Armchair Ribbons Research Articles

Strain-controlled charge and spin current rectifications in spin–orbit coupled graphene nano-ribbon: A new proposition

In this work, we investigate the possibilities of performing charge and spin current rectifications using graphene nano-ribbon in the presence of Rashba spin–orbit (SO) interaction. More specifically, we explore the specific role of mechanical strain on these two different types of current rectifications. The system is simulated by a tight-binding framework, where all the results are worked out based on the standard Green’s function formalism. In order to have current rectification, an asymmetry is required, which is incorporated through uncorrelated disorder among the constituent lattice points. From our extensive numerical analysis, we find that reasonably large charge and spin current rectifications can be obtained under strained conditions, and all the physical pictures are valid for a broad range of tight-binding parameters. The rectification properties are studied mostly for zigzag graphene nano-ribbons; however, an armchair ribbon is also taken into account for a clear comparison. Our work may provide a new direction of getting strain-controlled current rectifications in similar kinds of other physical systems as well.

Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry

Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su–Schrieffer–Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane–Mele model and provide valuable insights into the topological properties of such systems.

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.

Full analytical solution of finite-length armchair/zigzag nanoribbons

Finite-length armchair graphene nanoribbons can behave as one-dimensional topological materials, that may show edge states in their zigzag-terminated edges, depending on their width and termination. We show here a full solution of tight-binding graphene rectangles of any length and width that can be seen as either finite-length armchair or zigzag ribbons. We find exact analytical expressions for both bulk and edge eigenstates and eigenenergies. We write down exact expressions for the Coulomb interactions among edge states and introduce a Hubbard-dimer model to analyze the emergence and features of different magnetic states at the edges, whose existence depends on the ribbon length. We find ample room for experimental testing of our predictions in $N=5$ armchair ribbons. We compare the analytical results with ab initio simulations to benchmark the quality of the dimer model and to set its parameters. A further detailed analysis of the ab initio Hamiltonian allows us to identify those variations of the tight-binding parameters that affect the topological properties of the 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.

Transport Simulation of Graphene Devices with a Generic Potential in the Presence of an Orthogonal Magnetic Field.

The effect of an orthogonal magnetic field is introduced into a numerical simulator, based on the solution of the Dirac equation in the reciprocal space, for the study of transport in graphene devices consisting of armchair ribbons with a generic potential. Different approaches are proposed to reach this aim. Their efficiency and range of applicability are compared, with particular focus on the requirements in terms of model setup and on the possible numerical issues that may arise. Then, the extended code is successfully validated, simulating several interesting magnetic-related phenomena in graphene devices, including magnetic-field-induced energy-gap modulation, coherent electron focusing, and Aharonov–Bohm interference effects.

Inner-edge states in silicene nanoribbons and related applications to novel device design

We study the quantum transport in hybrid silicene nanoribbons in the presence of a spatially alternative electric field. We found that valley resolved inner-edge states can be obtained in zigzag nanoribbons with opposite electric fields applied in the upper and lower half-nanoribbons, and pure valley current is obtained. A dissipationless transistor is designed based on the inner-edge states. It is found that the inner-edge states are not robust, and defects on the interface between the upper and lower half-nanoribbons can change the conductance to zero. To improve the performance of the device, we consider a region without electric field between two regions with opposite electric fields. Electrons is not confined at the interface of the upper and lower half-nanoribbons, and they can transport in the region without electric field. Defects can also affect the conductance, but the conductance can not be changed to zero easily. Armchair nanoribbons are also considered in this study to design a dissipationless transistor, and the difference is that we do not consider the degree of freedom valley in the device based armchair ribbons. Our findings open the possibility of the dissipationless transistor design based on inner-edge states in silicene nanoribbons.

