Armchair Graphene Ribbons Research Articles

Correlation between energy band transition and optical absorption spectrum in bilayer armchair graphene nanoribbons

In this work, we investigate the intrinsic as well as modulated optical properties of the AB-stacking bilayer armchair graphene ribbons in the absence and presence of external electric fields. Single-layer ribbons are also considered for comparison. By using a tight-binding model in combination with the gradient approximation, we examine the energy bands, the density of states and the absorption spectra of the studied structures. Our results demonstrate that when external fields are not present, the low-frequency optical absorption spectra display numerous peaks and they vanish at the zero point. In addition, the number, the position, and the intensity of the absorption peaks are strongly associated with the ribbon width. With the wider ribbon width, more absorption peaks are present and a lower threshold absorption frequency is observed. Interestingly, in the presence of electric fields, bilayer armchair ribbons exhibit a lower threshold absorption frequency, more absorption peaks, and weaker spectral intensity. When increasing the strength of the electric field, the prominent peaks of the edge-dependent selection rules are lowered, and the sub-peaks satisfying the extra selection rules come to exist. The obtained results certainly provide a more comprehensive understanding of the correlation between the energy band transition and the optical absorption, in both single-layer and bilayer graphene armchair ribbons, and could provide new insights into developments of optoelectronic device applications based on graphene bilayer ribbons.

Intense Laser Pulse Interaction With Graphene and Graphene Ribbons.

In this work we investigate quantum mechanically the interaction of an intense ultrashort laser pulse with the graphene monolayer as well as with the armchair graphene ribbons of different widths. We consider a tight binding (TB) Hamiltonian of the monolayer graphene and give two rules for deriving the dispersion relations of the armchair graphene ribbons of any width, N, from the TB eigenvalues of the monolayer. The band structure of the monolayer and the armchair ribbons of different widths are discussed with illustrations. The time-dependent wavefunctions of the systems and the expectation values of interest are determined by solving the coupled equations of the band amplitudes “exactly” (numerically). First, simulations are made for the population excitation in the conduction band (CB) from the valence band (BV), the VB-CB interband correlation (or “coherence”), the intraband, the interband and the total currents in the monolayer graphene. The graphene currents are compared with the corresponding currents induced in an armchair ribbon (width, N = 3). The change from the 2D monolayer to the 1D ribbon shows a remarkable transition of the dominance of the intraband current that leads to a near steady total current in the monolayer, to a dominance of the interband current in the ribbon that induces an oscillatory current in the ribbon beyond the pulse duration. The difference observed might be a combined effect of the “confinement” in one dimention and a finite band-gap minimum in the case of the ribbon. However, this transition should be further investigated for better clarity. A brief comparison of the radiation spectra emitted from the monolayer and from the ribbon is also made. They show a grossly similar structure and a relative insensitivity with respect to the detailed structure of the targets chosen. This might be due to the dominance of virtual continuum-continuum transitions, to and from the bands states, that lie behind the fundamental quantum process of high harmonic emissions. Lastly, the dependence of the charge currents, induced in a ribbon of unit width (N = 1), on the carrier-envelope-phase (CEP) of the incident laser pulse is investigated. It is seen that the shape of the main part of the current produced in the ribbon can be fully reversed by changing the CEP of the ultrashort laser pulse from 0 to π. More generally, it is suggested that the pulse shape of the charge carriers in the ribbon could be designed by similarly tailoring the form of the vector potential of the incident laser pulse.

Effects of A Magnetic Field on the Transport and Noise Properties of a Graphene Ribbon with Antidots.

We perform a numerical simulation of the effects of an orthogonal magnetic field on charge transport and shot noise in an armchair graphene ribbon with a lattice of antidots. This study relies on our envelope-function based code, in which the presence of antidots is simulated through a nonzero mass term and the magnetic field is introduced with a proper choice of gauge for the vector potential. We observe that by increasing the magnetic field, the energy gap present with no magnetic field progressively disappears, together with features related to commensurability and quantum effects. In particular, we focus on the behavior for high values of the magnetic field: we notice that when it is sufficiently large, the effect of the antidots vanishes and shot noise disappears, as a consequence of the formation of edge states crawling along the boundaries of the structure without experiencing any interaction with the antidots.

