Chiral Graphene Nanoribbons Research Articles

Divacancy in graphene nano-ribbons

We have investigated the reconstruction and electronic structure of divacancy in chiral and achiral graphene nanoribbons as the defect moves to the ribbon edge. The new healing bonds introduce strain dictating the structure and its energetics. Unlike in infinite graphene, the ribbons can take advantage of the edge flexibility in relieving stress. The total energy depends on the defect orientation and its distance to the ribbon edge, and the disposal of the divacancy through the edge results in the energy gains up to ≈7.7 eV. This energy gain is closely related to the pentagon count in the final edge morphology. The divacancy has lower energy near the edge, and thus it is more likely to occur at the edges in the thermodynamic equilibrium. We find that the zigzag portions at the edge induce spin polarization even though the whole edge is not zigzag. However, the spin polarization from discontinuous zigzag portions are not strong and can be modified by the spin polarization around the defect. Moving the divacancy closer to an edge modifies the spin polarization on one side, and the magnetic structure becomes diverse especially in the achiral ribbons. The divacancy induces defect states near EF. The defect level and the extent of its mixing with native ribbon states depend on the defect orientation and distance to the edge.

Bottom-Up Synthesis of Heteroatom-Doped Chiral Graphene Nanoribbons.

Bottom-up synthesis of graphene nanoribbons (GNRs) has significantly advanced during the past decade, providing various GNR structures with tunable properties. The synthesis of chiral GNRs, however, has been underexplored and only limited to (3,1)-GNRs. We report herein the surface-assisted synthesis of the first heteroatom-doped chiral (4,1)-GNRs from the rationally designed precursor 6,16-dibromo-9,10,19,20-tetraoxa-9a,19a-diboratetrabenzo[ a, f, j, o]perylene. The structure of the chiral GNRs has been verified by scanning tunneling microscopy, noncontact atomic force microscopy, and Raman spectroscopy in combination with theoretical modeling. Due to the presence of oxygen-boron-oxygen (OBO) segments on the edges, lateral self-assembly of the GNRs has been observed, realizing well-aligned GNR arrays with different modes of homochiral and heterochiral inter-ribbon assemblies.

Bottom-Up Synthesis of Heteroatom-Doped Chiral Graphene Nanoribbons

Bottom-Up Synthesis of Heteroatom-Doped Chiral Graphene Nanoribbons

Unraveling the Electronic Structure of Narrow Atomically Precise Chiral Graphene Nanoribbons.

Recent advances in graphene-nanoribbon-based research have demonstrated the controlled synthesis of chiral graphene nanoribbons (chGNRs) with atomic precision using strategies of on-surface chemistry. However, their electronic characterization, including typical figures of merit like band gap or frontier band’s effective mass, has not yet been reported. We provide a detailed characterization of (3,1)-chGNRs on Au(111). The structure and epitaxy, as well as the electronic band structure of the ribbons, are analyzed by means of scanning tunneling microscopy and spectroscopy, angle-resolved photoemission, and density functional theory.

A Decatwistacene with an Overall 170° Torsion.

Two different lengths of twistacenes, namely hexatwistacene and decatwistacene, induced by steric hindrance between imide groups and neighboring annulated benzene rings, were synthesized by bottom-up synthesis of palladium-catalyzed Suzuki cross-coupling and C-H activation. Single-crystal X-ray analyses revealed that decatwistacene, which is the longest twistacene reported, exhibits an astonishing overall end-to-end torsion angle of about 170°, the largest torsion angle reported. Both twistacenes have an enhanced solubility and stability with respect to light and oxygen owing to their large twisting deformations together with much lower LUMO levels caused by the introduction of imide groups, opening a window to the narrowest chiral graphene nanoribbons with good stability and processability.

