Exploration of edge-dependent optical selection rules for graphene nanoribbons

Electronic, transport, magnetic and optical properties of graphene nanoribbons review

Low dimensional materials have attracted great research interest from both theoretical and experimental point of view. These materials exhibit novel physical and chemical properties due to the confinement effect in low dimensions. The experimental observations of graphene open a new platform to study the physical properties of materials restricted to two dimensions. This featured article provides a review on the novel properties of quasi one-dimensional (1D) material known as graphene nanoribbon. Graphene nanoribbons can be obtained by unzipping carbon nanotubes (CNTs) or cutting the graphene sheet. Alternatively, it is also called the finite termination of graphene edges. It gives rise different edge geometries namely zigzag and armchair among others. There are various physical and chemical techniques to realize these materials. Depending on the edge type termination, these are called the zigzag and armchair graphene nanoribbons (ZGNR and AGNR). These edges play an important role in controlling the properties of graphene nanoribbons. The present review article provides an overview of the electronic, transport, optical and magnetic properties of graphene nanoribbons. However, there are different ways to tune these properties for device applications. Here, some of them are highlighted such as external perturbations and chemical modifications. Few applications of graphene nanoribbon have and chemical modifications. Few applications of graphene nanoribbon have also been briefly discussed.

Biperiodic superlattices and transparent states in graphene

The transmission and transport properties of biperiodic graphene superlattices are studied theoretically. Special attention is paid to the so-called transparent states of biperiodic superlattices. A Dirac-like Hamiltonian is used to describe the charge carriers in graphene. The transfer matrix method and the Landauer-Büttiker formalism are implemented to obtain the transmittance and conductance, respectively. Similar results to those reported for Schrödinger electrons are obtained. However, in the case of Dirac electrons the splitted bands and the transparent states associated to the biperiodicity depend strongly on the angle of incidence as well as the character of the charge carriers. In fact, the dynamic of the splitted bands and transparent states is inverted for holes. The origin of transparent states is unveiled by obtaining an analytic expression for the transmittance. It is found that resonant transmission through single and double barriers gives rise to transparent states. Regarding the transport properties, it is possible to identify the fundamental changes caused by the biperiodicity. In particular, it is found a splitting, shifting, and diminishment of the conductance peaks with respect to the case of regular periodicity. This opens the door to corroborate experimentally the fundamental characteristics of biperiodic gated graphene superlattices through transport measurements.

Evaluation of graphene/crosslinked polyethylene for potential high voltage direct current cable insulation applications

This paper evaluates the potential usage of graphene/crosslinked polyethylene (graphene/XLPE) as the insulating material for high voltage direct current (HVDC) cables. Thermal, mechanical and electrical properties of blends with/without graphene were evaluated by differential scanning calorimetry (DSC), tensile strength, DC conductivity, space charge measurements and water tree aging test. The results indicate that 0.007–0.008% weight amount of graphene can improve the mechanical and electrical insulation properties of XLPE blends, namely higher tensile/yield strength, improved space charge distribution, and shorter/fewer water tree branches. The improvements mainly attribute to the high stiffness of graphene, deep traps introduced by the interaction zones of graphene and XLPE, and the blockage effect of graphene within XLPE. For thermal performance of XLPE blends, graphene nano-fillers have but limited improvement. The crystallinity of the blends barely changes with the addition of graphene. However, the crosslinking degree increases as the additive-like amounts of graphene doped. The above findings provide a guide for tailoring lightweight XLPE materials with excellent mechanical and electrical performances by doping them with a small amount of graphene.

Crossover point of the field effect transistor and interconnect applications in turbostratic multilayer graphene nanoribbon channel

The electrical transport properties of a turbostratic multilayer graphene nanoribbon (GNR) with various number of layers (1-8 layers) were investigated using a field effect transistor with a single GNR channel. In the turbostratic multilayer GNR with 5 layers or less, the carrier mobility and Ion/Ioff ratio in the FETs were improved by slightly increasing the conductance with increasing the number of layers, meaning that the excellent semiconducting characteristic. The improvement of the carrier transport properties promotes by the turbostratic stacking structure. In the turbostratic multilayer GNR with 6 layers or more, although the Ion/Ioff ratio degraded, the conductance extremely improved with increasing the number of layers. This indicates that the turbostratic multilayer GNR with thicker number of layers becomes the significantly lower resistivity wire as a metallic characteristic. We revealed that the crossover point of the physical properties between the semiconducting and metallic characteristics is determined by the strength to screen the surrounding environment effects such as charged impurity on the substrate. Our comprehensive investigation provides a design guidance for the various electrical device applications of GNR materials.

