Zigzag-edged Graphene Nanoribbons Research Articles

The Effect of Lithium Adsorption and Edge Modification in the Electronic Transport of Zigzag Graphene Nanoribbons

The influence of Lithium adatom and edge modification on the electronic structure and the transport properties of zigzag-edged graphene nanoribbons (ZGNRs) were studied using ab initio density functional theory in combination with the nonequilibrium green’s function methods. We find that lithium adatoms adsorb preferentially on hollow sites of ZGNRs with edge modifications. However, the interaction of Li with ZGNRs gradually decreases as the adsorption site is moved towards the center of the nanoribbons. The transmission conductance of hydrogen terminated ZGNR (ZGNR-H) and hydroxyl terminated ZGNR (ZGNR-OH) are similar which means that the incoming wave function is not scattered, resulting in ballistic transport. However, as a result of lithium adsorption a dip drop near the Fermi level is observed in both systems indicating a strong scattering at this energy level. Based on the transport calculation, we have found that the ZGNR-H shows the worst conductance among the three GNRs being studied.

Bias Dependence of Rectifying Direction in a Diblock Co-oligomer Molecule with Graphene Nanoribbon Electrodes

By applying nonequilibrium Green’s function method in combination with density functional theory, we study the rectifying properties of dipyrimidinyl-diphenyl co-oligomer molecules embedded in a carbon atomic chain sandwiched between two graphene nanoribbon (GNR) electrodes. Both the length of the carbon atomic chains and the edge geometry of the graphene nanoribbon electrodes are shown to play a significant role in determining the conductance behavior and rectifying performance of the molecular devices. As for GNRs with zigzag edges, the parallel (perpendicular) conformation between the principal plane of the molecule and the zigzag-edged GNR electrode is observed to be dependent on the odd (even) number of carbon atoms in the carbon chain, whereas for armchair-edged GNRs the parallel (perpendicular) case corresponds to an even (odd) number of carbon atoms. Taking an asymmetric arrangement of armchair and zigzag GNR electrodes, we demonstrate a molecular device having very interesting rectifying behaviors with marked rectification ratios at low bias voltages and inversion of rectifying direction when the bias voltage is large. Analysis of the transmission coefficients and molecular projected self-consistent Hamiltonian as well as band structures of the electrodes under various external bias voltages reveals an underlying mechanism of the observed results.

Spin filter effects in zigzag-edge graphene nanoribbons with symmetric and asymmetric edge hydrogenations

Using the non-equilibrium Green’s function method combined with the density functional theory, we investigate the magnetism and spin-dependent transport properties of symmetric and asymmetric zigzag–edged graphene nanoribbons (ZGNRs) passivated by monohydrogenation with [1, −1] magnetism configuration. The symmetric model H–6ZGNR–H shows a dual spin filter effect, but asymmetric H–5ZGNR–H behaves as a conductor with linear current–voltage relationships. We also investigate the magnetism and spin-dependent transport properties of H2–ZGNR–H with asymmetric edge hydrogenations, the perfect dual spin filtering effect is observed in both H2–5ZGNR–H and H2–6ZGNR–H. The transmission pathways and PDOS demonstrate that the edge of C-H2 bonds have important effects on the magnetism and spin-dependent transport properties as compared with the edge of C–H bonds.

Raman spectroscopy investigations of chemically derived zigzag edge graphene nanoribbons

We fabricated graphene nanoribbons (GNRs) chemically derived from expandable graphite. All GNRs exhibit atomically smooth edges that extended over their entire length. We investigated four of the fabricated GNRs using Raman spectroscopy. Two of the investigated GNRs show Raman spectra with a missing D-band peak, while D-band peaks can be clearly observed for the other two GNRs. The two GNRs which do not show the D-band peak are GNRs with zigzag edges, and the two other GNRs which show clearly the D-band peaks are possibly GNRs with armchair edges.