A Decatwistacene with an Overall 170° Torsion

AbstractTwo different lengths of twistacenes, namely hexatwistacene and decatwistacene, induced by steric hindrance between imide groups and neighboring annulated benzene rings, were synthesized by bottom‐up synthesis of palladium‐catalyzed Suzuki cross‐coupling and C−H activation. Single‐crystal X‐ray analyses revealed that decatwistacene, which is the longest twistacene reported, exhibits an astonishing overall end‐to‐end torsion angle of about 170°, the largest torsion angle reported. Both twistacenes have an enhanced solubility and stability with respect to light and oxygen owing to their large twisting deformations together with much lower LUMO levels caused by the introduction of imide groups, opening a window to the narrowest chiral graphene nanoribbons with good stability and processability.

Structure Dependence of Excitonic Effects in Chiral Graphene Nanoribbons**Supported by the National Key Scientific Research Projects of China under Grant No 2015CB932400, the National Natural Science Foundation of China under Grant Nos 11504158, 61474059, and U1432129, the Program for New Century Excellent Talents in University of Ministry of Education of China under Grant No NCET-11-1003, and the Jiangxi Provincial ‘Ganpo

We explore the excitonic effects in chiral graphene nanoribbons (cGNRs), whose edges are composed alternatively of armchair-edged and zigzag-edged segments. For cGNRs dominated by armchair edges, their energy gaps and exciton energies decrease with increasing chirality angles, and they, as functions of widths, oscillate with the period of three, while the exciton binding energies do not have such distinct oscillation. On the other hand, for cGNRs dominated by zigzag edges, all the energy gaps, exciton energies, and exciton binding energies show oscillation properties with their widths, due to the interactions between the edge states localized at the opposite zigzag edges. In addition, the triplet excitons are energy degenerate when the electrons are spin-unpolarized, while the degeneracy split when the electrons are spin-polarized. All the studied cGNRs show strong excitonic effects with the exciton binding energies of hundreds of meV.

Quantum correlations in chiral graphene nanoribbons

We compute the entanglement and the quantum discord (QD) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T (canonical ensemble). We show that the entanglement only exists in inter-edge coupled spin pairs, and there is no entanglement between any two spins at the same ribbon edge. By contrast, almost all edge spin pairs can hold non-zero QD, which strongly depends on the ribbon width and the Coulomb repulsion among electrons. More intriguingly, the dominant entanglement always occurs in the pair of nearest abreast spins across the ribbon, and even at room temperature this type of entanglement is still very robust, especially for narrow CGNRs with the weak Coulomb repulsion. These remarkable properties make CGNRs very promising for possible applications in spin-quantum devices.

Substrate-Independent Growth of Atomically Precise Chiral Graphene Nanoribbons.

Contributing to the need for new graphene nanoribbon (GNR) structures that can be synthesized with atomic precision, we have designed a reactant that renders chiral (3,1)-GNRs after a multistep reaction including Ullmann coupling and cyclodehydrogenation. The nanoribbon synthesis has been successfully proven on different coinage metals, and the formation process, together with the fingerprints associated with each reaction step, has been studied by combining scanning tunneling microscopy, core-level spectroscopy, and density functional calculations. In addition to the GNR’s chiral edge structure, the substantial GNR lengths achieved and the low processing temperature required to complete the reaction grant this reactant extremely interesting properties for potential applications.

Mechanical Properties of Hydrogen Edge–Passivated Chiral Graphene Nanoribbons

AbstractUniaxial tension of chiral graphene nanoribbons (GNR) with and without edge hydrogen passivation are simulated using molecular dynamics (MD) simulations to study their mechanical properties. The results demonstrate that hydrogen saturation generally weakens chiral GNRs, although its influence on armchair GNRs is almost negligible. Mechanical properties of GNRs depend on chiral angles. Zigzag GNRs (chiral angle 0°) are always the strongest, whereas armchair GNRs (chiral angle 30°) are weaker. The mechanical properties of other chiral GNRs evolve gradually from these two distinct cases from chiral angles of 30° to 0°, with the smallest value of failure stress and failure strain happening around a chiral angle of 20°. As for the width size effect, wider GNRs always have lower failure strains and failure stress regardless of having edge hydrogen passivation or not.