Method of lines for analysis of plane wave scattering by periodic arrays of magnetically-biased graphene strips

In this paper, efficient analysis of the plane wave scattering by periodic arrays of magnetically-biased graphene strips (PAMGS) is performed using the semi-numerical, semi-analytical method of lines (MoL). In MoL, all but one independent variable is discretized to reduce a system of partial differential equations to a system of ordinary differential equations. Since the solution in one coordinate direction is obtained analytically, this method is time effective with a fast convergence rate. In the case of a multi-layered PAMGS, the governing equations of the problem are discretized concerning periodic boundary conditions (PBCs) in the transverse direction. The reflection coefficient transformation approach is then used to obtain an analytical solution in the longitudinal direction. Here, magnetically-biased graphene strips are modeled as conductive strips with a tensor surface conductivity which is electromagnetically characterized with tensor graphene boundary condition (TGBC). The reflectance and transmittance of different multi-layered PAMGS are carefully obtained and compared with those of other methods reported in the literature. Very good accordance between the results is observed which confirms the accuracy and efficiency of the proposed method.

Chirality effects on an electron transport in single-walled carbon nanotube

In our work, we investigate characteristics of conductivity for single-walled carbon nanotubes caused by spin–orbit interaction. In the case study of chirality indexes, we especially research on the three types of single-walled carbon nanotubes which are the zigzag, the chiral, and the armchair. The mathematical analysis employed for our works is the Green-Kubo Method. For the theoretical results of our work, we discover that the chirality of single-walled carbon nanotubes impacts the interaction leading to the spin polarization of conductivity. We acknowledge such asymmetry characteristics by calculating the longitudinal current–current correlation function difference between a positive and negative wave vector in which there is the typical chiral-dependent. We also find out that the temperature and the frequency of electrons affect the function producing the different characteristics of the conductivity. From particular simulations, we obtain that the correlation decrease when the temperature increase for a low frequency of electrons. For high frequency, the correlation is nonmonotonic temperature dependence. The results of the phenomena investigated from our study express different degrees of spin polarization in each chiral of single-walled carbon nanotube and significant effects on temperature-dependent charge transport according to carrier backscattering. By chiral-induced spin selectivity that produces different spin polarization, our work could be applied for intriguing optimization charge transport.

Analytical study on strain tunable electronic structure and optical transitions in armchair black phosphorene nanoribbons

We theoretically investigate the electronic structure and optical absorption spectrum of armchair-edged black phosphorene nanoribbons (APNRs) with and without uniaxial strain based on the tight-binding Hamiltonian and Kubo formula. We analytically obtain the energy spectrum and wavefunction, and reveal the band gap scaling law as 1/(N + 1)² for APNRs in the presence and absence of uniaxial strain, where N is the number of armchair dimer across the ribbon. We find the band gap of APNRs linearly increases (decreases) with increasing in-plane uniaxial tensile (compressive) strain ɛ _x/y , but shows contrary dependence on the out-of-plane uniaxial strain ɛ _z . The effective mass versus strain exhibits the same behavior to that of band gap but with nonlinear dependence. Under an incident light linearly-polarized along the ribbon, we demonstrate that the inter-band optical transitions obey the selection rule Δn = n - n' = 0, but the intra-band transitions are forbidden for both pristine and strained APNRs originating from the orthogonality between the transverse wavefunctions of the sublattices belonging to different subbands. Importantly, the transverse electric field or impurities can release the optical selection rules by breaking the wavefunction orthogonality, which results in that the optical transitions between any subbands are all possible. Our findings provide further understanding on the electronic and optical properties of APNRs, which may pave the way for designing optoelectronic devices based on phosphorene.

Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene

We consider the effect of atomic impurities on the energy spectrum and electrical conductance of graphene. As is known, the ordering of atomic impurities at the nodes of a crystal lattice modifies the graphene spectrum of energy, yielding a gap in it. Assuming a Fermi level within the gap domain, the electrical conductance diverges at the ordering of graphene. Hence, we can conclude about the presence of a metal–dielectric transition. On the other hand, for a Fermi level occurring outside of the gap, we see an increase in the electrical conductance as a function of the order parameter. The analytic formulas obtained in the Lifshitz one-electron strong-coupling model, describing the one-electron states of graphene doped with substitutional impurity atoms in the limiting case of weak scattering, are compared to the results of numerical calculations. To determine the dependence of the energy spectrum and electrical conductance on the order parameter, we consider both the limiting case of weak scattering and the case of finite scattering potential. The contributions of the scattering of electrons on a vapor of atoms to the density of states and the electrical conductance of graphene with an admixture of interstitial atoms are studied within numerical methods. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized extrinsic states on the edges of the energy gap arising at the ordering of atoms of the admixture. If the Fermi level falls in the indicated spectral regions, the electrical conductance of graphene is significantly affected by the scattering of electrons on clusters of two or more atoms, and the approximation of coherent potential fails in this case.

2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons

Development of on-chip integrated carbon-based optoelectronic nanocircuits requires fast and non-invasive structural characterization of their building blocks. Recent advances in synthesis of single wall carbon nanotubes and graphene nanoribbons allow for their use as atomically precise building blocks. However, while cataloged experimental data are available for the structural characterization of carbon nanotubes, such an atlas is absent for graphene nanoribbons. Here we theoretically investigate the optical absorption resonances of armchair carbon nanotubes and zigzag graphene nanoribbons continuously spanning the tube (ribbon) transverse sizes from 0.5(0.4) nm to 8.1(12.8) nm. We show that the linear mapping is guaranteed between the tube and ribbon bulk resonance when the number of atoms in the tube unit cell is [Formula: see text], where [Formula: see text] is the number of atoms in the ribbon unit cell. Thus, an atlas of carbon nanotubes optical transitions can be mapped to an atlas of zigzag graphene nanoribbons.

