Bilayer Graphene Ribbons Research Articles

Electronic Properties of Single‐Layer and Bilayer Graphene Nanoribbons

Herein, a tight‐binding description is utilized to investigate electronic structures and density of states of single‐layer (SL) and bilayer (BL) graphene ribbons with and without the influence of external electric fields. Analyses are implemented to reveal the similarity and difference among electronic properties of three types of structures (specifically SL and BL ribbons with AA and AB stackings). Moreover, both armchair and zigzag edge orientations are considered. It is indicated in the results that variation in electronic properties of these structures in the presence of external electric fields depends on both structural form and edge orientation. The following two points are demonstrated: 1) a transverse field has a significant effect on adjusting bandgap of the zigzag configurations, whereas a vertical electric field has a distinct impact on energy bands of armchair edge structures, and 2) among considered structures, AB‐stacking BL ribbons are invariably the structures that are most strongly influenced by external fields. Interestingly, AB‐stacking BL ribbons are also capable of enlarging bandgap with both edge terminations. Herein, an insight into how the electronic structure and charge distribution of both SL and BL graphene nanoribbons can be controlled not only in armchair but also in zigzag edge terminations using electric stimulants is provided by the results.

Edge state in AB-stacked bilayer graphene and its correspondence with the Su-Schrieffer-Heeger ladder

We study edge states in AB-stacked bilayer graphene (BLG) ribbon where the Chern number of the corresponding two-dimensional (2D) bulk Hamiltonian is zero. The existence and topological features of edge states when two layers ended with the same or different edge terminations (zigzag, bearded, armchair) are discussed. The edge states (non-dispersive bands near the Fermi level) are states localized at the edge of graphene nanoribbon that only exists in certain range of momentum $k_y$. Their existence near the Fermi level are protected by the chiral symmetry with topology well described by coupled Su-Schrieffer-Heeger (SSH) chains model, i.e., SSH ladder, based on the bulk-edge correspondence of one-dimensional (1D) systems. These zero-energy edge states can exist in the whole $k_y$ region when two layers have zigzag and bearded edges, respectively. Winding number calculation shows a topological phase transition between two distinct non-trivial topological phases when crossing the Dirac points. Interestingly, we find the stacking configuration of BLG ribbon is important since they can lead to unexpected edge states without protection from the chiral symmetry both near the Fermi level in armchair-armchair case and in the gap within bulk bands that are away from Fermi level in the general case. The influence of interlayer next nearest neighbor (NNN) interaction and interlayer bias are also discussed to fit the realistic graphene materials, which suggest the robust topological features of edge states in BLG systems.

Controllable terahertz cross-shaped three-dimensional graphene intrinsically chiral metastructure and its biosensing application

In this research, a three-dimensional (3D) graphene intrinsically chiral metastructure in terahertz (THz) region was proposed and analyzed. The unit cell consists of bi-layer cross-shaped graphene ribbons in which the back layer is rotated compared to the front layer. Parameter retrieval method and Kramers–Kronig relations are used for theoretical analysis and derivation of the right-handed and left-handed electromagnetic effective refractive indices of the proposed structure. Based on our analysis, the proposed meta-structure has a tunable and controllable chiral response due to the tunability of graphene and circular dichroism (CD) was reached to 0.2. In order to evaluate the performance of the THz device in biosensor application, its characteristics in chiral biomolecule (collagen) sensing was analyzed. With an optimum design, our simulations show that the refractive index sensitivity value can be obtained as high as 0.96 THz per refractive index unit (THz/RIU) for the CD spectra. Proposed graphene chiral metastructure is promising enabler for controllable polarization-sensitive devices and systems such as tunable polarization filters, rotators, polarizers, biosensors, phase shifters, operating in the THz region.

Edge Doping in Graphene Devices on SiO2 Substrates

The conductivity of single layer and bilayer graphene ribbons 0.5–4 μm in width fabricated by oxygen plasma etching is studied experimentally. The dependence of the electron concentration in graphene on the ribbon width is revealed. This effect is explained by the edge doping of graphene due to defects arranged in SiO2 near the ribbon edges. The method of the formation of abrupt p–n junctions in graphene and structures with a constant electron concentration gradient in the graphene plane with the help of edge doping is proposed.

Краевое легирование в графеновых приборах на подложках SiO-=SUB=-2-=/SUB=-

AbstractThe conductivity of single layer and bilayer graphene ribbons 0.5–4 μm in width fabricated by oxygen plasma etching is studied experimentally. The dependence of the electron concentration in graphene on the ribbon width is revealed. This effect is explained by the edge doping of graphene due to defects arranged in SiO_2 near the ribbon edges. The method of the formation of abrupt p – n junctions in graphene and structures with a constant electron concentration gradient in the graphene plane with the help of edge doping is proposed.