Shrinkage-expansion of a tri-isometric knitting from graphene ribbons at finite temperature

A model of two-dimensional knitting system is constructed from graphene ribbons (GRs) aligned in the three isometric directions. It then recommends a process for fabrication of the nanotexture. Based on the model, its thermal stability is assessed via molecular dynamics simulations. The nanotexture may experience out-of-plane fold or in-plane shrinkage at different temperatures due to the three factors including bending of the ribbons, relative sliding between the ribbons at their overlapping areas, and strong van der Waals forces between the GRs. In addition to the global deformation of the nanotexture, it has experienced local deformation at pores which depends on the chirality and gaps of the GRs. For a nanotexture formed from armchair GRs, it is relaxed to be a quasi-periodic porous medium with similar pore size. The mechanism is that the armchair GRs have non-smooth edges, and are locked at their contact areas in relative sliding. In water, the in-plane shrunk nanotexture does not expand to be a plate even at 500 K. However, in argon, it expands to be a plate with periodic hexagon pores. The proposed nanotexture may have significant applications in the area of controllable shrinkage-expansion oriented nanomaterial/nanodevice.

Geometry-dependent conductance and noise behavior of a graphene ribbon with a series of randomly spaced potential barriers

We perform an envelope-function based numerical analysis of the effect of a sequence of randomly spaced potential barriers on the conductance and shot noise of an armchair graphene ribbon. The behavior is dominated by Klein tunneling and by resonant tunneling and strongly depends on the geometrical details of the device. Klein tunneling effectively filters the modes that can propagate through the device. For a large number of cascaded barriers, this gives rise to different transport regimes for metallic and semiconducting ribbons, with diverging shot noise behaviors. Resonant tunneling is instead energy selective and has quite a different effect depending on whether the barriers are identical or not. We also explore the effect of tilting the barriers with respect to the ribbon edges, observing a transition toward a diffusive transport regime and a one-third shot noise suppression. We investigate this effect, and we find that it takes place also in more traditional semiconducting materials. The results of our analysis could be instrumental for the fabrication of mode-filtering and energy-filtering graphene-based nanodevices. Moreover, our study highlights the importance of the measurement of shot noise as a probe for the nature of the transport regime.

Enhanced magneto-optical response due to the flat band in nanoribbons made from the α−T3 lattice

We study the optical response of nanoribbons made from the $\ensuremath{\alpha}\ensuremath{-}{T}_{3}$ lattice under a weak magnetic field in the terahertz to far-infrared regime. It is found that the magnetic field can open a gap in the band structure and induce a new absorption peak with much reduced frequency in metallic armchair ribbons and a class of zigzag ribbons with particular boundaries. This tunable magneto-optical modulation effect is attributed to the interband transitions between the flat band and the propagating bands. By contrast, this magnetic modulation of gap opening and optical conductance is much weaker in metallic armchair graphene ribbons (the case of $\ensuremath{\alpha}=0$) in which the flat band is absent. The enhancement in the $\ensuremath{\alpha}\ensuremath{-}{T}_{3}$ model is analytically investigated and explained within the perturbation theory for metallic armchair ribbons. The magnetic field induced valley degeneracy lifting and valley splitting of the absorption peak are also discussed in the case of zigzag ribbons. These findings pave the way for magneto-optics devices based on the $\ensuremath{\alpha}\ensuremath{-}{T}_{3}$ model materials.

Topological end states and Zak phase of rectangular armchair ribbon

We consider the end states of a half-filled rectangular armchair graphene ribbon (RAGR) in a staggered potential. Taking electron–electron interactions into account we find that, as the strength of the staggered potential varies, three types of couplings between the end states can occur: antiferromagnetic without or with spin splitting, and paramagnetic without spin-splitting. We find that a spin-splitting is present only in the staggered potential region 0<Δ<Δc. The transition from the antiferromagnetic state at Δ=0 to the paramagnetic state goes through an intermediate spin-split antiferromagnetic state, and this spin-splitting disappears suddenly at Δc. For small and large values of Δ the end charge of a RAGR can be connected to the Zak phase of the periodic armchair graphene ribbon (PARG) with the same width, and it varies continuously as the strength of the potential changes.

Envelope-Function-Based Transport Simulation of a Graphene Ribbon With an Antidot Lattice

We have performed numerical simulations to study the effect of a regular lattice of antidots on the conductance, and in particular on the gap, of an armchair graphene ribbon. We have used an envelope-function approach, with a nonzero mass term mimicking the presence of the antidots. With a very efficient simulation procedure, consisting in a reciprocal space solution of the envelope-function equation in the transverse direction followed by a recursive scattering matrix calculation in the transport direction, we have been able to analyze the impact of the different geometrical parameters characterizing the structure. We have observed that the conductance of the device rapidly reaches an asymptotic value when the length of the region containing the antidot lattice is increased. The dependence of the energy gap on the geometrical features of the antidot lattice is quite similar to that observed in unconfined graphene, excluding the cases of very small or distant antidots, for which the energy gap of the pristine graphene ribbons is recovered. The tilt angle of the lattice with respect to the transport direction has a negligible influence on the gap, which is also quite robust with respect to the introduction of disorder in the antidot lattice.

