Spontaneous twist and intrinsic instabilities of pristine graphene nanoribbons

In pristine graphene ribbons, disruption of the aromatic bond network results in depopulation of covalent orbitals and tends to elongate the edge, with an effective force of f _e ～ 2 eV/Å (larger for armchair edges than for zigzag edges, according to calculations). This force can have quite striking macroscopic manifestations in the case of narrow ribbons, as it favors their spontaneous twisting, resulting in the parallel edges forming a double helix, resembling DNA, with a pitch t of about 15–20 lattice parameters. Through atomistic simulations, we investigate how the torsion τ ～ 1/λ _t decreases with the width of the ribbon, and observe its bifurcation: the twist of wider ribbons abruptly vanishes and instead the corrugation localizes near the edges. The length-scale (λ _e) of the emerging sinusoidal “frill” at the edge is fully determined by the intrinsic parameters of graphene, namely its bending stiffness D=1.5 eV and the edge force f _e with λ _e ～D/f _e. Analysis reveals other warping configurations and suggests their sensitivity to the chemical passivation of the edges, leading to possible applications in sensors.      

Achieving large transport bandgaps in bilayer graphene

Since opening sizable bandgaps in bilayer graphene (BLG) was proven possible, BLG has attracted considerable attention as a promising high-mobility candidate material for many electronic and optoelectronic applications. However, the bandgaps observed in the transport experiments reported in the literature are far smaller than both the theoretical predictions and the bandgaps extracted from optical measurements. In this study, we investigate the factors preventing the formation of large bandgaps and demonstrate that a ~200-meV transport bandgap can be opened in BLG by scaling the gate dielectric and employing a ribbon channel to suppress the percolative transport. This is the largest transport bandgap that has been achieved in BLG to date.

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Band gap of strained graphene nanoribbons

The band structures of strained graphene nanoribbons (GNRs) are examined using a tight-binding Hamiltonian that is directly related to the type and magnitude of strain. Compared to a two-dimensional graphene whose band gap remains close to zero even if a large strain is applied, the band gap of a graphene nanoribbon (GNR) is sensitive to both uniaxial and shear strains. The effect of strain on the electronic structure of a GNR depends strongly on its edge shape and structural indices. For an armchair GNR, a weak uniaxial strain changes the band gap in a linear fashion, whereas a large strain results in periodic oscillation of the band gap. On the other hand, shear strain always tends to reduce the band gap. For a zigzag GNR, the effect of strain is to change the spin polarization at the edges of GNR, and thereby modulate the band gap. A simple analytical model, which agrees with the numerical results, is proposed to interpret the response of the band gap to strain in armchair GNRs.      

Fibers of reduced graphene oxide nanoribbons

Reduced graphene oxide nanoribbon fibers were fabricated by using an electrophoretic self-assembly method without the use of any polymer or surfactant. We report electrical and field emission properties of the fibers as a function of reduction degree. In particular, the thermally annealed fiber showed superior field emission performance with a low potential for field emission (0.7?V?μm(-1)) and a giant field emission current density (400?A?cm(-2)). Moreover, the fiber maintains a high current level of 300?A?cm(-2) corresponding to 1?mA during long-term operation.     

Strain effects in graphene and graphene nanoribbons: The underlying mechanism

A tight-binding analytic framework is combined with first-principles calculations to reveal the mechanism underlying the strain effects on electronic structures of graphene and graphene nanoribbons (GNRs). It provides a unified and precise formulation of the strain effects under various circumstances-including the shift of the Fermi (Dirac) points, the change in band gap of armchair GNRs with uniaxial strain in a zigzag pattern and its insensitivity to shear strain, and the variation of the k-range of edge states in zigzag GNRs under uniaxial and shear strains which determine the gap behavior via the spin polarization interaction.      

Efficient synthesis of graphene nanoribbons sonochemically cut from graphene sheets

We report a facile approach to synthesize narrow and long graphene nanoribbons (GNRs) by sonochemically cutting chemically derived graphene sheets (GSs). The yield of GNRs can reach ∼5 wt% of the starting GSs. The resulting GNRs are several micrometers in length, with ∼75% being single-layer, and ∼40% being narrower than 20 nm in width. A chemical tailoring mechanism involving oxygen-unzipping of GSs under sonochemical conditions is proposed on the basis of experimental observations and previously reported theoretical calculations; it is suggested that the formation and distribution of line faults on graphite oxide and GSs play crucial roles in the formation of GNRs. These results open up the possibilities of the large-scale synthesis and various technological applications of GNRs.      

Nonlocal exchange interaction removes half-metallicity in graphene nanoribbons

Band gap studies of zigzag-edge graphene ribbons are presented. While earlier calculations at LDA level show that zigzag-edge graphene ribbons become half-metallic when cross-ribbon electric fields are applied, our calculations with hybrid density functional demonstrate that finite graphene ribbons behave as half-semiconductors. The spin-dependent band gap can be changed in a wide range, making possible many applications in spintronics.     

Size-dependent non-linear mechanical properties of graphene nanoribbons

An atomistic, spring-based, non-linear finite element method is implemented in order to predict the non-linear mechanical behavior of graphene nanoribbons. According this method, appropriate non-linear springs are utilized to simulate each interatomic interaction. Their force–displacement curve follows the relation between the first differentiation of the potential energy of the corresponding interaction-bond deformation. The potential which corresponds to the bond angle variation is simulated by a torsional spring, while the bond stretching is simulated by a uniaxial compression/extension spring. The linear approximation, commonly made in the literature for the bond angle bending interaction, is not followed here and thus the overall non-linear response of the specific interaction is accurately introduced into the model. Following the proposed formulation, the tensile uniaxial stress–strain behavior for various graphene nanoribbons, of zigzag as well as armchair orientation, arise. The results demonstrate that the linear and non-linear mechanical properties are strongly dependent on the structure as well as on the size of the graphene strip tested.     