Phonon stiffen and soften at zigzag- and armchair-dominated edges of exfoliated bilayer graphene ribbon presented by Raman spectra

The Raman spectra at the edge of the exfoliated bilayer graphene ribbon (GR) were investigated in detail. Results show that both G and 2D phonons stiffen (wave number increases) at zigzag-dominated edge, while they soften at armchair-dominated edge compared with those at the middle position in the GR. Furthermore, the full widths at half maximum intensity of both G and 2D Raman peaks narrow at the zigzag-dominated edge, while they broaden at the armchair-dominated edge. The stiffness and softness are attributed to the C–C bonds at the edge. For zigzag-dominated edge, the stiffness may originate in the increase of the force constant induced by the shrinking of C–C bond. For armchair-dominated edge, the softness may be due to the decrease of the force constant induced by the unsaturated hanging bonds at edge, which is different from Kohn anomaly and charge doping. The analysis is in agreement well with others calculation results about C–C bonds and the edge energy. These results may be useful to understand physical properties at the bilayer graphene edge and for applications in the device by taking advantage of the edge states in bilayer graphene.

Transport properties of bilayer graphene nanoribbons with hydrogen adatoms

The transport characteristics of bilayer graphene nanoribbons with hydrogen adatoms in an external static electric field is studied. The adsorption of hydrogen atoms on the surface of bilayer graphene ribbons is considered within the single-impurity periodic Anderson model. The transport coefficients of impurity-doped bilayer graphene ribbons are simulated in the relaxation time approximation. At a constant concentration of hydrogen adatoms, a nonlinear dependence of the transport coefficients on the static electric field strength has been revealed. It is found that the electrical conductivity and the diffusion coefficient of electrons in bilayer graphene ribbons decrease with increasing concentration of hydrogen adatoms.

Electric gating induced bandgaps and enhanced Seebeck effect in zigzag bilayer graphene ribbons

We theoretically investigate the effect of a transverse electric field generated by side gates and a vertical electric field generated by top/back gates on energy bands and transport properties of zigzag bilayer graphene ribbons (Bernal stacking). Using atomistic tight binding calculations and Green’s function formalism we demonstrate that a bandgap is opened when either field is applied and even enlarged under simultaneous influence of the two fields. Interestingly, although vertical electric fields are widely used to control the bandgap in bilayer graphene, here we show that transverse fields exhibit a more positive effect in terms of modulating a larger range of bandgap and retaining good electrical conductance. The Seebeck effect is also demonstrated to be enhanced strongly—by about 13 times for a zigzag bilayer graphene ribbon with 16 chain lines. These results may motivate new designs of devices made of bilayer graphene ribbons using electric gates.

Designing graphene as a new frustrated Lewis pair catalyst for hydrogen activation by co-doping.

Boron and nitrogen co-doped bilayer graphene (BN-G) and graphene ribbon (BN-GR) as Frustrated Lewis Pair (FLP) catalysts are investigated for hydrogen molecule activation. The nitrogen and boron atoms are separated as they are in different layers of BN-G/GR. Calculations show that this novel FLP catalyst is capable of activating hydrogen molecules. From the Bader charge, Mayer bond order, and the geometrical structures, it can be seen that the hydrogen molecules undergo heterolytic scission and have a late product-like transition state. More interestingly, the active sites are identified as being the carbon atoms around dopants for BN-G. The BN-G/GR catalysts deliver performances comparable to that of the reported FLP catalyst when considering their barrier and reaction energy values. The current work demonstrates the great potential of doped carbon catalysts as FLP catalysts and paves the way to nanostructured carbon catalyst applications in reactions by directly utilizing hydrogen molecules.

Strain-dependent conductivity in biased bilayer graphene

Intrinsic bilayer graphene is a gapless semimetal. Under the application of a bias field it becomes a semiconductor with a direct band gap that is proportional to the applied field. Under a layer-asymmetric strain (where the upper layer undergoes compression and lower layer tension or visa-versa) we find that the band gap of a biased bilayer graphene ribbon becomes indirect and, for higher strains, becomes negative returning the material its original semimetal state. As a result, the conductivity of the ribbon increases and can be almost an order of magnitude larger that of the intrinsic unbiased material - a change that can be induced with a strain of only ~2-3%. The conductivity is proportional to the applied strain and the magnitude of the effect is tunable with the bias field. Such layer-asymmetric strains can be achieved by bending, with forces on the order of ~1nN resulting in a layer-asymmetric strain of ~1%. This new electromechanical effect has a wide potential for application in the areas of nano-force microscopy and pressure sensing on the atomic scale.

