu-doped ribbons are least energetically plausible. We predict that presence of Cu atoms in GNRs, significantly alter the band gap and can be used in band gap engineering of nanoribbons.     

Electronic properties and quantum transport in Graphene-based nanostructures

Carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) represent a novel class of low-dimensional materials. All these graphene-based nanostructures are expected to display the extraordinary electronic, thermal and mechanical properties of graphene and are thus promising candidates for a wide range of nanoscience and nanotechnology applications. In this paper, the electronic and quantum transport properties of these carbon nanomaterials are reviewed. Although these systems share the similar graphene electronic structure, confinement effects are playing a crucial role. Indeed, the lateral confinement of charge carriers could create an energy gap near the charge neutrality point, depending on the width of the ribbon, the nanotube diameter, the stacking of the carbon layers regarding the different crystallographic orientations involved. After reviewing the transport properties of defect-free systems, doping and topological defects (including edge disorder) are also proposed as tools to taylor the quantum conductance in these materials. Their unusual electronic and transport properties promote these carbon nanomaterials as promising candidates for new building blocks in a future carbon-based nanoelectronics, thus opening alternatives to present silicon-based electronics devices.     

Synthesis of graphene ribbons using selective chemical vapor deposition

A new method for implementing graphene ribbons using selective graphene growth on metal-sidewall by chemical vapor deposition has been proposed. In this method, Ni catalyst is pre-patterned before chemical vapor deposition, and graphene film is selectively grown on the sidewall of the nickel for graphene ribbons. The graphene ribbons were confirmed by TEM image and Raman spectroscopy, and the fabricated graphene ribbon transistors showed well gate-modulated output characteristics. We believe this sidewall-graphene could be useful for applications such as graphene sensors which require high surface area of graphene.     

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.     

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.     

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.     

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.     

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.     

自旋轨道耦合作用下石墨烯pn结的电子输运性质

本文研究了自旋轨道耦合作用下石墨烯纳米带pn结的电子输运性质. 当粒子的入射能量处于pn结两端势能之间时, 粒子将会以隧穿的形式通过石墨烯pn结, 同时伴随着电子空穴转换. 电导随费米能的变化曲线呈不等高阶梯状, 并在费米能位于pn结两端能量中点时取得最大值. 随着石墨烯pn结长度的增加, 电导以指数形式衰减. 自旋轨道耦合作用导致的能隙会使电导显著减小, 而边缘态的粒子则可以几乎毫无阻碍地通过pn结. 本文用一个简单的子带隧穿模型解释了上述特征. 最后还研究了在pn转换区中掺入替位杂质的情况. 在弱杂质下, 电导随费米能变化的曲线将不再对称; 当杂质较强时, 仅边界态的形成的电导台阶能够保持.     

The electronic properties of graphene and graphene ribbons under simple shear strain

A tight-binding model is used to study the energy band of graphene and graphene ribbon under simple shear strain. The ribbon consists of lines of carbon atoms in an armchair or zigzag orientation where a simple shear strain is applied in the x-direction keeping the atomic distances in the y-direction unchanged. Such modification in the lattice gives an energy band that differs in several aspects from the one without any shear and with pure shear. The changes in the spectrum depend on the line displacement of the ribbon, and also on the modified hopping parameter. It is also shown that this simple shear strain tunes the electronic properties of both graphene and graphene ribbon, opening and closing energy gaps for different displacements of the system. The modified density of states is also shown.