Intrinsic valley Hall effect in graphene

If electrons are incident from an armchair graphene ribbon into the bulk graphene region, the electronic diffraction occurs. Because of the different triangular wrapping of the energy dispersion between valleys K and K′, the electrons of valley K tend to be diffracted to one side and those of valley K′ to the other side. When the current is injected from the armchair ribbon of a four-terminal graphene device, the major portion of the incident current of valley K flows through one side arm and the minor portion through the other side arm. The ratio between them is derived to be 1+4E/3 in the low energy limit, where E is the energy in units of hopping parameter. The major arm for valley K is the minor arm for valley K′. This results in the rise of the valley Hall effect, which is an intrinsic property of graphene stemming from the different electronic structure of the two valleys. The valley Hall conductance is calculated to be (2E/3)G0 with G0 being the conductance supported by the injection ribbon.

Modulation of bandgap in bilayer armchair graphene ribbons by tuning vertical and transverse electric fields

We investigate the effects of external electric fields on the electronic properties of bilayer armchair graphene nano-ribbons. Using atomistic simulations with Tight Binding calculations and the Non-equilibrium Green's function formalism, we demonstrate that (i) in semi-metallic structures, vertical fields impact more effectively than transverse fields in terms of opening larger bandgap, showing a contrary phenomenon compared to that demonstrated in previous studies in bilayer zigzag graphene nano-ribbons; (ii) in some semiconducting structures, if transverse fields just show usual effects as in single layer armchair graphene nano-ribbons where the bandgap is suppressed when varying the applied potential, vertical fields exhibit an anomalous phenomenon that the bandgap can be enlarged, i.e., for a structure of width of 16 dimer lines, the bandgap increases from 0.255 eV to the maximum value of 0.40 eV when a vertical bias equates 0.96 V applied. Although the combined effect of two fields does not enlarge the bandgap as found in bilayer zigzag graphene nano-ribbons, it shows that the mutual effect can be useful to reduce faster the bandgap in semiconducting bilayer armchair graphene nano-ribbons. These results are important to fully understand the effects of electric fields on bilayer graphene nano-ribbons (AB stacking) and also suggest appropriate uses of electric gates with different edge orientations.

Reverse rectification and negative differential resistance effects in doped armchair graphene ribbons device

In the present work, we perform first-principles calculations based on density functional theory and non-equilibrium Green’s function to study the electronic transport properties of the 10-armchair graphene ribbons devices doped by boron and phosphorus atoms. Two kinds of device show a strong inverse rectification and negative differential resistance (NDR) effect. The effect of doping position on rectifying phenomenon are analyzed by calculating the transmission spectra and the energy band structures of the related electrodes as well as the projected density of states for two devices at different bias. And the observed NDR effect is explained by the local density of states. The results indicate that the asymmetric doping of the impurity atom contributes to the electron transport of the device, being used to design a molecular rectifier with good performance.

Topological gap states of semiconducting armchair graphene ribbons

In semiconducting armchair graphene ribbons a tensile strain can induce pairs of topological gap states with opposite energies. Near the critical value of the deformation potential these kink and antikink states become almost degenerate with zero energy and have a fractional charge of one-half. Such a semiconducting armchair ribbon represents a one-dimensional topological insulator with nearly zero energy end states. Using data collapse of numerical results we find that the shape of the kink displays an anomalous power-law dependence on the width of the local lattice deformation. We suggest that these gap states may be probed in optical measurements. However, ``metallic'' armchair graphene ribbons with a gap induced by many-electron interactions have no gap states and are not topological insulators.

Large on/off current ratio in hybrid graphene/BN nanoribbons by transverse electric field-induced control of bandgap

We propose an approach to design efficient electronic switches based on Graphene/BN heterostructures. By means of atomistic Tight Binding simulations, we investigate heterostructures made of an armchair BN nanoribbon sided by two armchair graphene ribbons where a significant bandgap can be opened. In particular, we show that a bandgap of about 0.55 eV can be strongly suppressed by applying a relatively weak transverse electric field of 10 mV/A. Additionally, by using non-equilibrium Green's function simulation, we show that this effect can be used to control the current in electron devices even at small bias and small length. An on/off current ratio higher than 104 is achieved at room temperature.

High-performance solution of the transport problem in a graphene armchair structure with a generic potential.

We propose an efficient numerical method to study the transport properties of armchair graphene ribbons in the presence of a generic external potential. The method is based on a continuum envelope-function description with physical boundary conditions. The envelope functions are computed in the reciprocal space, and the transmission is then obtained with a recursive scattering matrix approach. This allows a significant reduction of the computational time with respect to finite difference simulations.