Interlayer magnetoconductance of misoriented bilayer graphene ribbons

The coherent, interlayer conductance of misoriented bilayer graphene ribbons is a strong function of the Fermi energy and magnetic field. Edge states can result in a large peak in the interlayer transmission at the charge neutrality point that is several orders of magnitude larger than the surrounding low-energy transmission. The coherent interlayer conductance is consistently asymmetric around the charge neutrality point for all structures with the value differing by up to 3 orders of magnitude at Ef = ±0.05 eV. The low-energy states exhibit a high magnetoconductance ratio, and the magnetoconductance ratio tends to increase as the width of the ribbons decrease. The maximum value for the 35 nm wide bilayer ribbons at 10 T is 15 000%. Non-equilibrium Green's function calculations of the interlayer transport properties are also supported by semi-analytical calculations based on Fermi's Golden Rule.

Spin-polarized electrons in bilayer graphene ribbons

We show that a bilayer graphene ribbon deposited above a ferromagnetic insulator can behave as a spin-filtering device. The ferromagnetic material induces exchange splitting in the graphene ribbon, and due to the Fano antiresonances occurring in the transmission of the graphene ribbon as a function of ribbon length and energy, it is possible to obtain a net spin current. This happens when an antiresonance for one spin channel coincides with a maximum transmission for the opposite spin. We propose these structures as a means to obtain spin-polarized currents and spin filters in graphene-based systems.

Effect of an electric field on the transport and diffusion properties of bilayer graphene ribbons

The diffusion and conduction electrons in a bilayer graphene ribbon in an external electric field have been calculated. The Boltzmann kinetic equation in the semi-classical approximation of the relaxation time has been used. The analytical expressions for the diffusion of electrons and its nonlinear dependence on the electric field intensity were found. These relations are constructed and analyzed for different values of the electrostatic potential between the layers of a tape.

Gate-controlled conductance through bilayer graphene ribbons

We study the conductance of a biased bilayer graphene flake with monolayer nanoribbon contacts. We find that the transmission through the bilayer ribbon strongly depends on the applied bias between the two layers and on the relative position of the monolayer contacts. Besides the opening of an energy gap on the metallic bilayer, the bias allows to tuning the electronic density on the bilayer flake, making possible the control of the electronic transmission by an external parameter.

Formation and electronic properties of hydrogenated few layer graphene

Motivated by the controversial experimental conclusions on the affinity of few layergraphenes (FLGs) towards hydrogen plasma, we systematically investigate thehydrogenation of FLGs within the framework of density functional theory. The approachinghydrogen atoms from both sides of an FLG induce a structural transition from a layeredstructure into a hydrogen passivated thin diamond film (HP-TDF). The very low transitionbarrier of FLG hydrogenation indicates the feasibility of FLG hydrogenation through theproposed mechanism. The increasing formation energy with the thickness of FLGs impliesthat hydrogenation of single layer graphene is easier than that of FLG, which is inagreement with most experimental observations. Moreover, the electronic propertiesof HP-TDFs and the hydrogenated bilayer graphene ribbons are also studied.

Magnetoabsorption spectra of bilayer graphene ribbons with Bernal stacking

Magnetoabsorption spectra of bilayer graphene ribbons with Bernal stacking are studied by the Peierls-coupling tight-binding method. When the magnetic confinement prevails over the quantum confinement, low-energy spectra chiefly exhibit many Landau peaks, which are strongly modified by the inter-ribbon interactions and the magnetic-field magnitude $(B)$. The spectra show denser Landau peaks in bilayer graphene ribbon than in a monolayer ribbon with the same ribbon width. The absorption frequencies of Landau peaks of a wide monolayer ribbon show the $\sqrt{B}$ dependence, while those of a bilayer ribbon exhibit a varying $B$-field dependence. In the spectra region $\ensuremath{\omega}\ensuremath{\le}100\text{ }\text{meV}$, the absorption frequencies of Landau peaks are linearly dependent on the magnetic-field magnitude. At $\ensuremath{\omega}\ensuremath{\ge}100\text{ }\text{meV}$, they evolve from the $B$ dependence to the $\sqrt{B}$ dependence with the increase in the field strength. The absorption frequencies of Landau peaks exhibit $\sqrt{B}$ dependence at $B\ensuremath{\ge}20\text{ }\text{T}$. The relationship between the magneto-optical properties and electronic structures (the state energies and wave functions) are explored. The Landau wave functions are illustrated and used to identify the optical selection rule.