Zigzag-edged Graphene Research Articles

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.

Strain dependence of the heat transport properties of graphene nanoribbons

Using a combination of accurate density-functional theory and a nonequilibrium Green’s function method, we calculate the ballistic thermal conductance characteristics of tensile-strained armchair (AGNR) and zigzag (ZGNR) edge graphene nanoribbons, with widths between 3 and 50 Å. The optimized lateral lattice constants for AGNRs of different widths display a three-family behavior when the ribbons are grouped according to N modulo 3, where N represents the number of carbon atoms across the width of the ribbon. Two lowest-frequency out-of-plane acoustic modes play a decisive role in increasing the thermal conductance of AGNR-N at low temperatures. At high temperatures the effect of tensile strain is to reduce the thermal conductance of AGNR-N and ZGNR-N. These results could be explained by the changes in force constants in the in-plane and out-of-plane directions with the application of strain. This fundamental atomistic understanding of the heat transport in graphene nanoribbons paves a way to effect changes in their thermal properties via strain at various temperatures.

Electronic and magnetic properties of chevron-type graphene nanoribbon edge-terminated by oxygen atoms

The electronic and magnetic properties of the O-terminated chevron-type zigzag-edge graphene nanoribbons (CZGNR) connected by two different kinds of kink angles (120° or 60°) have been investigated by the first-principle calculations. It is found that the O termination on the CZGNR induces the richer electronic and magnetic features than on the straight zigzag-edge graphene nanoribbons, which are sensitive to their widths, lengths, and kink angles. Interestingly, asymmetric edge terminations with O and H atoms can be used to produce some ferromagnetic semiconductors of CZGNR, giving a new approach to tailor the GNRʼs properties and designing the carbon-based magnetic materials.

Valley and subband-selective electronic transport through a line defect embedded carbon nanotube

We theoretically demonstrate the possibility of realizing the valley and subband-selective electronic transport properties if line defects are embedded in an armchair carbon nanotube. The physical mechanism for such an interesting transport property is clearly due to the appearance of the special subband spanning two valleys without dispersion, caused by the presence of the line defect. In contrast to a perfect zigzag-edged graphene nanoribbon, which was previously suggested to be a nanodevice prototype to manipulate the valley and subband degrees of freedom, our structure, the line defect embedded carbon nanotube, is less demanding for the current nanotechnique. Therefore, our theoretical investigation provides an alternative and feasible structure to design carbon-based nanoelectronic devices.

Dirac-equation description of the electronic states of graphene with a line defect: Wave-function connection condition

The presence of an extended line defect in graphene brings about some interesting electronic properties to such a truly two-dimensional (2D) carbon material, such as the energy-band engineering and valley filtering. By establishing an appropriate connection condition for the spinor wave function across the line defect, we find that the massless Dirac equation is still a valid theoretical model to describe low-energy electronic properties of the line defect embedded graphene structure. To check the validity of the wave-function connection condition, we take two kinds of line defect embedded graphene structures as examples to study the low-energy electronic states by solving the Dirac equation. First, for a line defect embedded zigzag-edged graphene nanoribbon, we obtain analytical results about the subband dispersion and eigenwave function, which coincide well with the numerical results from the tight-binding approach. Then, for a 2D graphene embedded with an extended line defect, we get an exact expression about the valley polarized electronic transmission probability, which demonstrates the simple result estimated previously in the zero-energy limit. More interestingly, our analytical result indicates that in such a 2D graphene structure a quasi-one-dimensional (1D) electronic state occurs along the line defect. And the electronic group velocity in this quasi-1D electronic state can be readily modulated by applying a strain field around the line defect.

Boron-doping controlled peculiar transport properties of graphene nanoribbon p–n junctions

We construct two kinds of p–n junctions based on graphene nanoribbons with different doping concentration. The left part of junction is Boron-doped at the edge of zigzag-edge graphene nanoribbon, and the right part is Boron-doped at the center. The transport properties, calculated by nonequilibrium Green's function method combined with the density functional theory under external bias, show obvious rectification effect and interesting negative differential resistance phenomenon depending on Boron-doping density and position. Considering the interaction of charge carriers with impurity and the correlation between charges at the edges and center, the excellent nanoscale electronic devices have been achieved.

Tailoring atomic structure to control the electronic transport in zigzag graphene nanoribbon

We have performed ab initio density functional theory calculation to study the electronic transport properties of the tailored zigzag-edged graphene nanoribbon (ZGNR) with particular electronic transport channels. Our results demonstrated that tailoring the atomic structure had significantly influenced the electronic transport of the defective nanostructures, and could lead to the metal-semiconducting transition when sufficient atoms are tailored. The asymmetric I–V characteristics as a result of symmetry breaking have been exhibited, which indicates the route to utilize GNR as a basic component for novel nanoelectronics.