Structural, electronic and magnetic properties of transition-metal embedded zigzag-edged graphene nanoribbons

By means of ab initio calculations within density-functional theory, the structural, electronic and magnetic properties of a zigzag-edged graphene nanoribbon (ZGNR) with 3d transition-metal atoms (TMAs) (Sc–Zn) embedded in the periodically distributed single vacancies are systematically studied. Different from the pristine ZGNR, all of these composite structures show the subband structures with nontrivial spin polarizations, regardless of the type and the embedding position of the TMA. Embedding one kind of these atoms (V, Cr, Ni, Cu or Zn) near one ribbon edge can cause a notable edge distortion. Except for the cases of Sc, Fe and Co doping, other kinds of TMAs embedded near an edge of the ribbon can suppress the inherent magnetism of the zigzag edge. By further analysis, we find that two effects are responsible for the suppression of edge magnetism. One is the variation of the occupied spin-polarized subbands due to the hybridization of the edge state of the ZGNR and 3d atomic states of the dopant. The other is the delocalization of the edge state caused by the exotic TMA. The unilateral magnetism of these TMA-embedded ZGNRs can be utilized to realize the spin-polarized electronic transport, which is the key electronic property in the context of spintronics applications of carbon-based materials.

A valley-filtering switch based on the Stone-Wales defect array in carbon nanotube

We theoretically demonstrate that valley-filtering switch can be realized in a carbon nanotube (CNT) embedded with a series of Stone-Wales defects. It is due to the fact that such a CNT shows two peculiar subbands which span two Dirac valleys without nontrivial dispersion, just like the flat-bottomed subbands of a zigzag-edged graphene nanoribbon. Considering that similar defects have been experimentally patterned in a CNT in a controllable way, this kind of CNT is a promising device prototype for valleytronic applications.

Localized vibrational, edges and breathing modes of graphene nanoribbons with topological line defects

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.

Investigating the edge state of graphene nanoribbons by a chemical approach: Synthesis and magnetic properties of zigzag-edged nanographene molecules

The edge state, which is a peculiar magnetic state in zigzag-edged graphene nanoribbons (GNRs) originating from an electron–electron correlation in an edge-localized π-state, has promising applications for magnetic and spintronics devices and has attracted much attention of physicists, chemists, and engineers. For deeper understanding the edge state, precise fabrication of edge structures in GNRs has been highly demanded. We focus on [a.b]periacene, which are polycyclic aromatic hydrocarbons (PAHs) that have zigzag and armchair edges on molecular periphery, as a model compound for the understanding and actually prepare and characterize them. This review summarizes our recent studies on the origin of the edge state by investigating [a.b]periacene in terms of the relationship between the molecular structure and spin-localizing character.

Effects of size on the structure and the electronic properties of graphene nanoribbons

In view of the current interest in graphene, especially graphene nanoribbons (GNRs), we carried out investigations using the molecular orbital cluster approach to find suitable models for use in simulations involving GNRs. Two types of nanoribbons were modeled, namely armchair- and zigzag-edged GNRs. We used four properties in determining the suitable models: molecular orbitals, spin densities, charges, and bond lengths. Among these criteria, it was found that size has a highly prominent effect on the molecular orbitals and bond lengths. The results show that models of sizes C126H32 and C110H30 are needed to represent the electronic and structural properties of infinite zigzag-edged and armchair-edged GNRs.

Electronic properties of four typical zigzag-edged graphyne nanoribbons

The subband structures and edge magnetism of α-, β-, γ- and (6, 6, 12)-graphyne nanoribbons with zigzag edges are studied by means of ab initio calculations. Dispersionless subbands and antiparallel edge magnetic ordering occur in these nanostructures, just like in zigzag-edged graphene nanoribbons. More importantly, a very simple tight-binding model is established which can accurately describe the subband structures of these ribbons. From such a model we find that β-graphyne nanoribbon has many more transport modes than other graphyne and graphene nanoribbons, hence it can carry a much larger current. Such a tight-binding model provides a simple but effective way to study further the transport and optical properties of these graphyne nanoribbons.