Optical properties of chiral graphene nanoribbons: a first principle study

Recent successes in unzipping carbon nanotubes have introduced a new member of graphene nanoribbons (GNRs) family known as chiral GNRs. In this paper, optical properties of chiral GNRs both in longitudinal and transverse polarizations of incident beam have been studied using Density Functional Theory. We have shown that the selection rules, which were previously reported for armchair and zigzag GNRs, are no longer valid due to breaking symmetries in this new family. However, we have demonstrated that the edge states play a critical role in the dielectric constant. It has been shown that, depending on the polarization of incident beam the absorption peaks are different, although they are spread in the same energy range. We also suggested that the absorption energy range is sensitive to the chiral vectors and the light polarization. Due to breaking symmetries in chiral GNRs, absorption peaks are changed becoming approximately 1000 nm, thus a new potential of GNRs for optoelectronic devices is introduced.

Band gap oscillation and novel transport property in ultrathin chiral graphene nanoribbons

We report a numerical study of the edge states in chiral graphene nanoribbons (cGNRs) within the tight-binding approximation. For ultrathin ribbons, band gap oscillations are found as a function of the ribbon width, with a period of 3a, where a is the lattice constant of cGNRs. With the increasing ribbon width, the oscillation is found to be dampened at a critical width, depending on the chiral angle of the cGNRs. In addition, the chiral angle and the width of the cGNR also influence the generation of the edge states. Through the transfer matrix technique, we demonstrate that the energy dependence of the conductance exhibits an unusual step-like feature for cGNRs.

Mechanical properties of graphene nanoribbons with disordered edges

Using density functional theory (DFT), we investigate mechanical properties and failure characteristics of chiral and achiral graphene nanoribbons. Specifically, we study the dependence of maximum strength, Young’s modulus and failure pattern of nanoribbons on their widths, edge chirality and passivation. Besides investigating nanoribbons with perfect edges, nanoribbons with defective edges are considered and the impacts of the presence of Klein or edge pentagonal defects on the properties of nanoribbons are studied. Our DFT results show that as the width of achiral ribbons are reduced, their strength increases. Moreover, significant size effects on the Poisson’s ratio of armchair ribbons and Young’s modulus of zigzag ribbons are observed. The DFT modeling predicts that the presence of defects reduce the strength of chiral nanoribbons while defects might counter intuitively increase the Young’s modulus of chiral nanoribbons. The first-principle simulations show that achiral nanoribbons always fail along a zigzag surface, however the failure pattern of chiral nanoribbons can be more complicated and be accompanied by the nucleation of other kind of defects such as pentagonal–heptagonal rings prior to failure.

Edge magnetization and local density of states in chiral graphene nanoribbons

We study the edge magnetization and the local density of states of chiral graphene nanoribbons using a $\ensuremath{\pi}\text{-orbital}$ Hubbard model in the mean-field approximation. We show that the inclusion of a realistic next-nearest hopping term in the tight-binding Hamiltonian changes the graphene nanoribbon band structure significantly and affects its magnetic properties. We study the behavior of the edge magnetization upon departing from half-filling as a function of the nanoribbon chirality and width. We find that the edge magnetization depends very weakly on the nanoribbon width, regardless of chirality as long as the ribbon is sufficiently wide. We compare our results to recent scanning tunneling microscopy experiments reporting signatures of magnetic ordering in chiral nanoribbons and provide an interpretation for the observed peaks in the local density of states, that does not depend on the antiferromagnetic interedge interaction.

Interplay between symmetry and spin-orbit coupling on graphene nanoribbons

We study the electronic structure of chiral and achiral graphene nanoribbons with symmetric edges, including curvature and spin-orbit effects. Curved ribbons show spin-split bands, whereas flat ribbons present spin-degenerate bands. We show that this effect is due to the breaking of spatial inversion symmetry in curved graphene nanoribbons, while flat ribbons with symmetric edges possess an inversion center, regardless of their having chiral or achiral edges. We find an enhanced edge-edge coupling and a substantial gap in narrow chiral nanoribbons, which is not present in zigzag ribbons of similar width. We attribute these size effects to the mixing of the sublattices imposed by the edge geometry, yielding a distinct behavior of chiral ribbons from those with pure zigzag edges.

