Armchair Ribbons Research Articles

Electronic structure and transport of a carbon chain between graphene nanoribbonleads

The electronic structure and transport property of a carbon chain between two graphenenanoribbon leads are studied using an ab initio tight-binding (TB) model and Landauer’sformalism combined with a non-equilibrium Green’s function. The TB Hamiltonian andoverlap matrices are extracted from first-principles density functional calculations throughthe quasi-atomic minimal basis orbital scheme. The accuracy of the TB model isdemonstrated by comparing the electronic structure from the TB model with that fromfirst-principles density functional theory. The results of electronic transport on a carbonatomic chain connected to armchair and zigzag graphene ribbon leads, such asdifferent transport characters near the Fermi level and at most one quantizedconductance, reveal the effect of the electronic structure of the leads and the scatteringfrom the atomic chain. In addition, bond length alternation and an interestingtransmission resonance are observed in the atomic chain connected to zigzaggraphene ribbon leads. Our approach provides a promising route to quantitativeinvestigation of both the electronic structure and transport property of large systems.

Simulation of thermal conductance across dimensionally mismatched graphene interfaces

This paper considers phonon transport behavior in graphene nanoribbons (GNRs) that bridge semi-infinite graphene contacts. The work employs an atomistic Green’s function (AGF) method to investigate phonon wave effects in GNRs with both zigzag and armchair edges. Thermal conductances are found to be sensitive to the edge shape of the ribbons; a sandwiched zigzag GNR structure has almost twice the thermal conductance of the corresponding armchair structure. Results show that the graphene/GNR interface moderately reduces phonon conductance compared to a freestanding GNR. At fixed device lengths, conductance increases with the width of GNR. On the other hand, conductance decreases with GNR length. The zigzag ribbons show smaller reduction upon increasing of GNR length than armchair ribbons; the conductances of both ribbons converge to a length-independent value. For very short devices, thermal conductance can exceed that of a single graphene-GNR interface.

On the possibility of zigzag and armchair silicon nanoribbons having the graphene structure

The possibility of stable two dimensional armchair and zigzag silicon nanoribbons having the same structure as graphene is examined using Density Functional Theory (DFT). The calculations predict that armchair Si ribbons, but not zigzag ribbons, are stable two dimensional structures. The electronic and magnetic properties of undoped and hole and electron doped armchair Si ribbons are calculated. It is predicted that electron and hole doped Si armchair ribbons have the potential to be ferromagnetic semiconductors.

WKB analysis of edge states in graphene in a strong magnetic field

We investigate the fine structure of the edge states energy spectrum for zigzag and armchair ribbons of graphene in a strong magnetic field. At low energy, the spectra can be described by an effective Schrodinger Hamiltonian with a double well potential, symmetric in the zigzag case and asymmetric in the armchair case. We develop a semiclassical formalism based on the WKB approximation to calculate analytically the energy spectrum for the two types of edges, including regions which were not studied earlier. Our results are in very good quantitative agreement with numerical calculations. This approach leads to a qualitative description of the spectra in terms of the quantization of unusual classical orbits in the real space.

Edges Bring New Dimension to Graphene Nanoribbons

Chemistry at the edges of saturated graphene nanoribbons can cause ribbons to leave the plane and form three-dimensional helical structures. Calculations, based on density functional theory and enabled by adopting helical symmetry, show that F-terminated armchair ribbons are intrinsically twisted in helices, unlike flat H-terminated strips. Twisting ribbons of either termination couple the conduction and valence bands, resulting in band gap modulation. This electromechanical response could be exploited in switches and sensor applications.

Electronic and magnetic properties of graphane nanoribbons

In this study, we investigate the electronic and magnetic properties of graphane nanoribbons. We find that zigzag and armchair graphane nanoribbons with H-passivated edges are nonmagnetic semiconductors. While bare armchair ribbons are also nonmagnetic, adjacent dangling bonds of bare zigzag ribbons have antiferromagnetic ordering at the same edge. Band gaps of the H-passivated zigzag and armchair nanoribbons exponentially depend on their width. Detailed analysis of adsorption of C, O, Si, Pt, Ti, V and Fe atoms on the graphane ribbon surface reveal that functionalization of graphane ribbons is possible via these adatoms. It is found that C, O, V and Pt atoms have tendency to replace H atoms of graphane. We showed that significant spin polarizations in graphane can be achieved through creation of domains of H-vacancies and CH-divacancies.