Graphene with the secondary amine-terminated zigzag edge as a line electron emitter

An extraordinary low vacuum barrier height of 2.30 eV has been found on the zigzag-edge of graphene terminated with the secondary amine via the ab initio calculation. This edge structure has a flat band of edge states attached to the gamma point where the transversal kinetic energy is vanishing. We show that the field electron emission is dominated by the flat band. The edge states pin the Fermi level to a constant, leading to an extremely narrow emission energy width. The graphene with such edge is a promising line field electron emitter that can produce a highly coherent emission current.

Strain-induced ferromagnetism in zigzag edge graphene nanoribbon with a topological line defect

The electronic and magnetic properties of the zigzag edge graphene nanoribbon with a topological line defect (LD-ZGNR) have been studied under an external strain along ribbon axis by using first-principle calculations. It is found that the applied strain induces the local magnetic moments on the line defect, whose coupling with those on the edges leads to a turnover of the spin polarization on one edge, making the LD-ZGNR become a ferromagnetic (FM) metal at a large enough strain. When the strain increases to larger than 16$%$, a transition from a FM metal to a FM semiconductor will happen. Our calculation results suggest a possible way to tune the magnetic and transport properties of the LD-ZGNR by applying the strain, which is very useful for applications of the graphene ribbon in spintronics and electromechanical devices.

Bosonic field theory of tunable edge magnetism in graphene

A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a \phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods.

Stabilizing the ground state in zigzag-edged graphene nanoribbons by dihydrogenation

The dihydrogenation effects in the zigzag-edged graphene nanoribbons (ZGNRs) have been systematically investigated by first-principles calculations. Due to the dihydrogenation, the edges effectively turn to the so-called Klein edges, which results in localized edge states in (0,$\frac{2}{3}\ensuremath{\pi}$) and extended bulk states in ($\frac{2}{3}\ensuremath{\pi},\ensuremath{\pi}$). Compared with monohydrogenation, the edge magnetic moment is substantially increased and the edge states get much more delocalized, which results in the most attractive observation that the energy difference between the antiferromagnetic (AFM) and ferromagnetic (FM) configurations is greatly increased by nearly one order of magnitude from the general several meV and thus the AFM ground state of certain ZGNRs becomes stable at room temperature. This suggests that the dihydrogenated ZGNRs are more promising than monohydrogenated ones for spintronic devices. Our finding provides an enlighening hint for stablizing the ground AFM state in ZGNRs.

The optical conductivity of bilayer zigzag-edge graphene nanoribbons with external transverse electric fields

The optical absorption properties of bilayer zigzag-edge graphene nanoribbons (BL-ZGNRs) with external transverse electric fields are investigated by taking into account the Coulomb interaction effect in the Hartree–Fock approximation. We study the phase transitions of BL-ZGNRs induced by external electric fields and also the optical selection rules for the incident light polarized along the longitudinal and transverse directions. We find that the excitations from the edge states are crucial for the optical properties of BL-ZGNRs in the antiferromagnetic phase. We show that the low energy part of the optical absorption can be modulated by the external transverse electric field, and there is a broad band low frequency absorption enhancement for the transverse-polarized incident light in the charge-polarized state of BL-ZGNRs.

Rectifying regularity for a combined nanostructure of two trigonal graphenes with different edge modifications

The metal- or nonmetal-terminated left zigzag-edge trigonal graphene (M-LTGN or NM-LTGN) is linked to the H-terminated right zigzag-edge trigonal graphene (H-RTGN) through their vertex atoms wholly attached onto Au electrodes to construct nanojunctions. Calculated results show that their rectifying behaviors have very interesting regularities: the rectifying directions for M-LTGN/H-RTGN nanojunction and NM-LTGN/H-RTGN nanojunction are opposite, and the stronger the nonmetallic (metallic) behavior for atom terminated at edge of the LTGN, the larger its rectification ratio for a forward (reverse) rectification. The intrinsic mechanism for these features can be attributed to a Schottky barrier on interface when they are combined due to the charge shifting doping between them. Findings unveiled here are of importance for achieving a profound understanding and developing nanoelectronic devices on the TGN functionalized by edge modification.

Orbital symmetry induced conductance switching in a graphene nanoribbon heterojunction with different edge hydrogenations

First principles calculations are performed to investigate the electron transport through a zigzag-edged graphene nanoribbon (ZGNR) heterojunction constructed by connecting a monohydrogenated ZGNR and a dihydrogenated ZGNR and its response to external magnetic fields. It is found that the heterojunction can be switched between a conducting state and an insulating state by tuning the magnetic fields. It arises from the matching or mismatching between the π or π* states of the two ribbons under different magnetic fields. This mechanism of conductance switching by tuning the orbital symmetry can be considered in the future design of graphene based electronic devices.