Magnetoelectric torque and edge currents in spin-orbit coupled graphene nanoribbons

For graphene nanoribbons with Rashba spin-orbit coupling, the peculiar magnetic response due to the presence of a magnetization and geometric confinement are analyzed within a tight-binding model. We observe a sizable transverse susceptibility that can be considered as a gate voltage-induced magnetoelectric torque without the need of a bias voltage, with different directions for zigzag and armchair ribbons. The local torque generates non-collinear spin polarization between the two edges and/or along the ribbon, and the net torque averages to zero if the magnetization is homogeneous. Nevertheless, a nonzero net torque can appear in partially magnetized nanoribbons or in nanoflakes of irregular shapes. The equilibrium spin current produced by the spin-orbit coupling also appears in nanoribbons, but the component flowing in the direction of confinement is strongly suppressed. Even without the magnetization, an out-of-plane polarized chiral edge spin current is produced, resembling that in the quantum spin Hall effect. Moreover, a magnetization pointing perpendicular to the edge produces a laminar flow of edge charge currents, whose flow direction is symmetric (non chiral) or antisymmetric (chiral) between the two edges depends on whether the magnetization points in-plane or out-of-plane.

Thermoelectric properties of in-plane 90°-bent graphene nanoribbons with nanopores

We study the thermoelectric performance of 90°-bent graphene nanoribbons containing nanopores for optimized design of multiple functional circuits including thermoelectric generators. We show that the thermal conductance of the 90°-bent ribbons is lower from few times to an order of magnitude compared to that of pristine armchair and zigzag straight ribbons. Consequently, the thermoelectric performance of the bent ribbons is better than its straight ribbon counterparts, in particular at high temperatures above 500 K. More importantly, the introduction of nanopores is demonstrated to strongly enhance their thermoelectric capacity. At 500 K, the figure of merit ZT increases by more than 160% (from 0.39 without pores to 0.64) with 3 nanopores incorporated, and by more than 200% (up to 0.88) when 24 nanopores are introduced. ZT 1 can be achieved at a temperature of about 1000 K. In addition, the thermoelectric performance is shown to be further improved by adopting asymmetrical leads. This study demonstrates that 90°-bent ribbons with nanopores have decent thermoelectric performance for a wide range of temperatures and may find application as efficient thermoelectric converters.

Transport model with atomistic band structure of graphene nanoribbon

The aim of the paper is to study the ballistic quantum transport in armchair graphene nanoribbon by developing a transport model followed by subsequent simulation. Electron transport in nanodevices can be studied by two different methods viz. wave function method and non-equilibrium Green function method. Here, we use the wave function method based transport mechanism with a view point on an atomistic quantum modeling of band structure. The interaction effects, unlike in Green function method, are included in a semi-empirical way where the resulting parameters are evaluated by fitting to experimental results. Interesting finding hitherto unknown to the graphene community, to the best belief of the authors, is that the current in armchair graphene nanoribbon starts to conduct only from a definite channel which is very much dimension-specific. As example, current conduction observed in the ribbon of dimension of seven atoms width starts only from the second channel. It is also noticed that a width dependent bandgap manifests the armchair ribbon to behave both as a semiconductor and semimetal depending on which family the ribbon belongs to. Further, the conductance of the ribbon is seen to have plateaus and current in it rises up in steps with increase of bias.

Covalent functionalization in graphene nanoribbon: Theoretical modeling and sensitivity analysis

The alteration of electronic properties in chemically modified graphene can be utilized for chemical and biosensing applications. Thus, it is essential to understand how the alteration of density of states and conductance spectra of functionalized zigzag and armchair graphene nanoribbon (GNR) affects its sensitivity. In this aspect, the current–voltage characteristics of GNR based sensors are modeled using the non-equilibrium Green's function method. Our findings show that the presence of chemical moiety at one edge of the zigzag GNR structure opens the bandgap that reduces the current conduction and enhances the sensitivity for detection. However, double edge functionalization restores the semi-metallic character of the zigzag ribbon that reduces the sensitivity. Both single and double edge atomic substitution in armchair ribbon makes it n-type, which shows the alteration in current conduction for detecting the presence of the chemical species. We further found that increasing the width of the ribbon decreases the device sensitivity while it increases for the double edge substituted zigzag structure. The study thus provides essential information and insights into utilizing and operating different edge structures of graphene based sensors for effective detection of chemical and biomolecular species.