Focusing of electron flow in a bipolar graphene ribbon with different chiralities

The focusing of electron flow in a symmetric p-n junction (PNJ) of graphene ribbon with different chiralities is studied. Considering the PNJ with the sharp interface, in a armchair ribbon, the electron flow emitting from $(-L,0)$ in n-region can always be focused perfectly at $(L,0)$ in p-region in the whole Dirac fermion regime, i.e. in whole regime $E_0<t$ where $E_0$ is the distance between Dirac-point energy and Fermi energy and $t$ is the nearest hopping energy. For the bipolar ribbon with zigzag edge, however, the incoming electron flow in n-region is perfectly converged in p-region only in a very low energy regime with $E_0<0.05t$. Moreover, for a smooth PNJ, electrons are backscattered near PNJ, which weakens the focusing effect. But the focusing pattern still remains the same as that of the sharp PNJ. In addition, quantum oscillation in charge density occurs due to the interference between forward and backward scattering. Finally, in the presence of weak perpendicular magnetic field, charge carriers are deflected in opposite directions in the p-region and n-region. As a result, the focusing effect is smeared. The lower energy $E_0$, the easier the focusing effect is destroyed. For the high energy $E_0$ (e.g. $E_0=0.9t$), however, the focusing effect can still survive in a moderate magnetic field on order of one Tesla.

Nernst and Seebeck effects in a graphene nanoribbon

The thermoelectric power, including the Nernst and Seebeck effects, in graphene nanoribbon is studied. By using the non-equilibrium Green function combining with the tight-binding Hamiltonian, the Nernst and Seebeck coefficients are obtained. Due to the electron-hole symmetry, the Nernst coefficient is an even function of the Fermi energy while the Seebeck coefficient is an odd function regardless of the magnetic field. In the presence of a strong magnetic field, the Nernst and Seebeck coefficients are almost independent of the chirality and width of the nanoribbon, and they show peaks when the Fermi energy crosses the Landau levels. The height of $n$-th (excluding $n=0$) peak is $[\ln2/|n|]$ for the Nernst effect and is $\ln2/n$ for the Seebeck effect. For the zeroth peak, it is abnormal with height $[2\ln2]$ for the Nernst effect and the peak disappears for the Seebeck effect. When the magnetic field is turned off, however, the Nernst effect is absent and only Seebeck effect exists. In this case, the Seebeck coefficient strongly depends on the chirality of the nanoribbon. The peaks are equidistant for the nanoribbons with zigzag edge but are irregularly distributed for the armchair edge. In particular, for the insulating armchair ribbon, the Seebeck coefficient can be very large near the Dirac point. When the magnetic field varies from zero to large values, the differences among the Seebeck coefficients for different chiral ribbons gradually vanish and the nonzero value of Nernst coefficient appears first near the Dirac point then gradually extents to the whole energy region.

The thermodynamic stability and simulated STM images of graphene nanoribbons

AbstractIn this study, we investigated the edge formation energy of hydrogen‐terminated graphene nanoribbons as a function of the chemical potential of the environment as well as their electronic and magnetic properties by means of density functional theory. The single‐hydrogen‐terminated zigzag ribbons, well known for their antiferromagnetic edge states, were found to be stable only under extremely low vacuum pressures. At more standard conditions, the most stable structures are the single‐ and double‐hydrogenated armchair edges and a zigzag edge configuration with one double‐ and two single‐hydrogenated sites. At high hydrogen pressure, the edge formation energy becomes negative, meaning that graphene spontaneously breaks into ribbons. Clar type bond formulas proved to be an excellent tool for the rationale behind the stability, existence of edge states, and appearance of magnetism, and they are in perfect agreement with simulated scanning tunneling microscope (STM) images of the ribbons.Bond formulas and simulated STM images show an identical pattern of Clar sextets. Left: single‐hydrogen‐terminated armchair ribbon. Right: double‐hydrogen‐terminated armchair ribbon. U = −0.5 V, sample–tip distance fixed at 3 Å. magnified image

Low-energy electron transport in semimetal graphene ribbon junctions

Based on the nearest-neighbor tight-binding model, we present analytical description of single-mode electron transport through a common-edged junction connecting two semimetal armchair ribbons of different width. The results obtained demonstrate the transmission suppression in the vicinity of the neutrality point except for the junction of the ribbons consisting of 3p-1 and 3p+2 dimer lines, p is odd. Unlike other interconnections, this junction is shown to be free of local levels arising at the junction interface and exhibits electron backscattering to be inversely as the square of 2p+1. We also demonstrate that non-zero propagation through a graphene junction can be described by the same relation as that for linear undimerized chain of atoms with one defect bond.

Effective time-reversal symmetry breaking and energy spectra of graphene armchair rings

We study the energy spectra and wavefunctions of graphene rings formed from metallic armchair ribbons, near zero energy, to search for properties which may be identified with "effective broken time reversal symmetry" (EBTRS). Appropriately chosen corner junctions are shown to impose phase shifts in the wavefunctions that at low energies have the same effect as effective flux tubes passing near the ribbon surface. Closing the ribbon into a ring captures this flux and yields properties that may be understood as signatures of EBTRS. These include a gap in the spectrum around zero energy, which can be removed by the application of real magnetic flux through the ring. Spectra of five and seven sided rings are also examined, and it is shown these do not have particle-hole symmetry, which may also be understood as a consequence of EBTRS, and is connected to the curvature induced in the system when such rings are formed. Effects of deviations from the ideal geometries on the spectra are also examined.