Carbon nanotube-dependent synthesis of armchair graphene nanoribbons

Sub-nanometer armchair graphene nanoribbons(GNRs)with moderate band gap have great potential towards novel nanodevices.GNRs can be synthesized in the confined t...     

Excitonic effects in the optical spectra of graphene nanoribbons

We present a first-principles calculation of the optical properties of armchair-edged graphene nanoribbons (AGNRs) with many-electron effects included. The reduced dimensionality of the AGNRs gives rise to an enhanced electron-hole binding energy for both bright and dark exciton states (0.8-1.4 eV for GNRs with width approximately 1.2 nm) and dramatically changes the optical spectra owing to a near complete transfer of oscillator strength to the exciton states from the continuum transitions. The characteristics of the excitons of the three distinct families of AGNRs are compared and discussed. The enhanced excitonic effects found here are expected to be of importance in optoelectronic applications of graphene-based nanostructures.     

Quantum inductance and high frequency oscillators in graphene nanoribbons

Here we investigate high frequency AC transport through narrow graphene nanoribbons with top-gate potentials that form a localized quantum dot. We show that as a consequence of the finite dwell time of an electron inside the quantum dot (QD), the QD behaves like a classical inductor at sufficiently high frequencies ω ≥ GHz. When the geometric capacitance of the top-gate and the quantum capacitance of the nanoribbon are accounted for, the admittance of the device behaves like a classical serial RLC circuit with resonant frequencies ω ～ 100-900 GHz and Q-factors greater than 10(6). These results indicate that graphene nanoribbons can serve as all-electronic ultra-high frequency oscillators and filters, thereby extending the reach of high frequency electronics into new domains.     

Electronic states of graphene nanoribbons and analytical solutions

Abstract

Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.     

Low-loss, high-permittivity composites made from graphene nanoribbons

A new composite material was prepared by incorporation of graphene nanoribbons into a dielectric host matrix. The composite possesses remarkably low loss at reasonably high permittivity values. By varying the content of the conductive filler, one can tune the loss and permittivity to desirable values over a wide range. The obtained data exemplifies how nanoscopic changes in the structure of conductive filler can affect macroscopic properties of composite material.     

Synthesis of graphene nanoribbons encapsulated in single-walled carbon nanotubes

A novel material, graphene nanoribbons encapsulated in single-walled carbon nanotubes (GNR@SWNT), was synthesized using confined polymerization and fusion of polycyclic aromatic hydrocarbon (PAH) molecules. Formation of the GNR is possible due to confinement effects provided by the one-dimensional space inside nanotubes, which helps to align coronene or perylene molecules edge to edge to achieve dimerization and oligomerization of the molecules into long nanoribbons. Almost 100% filling of SWNT with GNR is achieved while nanoribbon length is limited only by the length of the encapsulating nanotube. The PAH fusion reaction provides a very simple and easily scalable method to synthesize GNR@SWNT in macroscopic amounts. First-principle simulations indicate that encapsulation of the GNRs is energetically favorable and that the electronic structure of the encapsulated GNRs is the same as for the free-standing ones, pointing to possible applications of the GNR@SWNT structures in photonics and nanoelectronics.     

Electronic structure and stability of semiconducting graphene nanoribbons

We present a systematic density functional theory study of the electronic properties, optical spectra, and relative thermodynamic stability of semiconducting graphene nanoribbons. We consider ribbons with different edge nature including bare and hydrogen-terminated ribbons, several crystallographic orientations, and widths up to 3 nm. Our results can be extrapolated to wider ribbons providing a qualitative way of determining the electronic properties of ribbons with widths of practical significance. We predict that in order to produce materials with band gaps similar to Ge or InN, the width of the ribbons must be between 2 and 3 nm. If larger bang gap ribbons are needed (like Si, InP, or GaAs), their width must be reduced to 1-2 nm. According to the extrapolated inverse power law obtained in this work, armchair carbon nanoribbons of widths larger than 8 nm will present a maximum band gap of 0.3 eV, while for ribbons with a width of 80 nm the maximum possible band gap is 0.05 eV. For chiral nanoribbons the band gap oscillations rapidly vanish as a function of the chiral angle indicating that a careful design of their crystallographic nature is an essential ingredient for controlling their electronic properties. Optical excitations show important differences between ribbons with and without hydrogen termination and are found to be sensitive to the carbon nanoribbon width. This should provide a practical way of revealing information on their size and the nature of their edges.     

Gate electrostatics and quantum capacitance of graphene nanoribbons

Capacitance-voltage (C-V) characteristics are important for understanding fundamental electronic structures and device applications of nanomaterials. The C-V characteristics of graphene nanoribbons (GNRs) are examined using self-consistent atomistic simulations. The results indicate strong dependence of the GNR C-V characteristics on the edge shape. For zigzag edge GNRs, highly nonuniform charge distribution in the transverse direction due to edge states lowers the gate capacitance considerably, and the self-consistent electrostatic potential significantly alters the band structure and carrier velocity. For an armchair edge GNR, the quantum capacitance is a factor of 2 smaller than its corresponding zigzag carbon nanotube, and a multiple gate geometry is less beneficial for transistor applications. Magnetic field results in pronounced oscillations on C-V characteristics.