Quantum Monte Carlo studies of edge magnetism in chiral graphene nanoribbons

We investigate chiral graphene nanoribbons using projective quantum Monte Carlo simulations within the local Hubbard model description and study the effects of electron-electron interactions on the electronic and magnetic properties at the ribbon edges. Static and dynamical properties are analyzed for nanoribbons of varying width and edge chirality, and compared to a self-consistent Hartee-Fock mean-field approximation. Our results show that for chiral ribbons of sufficient width, the spin correlations exhibit exceedingly long correlation lengths, even between zigzag segments that are well separated by periodic armchair regions. Characteristic enhancements in the magnetic correlations for distinct ribbon widths and chiralities are associated with energy gaps in the tight-binding limit of such ribbons. We identify specific signatures in the local density of states and low- energy modes in the local spectral function which directly relate to enhanced electronic correlations along graphene nanoribbons and which can be accessed scanning tunneling spectroscopy.

Chiral graphene nanoribbons: Objective molecular dynamics simulations and phase-transition modeling

There is a growing need to understand the stability of quasi-one-dimensional one-layer-thick graphene nanoribbons. Objective molecular dynamics based on density-functional tight-binding models are used to investigate the stability against torsional deformations of nanoribbons with bare, F-, and OH-decorated armchair edges. The prevalence of chiral nanoribbons, including homochiral ones, prompted the construction of a simple phenomenological model inspired from the Landau phase transition theory. Our model is based on atomistic data and gives the structural parameters of the nanoribbon as a function of its edge chemistry and axial strain.

Strong current polarization and negative differential resistance in chiral graphene nanoribbons with reconstructed (2,1)-edges

We investigate electronic structures and transport properties of chiral-graphene-nanoribbons (CGNRs) with reconstructed (2,1)-edges. First principles results reveal that the (2,1)-CGNRs can be either spin non-polarized or polarized, depending on whether the edges are H-saturated or unsaturated. H-saturated systems are semiconductors with width-dependent transmission gap, while unsaturated systems are metallic at non-polarized state or at antiferromagnetic state and they are semiconductors at ferromagnetic state. Moreover, unsaturated systems possess strong current polarizations (nearly 100%) and a striking negative differential resistance behavior (with a peak-to-valley ratio about 105). These remarkable properties suggest the potential application of (2,1)-CGNRs in molectronics and spintronics.

Edge currents and nanopore arrays in zigzag and chiral graphene nanoribbons as a route toward high-ZTthermoelectrics

We analyze electronic and phononic quantum transport through zigzag or chiral graphene nanoribbons (GNRs) perforated with an array of nanopores. Since local charge current profiles in these GNRs are peaked around their edges, drilling nanopores in their interior does not affect such edge charge currents while drastically reducing heat current carried by phonons in sufficiently long wires. The combination of these two effects can yield highly efficient thermoelectric devices with maximum $ZT \simeq 11$ at liquid nitrogen temperature and $ZT \simeq 4$ at room temperature achieved in $\sim 1$ $\mu$m long zigzag GNRs with nanopores of variable diameter and spacing between them. Our analysis is based on the $\pi$-orbital tight-binding Hamiltonian with up to third nearest-neighbor hopping for electronic subsystem, the empirical fourth-nearest-neighbor model for phononic subsystem, and nonequilibrium Green function formalism to study quantum transport in both of these models.

Optical Control of Edge Chirality in Graphene

We performed optical annealing experiments at the edges of nanopatterned graphene to study the resultant edge reconstruction. The lithographic patterning direction was orthogonal to a zigzag edge. μ-Raman spectroscopy shows an increase in the polarization contrast of the G band as a function of annealing time. Furthermore, transport measurements reveal a 50% increase of the GNR energy gap after optical exposure, consistent with an increased percentage of armchair segments. These results suggest that edge chirality of graphene devices can be optically purified post electron beam lithography, thereby enabling the realization of chiral graphene nanoribbons and heterostructures.