Ballistic thermal conductance of electrons in graphene ribbons

We investigate the ballistic thermal conductance of electrons in gated graphene ribbons with width above 20 nm and clarify both the temperature and the Fermi-level dependences. In the intrinsic graphene ribbons, the normalized thermal conductance by the quantum conductance, ${\ensuremath{\kappa}}_{0}$, increases monotonically with temperature. In the gated graphene ribbons, the normalized thermal conductance increases steplikely as the Fermi level increases but it has nonmonotonic temperature dependence when the Fermi level is a little larger than the bottom of the subband. The value of the step height changes from $4{\ensuremath{\kappa}}_{0}$ to $2{\ensuremath{\kappa}}_{0}$ with increasing temperature. The ballistic electron thermal conductance per unit width of graphene ribbons is smaller than those of corresponding single-walled nanotubes and a graphene sheet and it approaches at 100 K that of a graphene sheet above the ribbon width of about 80 and 50 nm for zigzag ribbons and armchair ribbons, respectively.

Structure−Reactivity Relationships for Graphene Nanoribbons

The first structure−reactivity relationships for electron-transfer reactions of graphene nanoribbons (GNR) have been derived. These relationships are represented as relative reaction rate constants calculated by considering different electronic structure approximations of GNR and the Gerischer−Marcus (GM) or Marcus theories of electron transfer. The reactivity of GNR is observed to directly depend on the ribbon width and the orientations of carbon atoms at their edges. A comparison of relative rate constants for the more accurate GM electron-transfer theory and tight-binding approximations predicts that armchair and zigzag GNR have opposite trends in reactivity with the former increasing with width and the latter decreasing. For zigzag ribbons, the major reactivity contribution comes from their edge states, and hence, ribbons of small widths are predicted to be the most reactive among all ribbons including armchair ribbons. The reactivity trend for zigzag GNR is reversed, however, when recent first-princi...

Transport in disordered graphene nanoribbons

We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size. We find that in this case, the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure. We then provide numerical evidence and qualitative arguments that similar behavior also occurs in the limit of strong uncorrelated boundary disorder.

Perfect Reflection of Chiral Fermions in Gated Graphene Nanoribbons

We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a nonequilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find perfect reflection of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.

Anomalous Doping Effects on Charge Transport in Graphene Nanoribbons

We present first-principles calculations of quantum transport in chemically doped graphene nanoribbons with a width of up to 4 nm. The presence of boron and nitrogen impurities is shown to yield resonant backscattering, whose features are strongly dependent on the symmetry and the width of the ribbon, as well as the position of the dopants. Full suppression of backscattering is obtained on the pi-pi* plateau when the impurity preserves the mirror symmetry of armchair ribbons. Further, an unusual acceptor-donor transition is observed in zigzag ribbons. These unconventional doping effects could be used to design novel types of switching devices.

Quantum conductance of achiral graphene ribbons and carbon tubes

Explicit expressions of the band spectrum near the neutrality point are derived for armchair and zigzag graphene ribbons and carbon tubes. Several spectral features, which were previously observed only in numerical calculations, are given an adequate analytic description in terms of elementary functions. The obtained dispersion relations are used for a comparison of conductance ladders of graphene-based wires; these relations are also beneficial for many other applications.

Electric-field induced modification of electronic properties of few-layer graphene nanoribbons

In the presence of electric fields, the low-energy electronic properties of AB-stacked few-layer graphene nanoribbons are studied by using the tight-binding model. They are strongly dependent on the geometric structures (the interlayer interactions, the ribbon edges, the ribbon width Ny, and the ribbon number Nz) and the field strength. The interlayer interactions significantly affect density of states (DOS), energy gap (Eg), band structure, and free carriers. DOS exhibits many special structures including plateau, discontinuities, and divergent peaks. The effective electric field modifies the energy dispersions, alters the subband spacing, changes the subband curvature, produces the new edge state, switches the band gap, and causes the metal-semiconductor (or semiconductor-metal) transitions. In gapless zigzag ribbons, electric fields not only lifts the degeneracy of partial flatbands at EF but also induces an energy gap. Eg is dependent on the ribbon width, ribbon edges, and the field strength. The semiconductor-metal transitions occur in both armchair ribbons and zigzag ribbons in the increase in electric fields. Due to electric fields, the above-mentioned effects are completely reflected in the features of DOS, such as the generation of special structures, the shift of peak position, the change in peak height, and the alternation of band gap. The predicted electronic properties could be examined by the experimental measurements on absorption spectra and transport properties.

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.

Unscreened Coulomb Interactions and the Quantum Spin Hall Phase in Neutral Zigzag Graphene Ribbons

A study of the effect of unscreened Coulomb interactions on the quantum spin Hall phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit (ISO) interaction, exact expressions for band structures and edge-state wave functions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wave functions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb interactions opens a gap in the charge sector with a gapless spin sector. In contrast to armchair terminations, the charge gap vanishes exponentially with the ribbon width and its amplitude and decay length are strongly dependent on the ISO coupling. Comparison with reported ab initio calculations are presented.