Thermal wave propagation in graphene studied by molecular dynamics simulations

The transient heat conduction in both armchair and zigzag-edged graphene ribbons pulsed by local heating with a duration of 1 ps was studied using nonequilibrium molecular dynamics simulations. The results show that the heat pulse excites two waves which indicates non-Fourier heat conduction. One of the two waves is a sound wave (first sound), which has macroscopic momentum and propagates at the speed of sound. The other is a thermal wave (second sound), whose propagation speed is \( 1/\sqrt 3 \) of the sound velocity. The sound wave excited by the heat pulse is a longitudinal wave, whose energy is only transported in the longitudinal direction. The thermal wave excited by the heat pulse is generated by transverse lattice vibrations, with the energy only having the transverse component. The observed anisotropy of the transient heat conduction suggests that the system is in a non-equilibrium state during propagation of the heat pulse. Further statistical analyses show that the displacement of the heat pulse energy is related to the time as \( \langle \sigma^{2}\rangle \propto t^{1.80} \), which implies that heat transport is ballistic-diffusive transport in graphene. The higher proportion of the ballistic transport will lead to stronger heat waves. At the crest of the thermal wave, energy is transported ballistically, while in the diffusive region and during attenuation of the thermal wave, the energy is transported diffusively.

The effect of interlayer coupling on electron transport in graphene nanoribbons: a potential method for nanoposition sensing

We report a study on the effect of electron transport in a monolayer armchair graphene nanoribbon due to coupling to another monolayer armchair graphene ribbon, which is put on top of the first one. The conductance of the bottom ribbon oscillates when the top ribbon moves, and the oscillation can be used to determine stepwise position changes of the top ribbon for step sizes as small as 3.68 Å. The conductance oscillation arises from the rapid electron probability oscillations in the lowest three subbands of an armchair graphene ribbon. The phenomenon has potential applications in nanoposition sensing.

Graphene nanopores: electronic transport properties and design methodology

Graphene nanopores (GNPs) hold great promise as building blocks for electronic circuitry and sensors for biological and chemical sensing applications. Methods to design graphene nanopores that achieve desirable conduction performance and sensing characteristics have not been previously described. Here we present a study of the quantum transport properties of GNPs created by drilling pores in armchair and zigzag graphene ribbons. For the first time, our study reveals that the quantum transmission spectra of GNPs are highly tunable and GNPs with specific transport properties can be produced by properly designing pore shapes. Our investigation shows that the biological sensing capabilities of GNPs are transmission spectrum dependent, can vary dramatically, and are critically dependent on pore geometry. Our study provides design guidelines for creating graphene nanopores with specific transport properties to meet the needs of diverse applications and for developing sensitive biological/chemical sensors with required performance characteristics.

Admittance of T-stub graphene nanoribbon structure

In this work, we studied ac responses of T-stub structures that are composed of armchair and zigzag graphene ribbons. Compared with uniform graphene ribbons, the T-stub structures show extraordinary properties. The ac responses of armchair and zigzag T-stub structures show different behaviors for different edge configurations. The imaginary part of admittance can be capacitive or inductive depending on the Fermi energy and structural parameters. These properties provide deeper understanding of dynamic processes of electrons in graphene-based nanodevices.

Terahertz resonances due to edge magnetoplasmons in a wide armchair graphene ribbon with a weak superlattice potential

A strong modulation of the resonance frequencies and the gaps of edge magnetoplamons (EMPs), in the ribbon at the ν = 2 quantum Hall effect regime with a superlattice and a smooth steplike electrostatic lateral potential, due to a modulation of the interedge distance is shown. We obtain that, in a wide range of the interedge distances, within THz region the EMPs show wide frequency gaps and at peculiar frequencies the response of the system should manifest resonances. For the latter frequencies the group velocities are nullified.

Edge magnetoplasmons in a wide armchair graphene ribbon with a weak superlattice potential: Finite-frequency gaps and zero group velocity

We show strong effects of a weak and smooth, on the magnetic length, superlattice potential upon edge magnetoplasmons (EMPs) at the armchair edge, with a smooth steplike electrostatic lateral confining potential, of a wide graphene channel in the $\nu=2$ quantum Hall effect regime. The superlattice potential leads to essential enlargement of a number of EMPs, descend from two fundamental EMPs in the absence of superlattice. For the wave vector $k_{x}$ within the first Brillouin zone, the EMPs show as the regions of acoustical or quasi-acoustical dispersion, with a finite value of group velocity, so the regions with frequency gaps, where a group velocity is nullified at some $k_{x}$. We obtain that for $k_{x} \to 0$ only for two EMPs the frequency tends to zero as for other EMPs it obtains finite values. Strong dependence of dispersion relations of the EMPs from the period of the superlattice $a_{0}$ and the distance $d$ from a metallic gate is shown; in particular, for typical size of a gap, for characteristic value of the frequency and $k_{x}$ at which the group velocity is reduced to zero. At the frequency that corresponds to zero group velocity of pertinent fundamental EMP branch the response of the system should present a strong resonance.