Stacking stability of C2N bilayer nanosheet

In recent years, a 2D graphene-like sheet: monolayer C₂N was synthesized via a simple wet-chemical reaction. Here, we studied the stability and electronic properties of bilayer C₂N. According to a previous study, a bilayer may exist in one of three highly symmetric stacking configurations, namely as AA, AB and AB′-stacking. For the AA-stacking, the top layer is directly stacked on the bottom layer. Furthermore, AB- and AB′-stacking can be obtained by shifting the top layer of AA-stacking by a/3-b/3 along zigzag direction and by a/2 along armchair direction, respectively, where a and b are translation vectors of the unit cell. By using first-principles calculations, we calculated the stability of AA, AB and AB′-stacking C₂N and their electronic band structure. We found that the AB-stacking is the most favorable structure and has the highest band gap, which appeared to agree with previous study. Nevertheless, we furthermore examine the energy landscape and translation sliding barriers between stacking layers. From energy profiles, we interestingly found that the most stable positions are shifted from the high symmetry AB-stacking. In electronic band structure details, band characteristic can be modified according to the shift. The interlayer shear mode close to local minimum point was determined to be roughly 2.02 × 10¹² rad/s.

Spin-polarized magneto-electronic properties in buckled monolayer GaAs

We develop the generalized tight-binding model to fully explore the magneto-electronic properties of monolayer GaAs, where the buckled structure, multi-orbital chemical bondings, spin-orbit coupling, electric field, and magnetic field are considered simultaneously. The diverse magnetic quantization covers three groups of spin-polarized Landau levels (LLs) near the Fermi level, with the unique initial energies, LL degeneracy, energy spacings, magnetic-field-dependence, and spin splitting. Furthermore, the Landau state probabilities exhibit specific oscillation patterns, being composed of the localization centers, node regularities, and energy-dependent variations of the dominating orbitals. The density of states directly reflects the main features of the LL energy spectra in the form, height, number, and frequency of the spin-split delta-function-like prominent peaks. The electric field leads to the monotonous/nonmonotonous LL energy dispersions, LL crossing behavior, gap modulation, phase transition and enhancement of spin splitting. The complex gap modulations and even semiconductor-semimetal transitions are attributed to the strong competition among the intrinsic interactions, magnetic field, and electric field. Such predicted magneto-electronic properties could be verified by scanning tunneling spectroscopy and are helpful in designing the top-gated and phase-change electronic devices.

Electronic and optical responses of quasi-one-dimensional phosphorene nanoribbons to strain and electric field

Electronic and optical responses of zigzag- and armchair-edge quasi-one-dimensional phosphorene nanoribbons (Q1D-PNRs) to strain and external field are comparatively studied based on the tight-binding calculations. The results show that: (i) Zigzag-edge Q1D-PNR has the metallic ground state; applying global strains can not open the gap at the Fermi level but applying the electric field can achieve it; the direct/indirect character of the field-induced gap is determined by the electron-hole symmetry; an electric-field-enhanced optical absorption of low-energy photons is also predicted. (ii) Armchair-edge Q1D-PNR turns out an insulator with the large direct band gap; the inter-plane strain modulates this gap non monotonically while the in-plane one modulates it monotonically; in addition, the gap responses to electric fields also show strong direction dependence, i. e., increasing the inter-plane electric field will monotonically enlarge the gap but the electric field along the width direction modulates the gap non monotonically with three characteristic response regions.

Third-order terahertz response of gapped, nearly-metallic armchair graphene nanoribbons

We use time dependent perturbation theory to study the terahertz nonlinear response of gapped intrinsic and extrinsic nearly-metallic armchair graphene nanoribbons of finite length under an applied electric field. Generally, the nonlinear conductances exhibit contributions due to single-photon, two-photon, and three-photon processes. The interference between each of these processes results in remarkably complex behavior for the third-order conductances, including quantum dot signatures that should be measurable with a relatively simple experimental configuration. Notably, we observe sharp resonances in the isotropic third-order response due to the Van Hove singularities in the density of states at one-, two-, and three-photon resonances. However, these resonances are absent in the anisotropic third-order response; a result of the overall symmetry of the system.

Electronic and optical properties of graphene nanoribbons in external fields

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

Optical properties of graphene superlattices

In this work, the optical responses of graphene superlattices, i.e. graphene subjected to a periodic scalar potential, are theoretically reported. The optical properties were studied by investigating the optical conductivity, which was calculated using the Kubo formalism. It was found that the optical conductivity becomes dependent on the photon polarization and is suppressed in the photon energy range of (0, Ub), where Ub is the potential barrier height. In the higher photon energy range, i.e. Ω > Ub, the optical conductivity is, however, almost identical to that of pristine graphene. Such behaviors of the optical conductivity are explained microscopically through the analysis of the elements of optical matrices and effectively through a simple model, which is based on the Pauli blocking mechanism.