Nanostructural Effects on Thermoelectric Power of Graphene Nanoribbons

Nanostructural effects on the thermoelectric power of graphene nanoribbons (GNRs) are revealed through first-principles simulation based on the density functional theory combined with nonequilibrium Green's function theory. The thermoelectric power of GNRs exhibits essentially different behavior depending on their edge structure and ribbon width. For zigzag-edged GNRs, the thermoelectric power shows a peculiar energy dependence originating from edge-localized electronic states with energy near the Fermi level. On the other hand, for armchair-edged GNRs (AGNRs), the thermoelectric power is classified into three categories depending on the ribbon width. Among AGNRs with similar ribbon width, an AGNR belonging to a category satisfying mod(Na, 3)=1 displays the largest thermoelectric power, where Na is the integer determining the ribbon width of an AGNR.

Thermopower and thermoconductance properties of zigzag edged graphene nanoribbon based thermoelectric module

Abstract The thermopower S and thermoconductance κ properties of graphene nanoribbon based three terminal thermoelectric module are studied theoretically in two cases: with magnetic field and without magnetic field. By using the non-equilibrium Greenʼs function method combined with the Landauer–Buttiker formula, the electric current and linear electrical conductance through the system is obtained. The S – E F curves show a series of peaks and dips and κ – E F curves show plateau structures. The κ – E F relation is roughly linear when there is no magnetic field and is parabolic when in the quantum Hall regime because of the unique Dirac fermion in graphene. The dependence of S and κ on the on-site energy of the terminals, sample size and Anderson disorder are investigated as well.

A theoretical investigation on the possible improvement of spin-filter effects by an electric field for a zigzag graphene nanoribbon with a line defect

The spin-polarized electronic properties for a zigzag-edge graphene nanoribbon (ZGNR) with an extended line defect are investigated, particularly focusing on controlling the effects of an external transverse electric field (Eext). An ab initio scanning tunneling microscope image for the defective ZGNR is also predicted. Results show that such a ZGNR can exhibit a strong spin polarization and ferromagnetic state, and the spin-filter effect can be significantly tuned and improved by the Eext. The spin-filter efficiency for our proposed device is predicted to be able to reach up to 60–81% in a large bias range of 0–0.6V at Eext=3.0V/nm. Mechanisms for such results and the experimental feasibility for the device are suggested. These findings suggest a new possibility for developing nanometer-scale all-carbon spintronic devices.

Gate modulation on angle-resolved photoabsorption spectra of zigzag-edge graphene nanoribbons

Graphene nanoribbons (GNRs) exhibit novel and special electronic and optical properties with promising technological applications. The gate modulation on angle-resolved photoabsorption spectra of zigzag-edge GNRs (ZGNRs) is investigated based on the Hubbard model in the Hartree-Fock approximation. By examining the electron transition processes and the optical selection rules taking into account the Coulomb interaction effect, we demonstrate that the excitations from the edge states of ZGNRs are essential for the optical properties in the neutral case, and show the energy of the absorption peaks has the dispersion and splitting effects with increasing momentum transfer from the incident light. By modulating the chemical potential of ZGNRs, the intraband transitions which are forbidden for the neutral ZGNRs at zero temperature become important for the low energy optical properties, and a Drude peak of the optical conductivity emerges in the low frequency region.

Erratum: Strain-induced ferromagnetism in zigzag edge graphene nanoribbon with a topological line defect [Phys. Rev. B86, 125420 (2012)

Erratum: Strain-induced ferromagnetism in zigzag edge graphene nanoribbon with a topological line defect [Phys. Rev. B86, 125420 (2012)

Geometric and electronic structures of sulfur-edge-terminated zigzag edge graphene nanoribbons

The stable geometric and electronic structures of the fully and half sulfur-edge-functionalized ZGNRs at their widths of four zigzag carbon chains (S-4-ZGNRs) have been studied by using the ab initio density-functional method. It is found from our calculations that (1) under the periodic boundary condition, the two-dimensional plane structures are the most stable ground states in all the possible isomers of the S-4-ZGNRs at both 100% and 50% terminations, which are all metallic. (2) A much delocalized characteristic S-px lone-pair electron's band crossing its Fermi level appears in the case of fully S-edge-termination, which is more extended in a large energy range of over 8.0eV, in contrast to the corresponding oxygen-px (O-px) band of the O-4-ZGNR, covering only a small energy range of 3.2eV. In the case of half S-edge-termination, however, the S-px band is found to be much more localized, which forms two almost flat bands at about+3.0eV above its Fermi level. (3) More interestingly, at 50% S-edge-termination, a flat portion of the π-electron edge states is found to lie a little bit below its Fermi level, making its unpolarized ground state unstable. And thus the spin-polarized antiferromagnetic (AFM) state is found to be the real ground state of the half S-4-ZGNR, which is a semiconductor with an indirect energy gap of about 0.16eV. In the AFM ground state, there exists magnetic moments of about 0.2μB on each edge carbon atom, which is FM coupling along the same edge, but AFM coupling between its two edges.