Edge chemistry and tensile strain effects on the magnetic properties of 1D VSe2 structures

The first-principles calculations show that the simple edge chemistry can make VSe2 armchair ribbons generate various favorable magnetic phases, and the tensile strain can flexibly tune their magneto-electronic properties.

Electron transport properties of graphene nanoribbons with Gaussian deformation

Gaussian deformation in graphene structures exhibits an interesting effect in which flower-shaped confinement states are observed in the deformed region [Carrillo-Bastos et al., Phys. Rev. B 90 041411 (2014)]. To exploit such a deformation for various applications, tunable electronic features including a bandgap opening for semi-metallic structures are expected. Besides, the effects of disorders and external excitations also need to be considered. In this work, we present a systematic study on quantum transport of graphene ribbons with Gaussian deformation. Different levels of deformation are explored to find a universal behavior of the electron transmission. Using a tight-binding model in combination with Non-Equilibrium Green Functions formalism, we show that Gaussian deformation influences strongly the electronic properties of ribbons in which the electron transmission decreases remarkably in high energy regions even if small deformations are considered. Interestingly, it unveils that the first plateau of the transmission of semi-metallic armchair ribbons is just weakly affected in the case of small deformations. However, significant large Gaussian bumps can induce a strong drop of this plateau and a transport gap is formed. The transmission at the zero energy is found to decrease exponentially with increasing the size of the Gaussian bump. Moreover, the gap of semi-conducting ribbons is enlarged with large deformations. The opening or the widening of the transport gap in large deformed armchair structures is interpreted by a formation of a three-zone behavior along the transport direction of the hopping profile. On the other hand, a transport gap is not observed in zigzag ribbons regardless of the size of Gaussian bumps. This behavior is due to the strong localization of edge states at the energy point E = 0...

Energy and Mode Filtering in a Graphene Channel With Unevenly Spaced Barriers with a Smooth Profile

We simulate the transport and shot noise behavior of graphene armchair ribbons with a series of parallel, unevenly spaced potential barriers with a smooth profile (which could result from the electrostatic effect of negatively biased gates). We analyze the effect of Klein tunneling and resonant tunneling on the individual modes propagating through the graphene channel, showing that this structure can behave as a mode and an energy filter for the charges injected from the contacts. Moreover, we study the different transport regimes (ballistic, strong localized, and diffusive) that can take place inside the graphene ribbon and the effect on the shot noise behavior of the device

Graphenylene nanoribbons: electronic, optical and thermoelectric properties from first-principles calculations

Recently synthesized two-dimensional graphene-like material referred to as graphenylene is a semiconductor with a narrow direct bandgap that holds great promise for nanoelectronic applications. The significant bandgap increase can be provided by the strain applied to graphenylene crystal lattice or by using nanoribbons instead of extended layers. In this paper, we present the systematic study of the electronic, optical and thermoelectric properties of graphenylene nanoribbons using calculations based on the density functional theory. Estimating the binding energies, we substantiate the stability of nanoribbons with zigzag and armchair edges passivated by hydrogen atoms. Electronic spectra indicate that all considered structures could be classified as direct bandgap semiconductors. From the calculated dependence of bandgap on nanoribbon width we observe the identical scaling rule for armchair and zigzag graphenylene ribbons. A family-based classification used for the electronic structure of armchair graphene nanoribbons can not be extended to the case of graphenylene ones. The absorption coefficient, optical conductivity, and complex refractive index are calculated by means of the first-principles methods and the Kubo–Greenwood formula. It has been shown that graphenylene ribbons effectively absorb visible-range electromagnetic waves. Due to this absorption the conductivity is noticeably increased in this range. The transport coefficients and thermoelectric figure of merit are calculated by the nonequilibrium Green functions method. Summarizing the results, we discuss the possible use of graphenylene films and nanoribbons in nanoelectronic devices.