Tuning Charge and Spin Excitations in Zigzag Edge Nanographene Ribbons

Graphene and its quasi-one-dimensional counterpart, graphene nanoribbons, present an ideal platform for tweaking their unique electronic, magnetic and mechanical properties by various means for potential next-generation device applications. However, such tweaking requires knowledge of the electron-electron interactions that play a crucial role in these confined geometries. Here, we have investigated the magnetic and conducting properties of zigzag edge graphene nanoribbons (ZGNRs) using the many-body configuration interaction (CI) method on the basis of the Hubbard Hamiltonian. For the half-filled case, the many-body ground state shows a ferromagnetic spin-spin correlation along the zigzag edge, which supports the picture obtained from one-electron theory. However, hole doping reduces the spin and charge excitation gap, making the ground state conducting and magnetic. We also provide a two-state model that explains the low-lying charge and spin excitation spectrum of ZGNRs. An experimental setup to confirm the hole-mediated conducting and magnetic states is discussed.

Wave packet simulations of phonon boundary scattering at graphene edges

Wave packet dynamics is used to investigate the scattering of longitudinal (LA), transverse (TA), and bending-mode (ZA) phonons at the zigzag and armchair edges of suspended graphene. The interatomic forces are calculated using a linearized Tersoff potential. The strength of a boundary scattering event at impeding energy flow is described by a forward scattering coefficient, similar in spirit to a specularity parameter. For armchair boundaries, this scattering coefficient is found to depend strongly on the magnitude, direction, and polarization of the incident wavevector, while for zigzag boundaries, the forward scattering coefficient is found to always be unity regardless of wavevector and polarization. Wave packet splitting is observed for ZA phonons incident on armchair boundaries, while both splitting and mode conversion are observed for LA and TA phonons incident on both zigzag and armchair boundaries. These simulation results show that armchair boundaries impede the forward propagation of acoustic phonon energy much more strongly than zigzag boundaries do, suggesting that graphene nanoribbons will have substantially lower thermal conductivity in armchair rather than zigzag orientation.

Transport properties of zigzag graphene nanoribbons with oxygen edge decoration

Using the density functional theory in combination with the nonequilibrium Green’s function method, we investigate the transport properties of zigzag-edged graphene nanoribbons (ZGNRs) with oxygen edge decoration (passivated by the ketone (CO) or ether (C–O–C), denoting as ZGNR-CO and ZGNR-C2O, respectively). We find that both ZGNR-CO and ZGNR-C2O induce the semiconductor-metal transition and enhance the transmission conductance within ‘transparent’ electrodes. However, sandwiched by Au (111) electrodes, Au∣ZGNR−CO∣Au enhances the transport properties while Au∣ZGNR−C2O∣Au depresses the transport properties in comparison with Au∣ZGNR−H∣Au. It is found that the transport properties of the edge oxidized ZGNRs within Au (111) electrodes depend on the electronic states around the Fermi level which determine the number of the effective transport channels. The states of Au∣ZGNR−CO∣Au are delocalized on the edge oxygen atoms as well as the inner edge carbon atoms, introducing extra transport channels. Moreover, in comparison with Au∣ZGNR−H∣Au, the effective transport channels of Au∣ZGNR−CO∣Au increase at given applied bias. However, the states of Au∣ZGNR−C2O∣Au are localized on the ribbon, blocking the effective transport channels.

Altering regularities of electronic transport properties in twisted graphene nanoribbons

Based on density-function theory combined with nonequilibrium Green’s function method, the electronic transport properties of twisted armchair- and zigzag-edge graphene nanoribbons (AGNRs and ZGNRs) are investigated. Results show that electronic transport properties are sensitive to twisting deformations for semiconductor-type AGNRs, but are robust against twisting deformations for quasi-metallic AGNRs and ZGNRs. The electronic conduction becomes weaker gradually for moderate-gap semiconductor-type AGNRs, but gets stronger for wide-gap semiconductor-type AGNRs when the twisted angle increases to 120°. While for quasi-metallic AGNRs and ZGNRs, the electronic conduction is strong and obeys Ohm’s law of resistance strictly. Mechanisms for such results are suggested.

Valley polarized electronic transmission through a line defect superlattice of graphene

The band structure of a one-dimensional superlattice formed by patterning graphene lattice with a periodic line defect array is calculated. The lowest conduction subband of such a superlattice connects two inequivalent Dirac points with flat dispersion, which is reminiscent of the flat-bottomed subband of a zigzag-edged graphene nanoribbon (ZEGNR). According to such a subband characteristic, a finite length line defect superlattice in graphene, instead of a ZEGNR, can be utilized to realize valley filtering function. The calculated electronic transmission spectrum of such a structure shows the nearly perfect valley polarization for low energy incident electrons.

Electromechanical switch in metallic graphene nanoribbons via twisting

We imposed screwing operation to a metallic ferromagnetic zigzag-edged graphene nanoribbon (ZGNR) with a narrow width and a finite length, and the polarized charge transport is investigated by using Nonequilibrium Green's function in combination with density functional theory. The current are nearly completely suppressed when the ZGNRs are overturned. Inspiringly, this metal-to-semiconductor transition tuned by screwing operation is reversible. Hence our investigation brings forward a novel electromechanical switch, and such a switch is equivalent to a spin valve without resort to an external magnetic field.