Spin polarization effects of zigzag-edge graphene electrodes on the rectifying performance of the D-σ-A molecular diode

Sandwiching the D-σ-A molecule between zigzag-edge graphene nanoribbon (ZGNR) electrodes to construct a particular diode and simultaneously considering the reported experimental results that the demonstration of different spin-polarized states of ZGNRs is possible under different conditions, we perform the first-principles calculations on rectifying behaviors of such a diode. It has been found that its rectification ratio is greatly enhanced by ZGNR electrodes (the maximum rectification ratio >700) as compared with that by metal electrodes where its highest rectification ratio only in the order of 10 was reported. Also predicted is that its rectifying behaviors strongly depends on spin-polarized states of ZGNR electrodes, when electrodes take the AFM state (anti-ferromagnetic state), it has a best rectifying behavior.

Electronic transport between quantum Hall states and quantum anomalous Hall states in a graphene nanoribbon based heterojunction

We theoretically investigate the electronic transport between quantum Hall states and quantum anomalous Hall states in a zigzag edged graphene nanoribbon based two-terminal heterojunction. The electrical conductance of the system is calculated by the method of the non-equilibrium Green’s function and Landauer–Büttiker formula. We find perfect transmission through the junction when the propagation direction of the charge carriers is the same at the same edge in both regions. However, when the propagation direction at the same edge is the opposite, the electrical conductance is smaller than the quantized value. In this case, snake states at the interface are responsible for the transmission. The results are explained with the aid of the local density of states near the interface. For higher magnetic field in the quantum Hall region or larger ribbon width, the edge states are better realized and quantized electrical conductance is strengthened. Finally, the effects of Anderson disorder and dephasing on the transmission are discussed.

Synthesis and Characterization of Quarteranthene: Elucidating the Characteristics of the Edge State of Graphene Nanoribbons at the Molecular Level

The characteristics of the edge state, which is a peculiar magnetic state in zigzag-edged graphene nanoribbons (ZGNRs) that originates from electron-electron correlation in an edge-localized π-state, are investigated by preparing and characterizing quarteranthene molecules. The molecular geometry that was determined from the X-ray analysis is consistent with a zigzag-edge-localized structure of unpaired electrons. The localized electrons are responsible for the peculiar magnetic (room-temperature ferromagnetic correlation), optical (the lowest-lying doubly excited state), and chemical (peroxide bond formation) behaviors. On the basis of these distinguishing properties and a careful consideration of the valence bonding, insight into the edge state of ZGNRs can be gained.

Twisting effects on energy band structures and transmission behaviors of graphene nanoribbons

By using the first-principles method based on the density-functional theory, twisting- deformation-dependent electrical characteristics of graphene nanoribbons (GNRs) are studied systematically. It is shown that the energy gap of the zigzag-edge graphene nanoribbon (ZGNR) is the most insensitive to twisting deformation, and it almost keeps metallicity unchanged, next is the armchair-edge graphene nanoribbons (AGNRs) by width W=3p-1 (p is a positive integer), and its gap has only a small change when twisting deformation occurs. However, the gap of AGNR with width W=3p+1 is extremely sensitive to twisting deformation, and it can display a variation from wide-gap semiconductor to moderate-gap semiconductor, quasi-metal, and metal, next is AGNR with W=3p. In other words, the larger the band gap for GNR in the absence of twisting deformation, the more significant the change (becoming small) of its band gap with twisting deformation. Additionally, for the whole electronic structure and transmission behavior, one can find that there is a much larger influence under twisting deformation in AGNR than in ZGNR. These studies suggest that it is necessary to take the effect of twisting deformation on the electrical characteristics into account in designing GNR-based nanodevices.