A computational study of electric and magnetic properties of silicon carbon (SiC) armchair nanoribbons

SiC is a two-dimensional semiconductor with a direct band gap. Many authors studied its electric and magnetic properties in sheet and ribbon shapes. The previous papers have shown that SiC sheet and full saturated armchair ribbons are non-magnetic (NM) semiconductor while zigzag ribbons are ferromagnetic (FM) semiconductor. In this paper, we saturate only C (CH) and Si (SiH) atoms of armchair ribbon by hydrogen and study its electric and magnetic properties by density functional theory (DFT). Our results show that CH, saturated carbon atoms in armchair ribbon, can show both FM and antiferromagnetic (AFM) semiconductor states while SiH, saturated silicon atoms in armchair ribbon, can show both FM half-metal and AFM metallic states. We found that the total magnetic moment of the unit cell is about 2 μB. Our results confirm that armchair ribbons can show many different magnetic states only by hydrogen saturation.

Metallic Phases on a Pristine Si(111) Surface

We present the surface structures of pristine silicon with novel structural and electronic properties based on first-principles calculations. The surfaces are composed of connected armchair ribbons, resulting in quadrilateral, hexagonal, and elongated octagonal structures, in which the constituent Si atoms are threefold (dangling bonds) or fourfold coordinated. Some of the subsurface Si atoms below the surface layer are fivefold-coordinated (floating bonds). Despite having higher formation energies than the conventional Si(111) surfaces (e.g., 0.5 eV/(1 × 1) higher than the Pandey chain model), the structures have unique structural and electronic properties. One of the interesting structural properties is that the surface is nearly flat (average height difference of ∼0.02 A) unlike the typical Si surfaces with large atomic bucklings. The calculated electronic structures show that the surfaces are metallic, as in topological insulators, in which the insulating bulk is surrounded by metallic surfaces.

Intervalley conversion in bilayer-monolayer graphene junctions

We studied the valley dependent transport properties of bilayer-monolayer graphene junctions consisting of a device region of bilayer zigzag ribbon connected to monolayer zigzag ribbon leads. We determined numerically using the python package Kwant the valley dependent conductance through the junctions in an energy range in which each valley has at most two subbands in a single layer ribbon. There is a Fermi energy in this range in which the K to K conductance drops significantly to below 0.2e2/h (spin degree of freedom is included), while the K to K′ conductance remains high. This means a high percentage of the incident K electrons are transferred to the K′ valley in the outgoing lead. A number of junctions can be designed with K to K′ conductance larger than 1.2e2/h, which have a conversion efficiency higher than 84% and there are also junctions with K to K′ conductance between 1.2e2/h and 0.6e2/h (the conversion efficiency > 66%). Changing the transverse dimension, the conductance features are shifted in energy without significant change to the qualitative behavior. When the longitudinal dimension of the junction is changed, the qualitative features are changed in a way, which resembles the relation between the band structure of armchair ribbons and the dimer numbers along the ribbon's transverse direction. For some junctions, this interesting intervalley scattering property can be explained by Fano resonance. Our results show that these bilayer-monolayer junctions can be used as efficient intervalley converters in valleytronic devices.

Chiral Phonon Transport Induced by Topological Magnons.

The plethora of recent discoveries in the field of topological electronic insulators has inspired a search for boson systems with similar properties. There are predictions that ferromagnets on a two-dimensional honeycomb lattice may host chiral edge magnons. In such systems, we theoretically study how magnons and phonons couple. We find topological magnon polarons around the avoided crossings between phonons and topological magnons. Exploiting this feature along with our finding of Rayleigh-like edge phonons in armchair ribbons, we demonstrate the existence of chiral edge modes with a phononic character. We predict that these modes mediate a chirality in the coherent phonon response and suggest measuring this effect via elastic transducers. These findings reveal a possible approach towards heat management in future devices.

Theoretical study of scattering in graphene ribbons in the presence of structural and atomistic edge roughness

We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation.