In this work we argue that it is important to make a proper choice of the unit cell within tight-binding theory if one aims to compute the optical matrix elements. By considering zigzag graphene nanoribbons, we demonstrate that the band structure is insensitive to the choice of the unit cell. However, if the chosen unit cell does not incorporate the symmetries of the system, wrong values of optical matrix elements are obtained, leading to the violation of well-known selection rules. This result holds irrespective of the formalism utilized for calculating the optical matrix elements.
The electronic and transport properties of an extended linear defect embedded in a zigzag nanoribbon of realistic width are studied, within a tight binding model approach. Our results suggest that such defect profoundly modify the properties of the nanoribbon, introducing new conductance quantization values and modifying the conductance quantization thresholds. The linear defect along the nanoribbon behaves as an effective third edge of the system, which shows a metallic behavior, giving rise to new conduction pathways that could be used in nanoscale circuitry as a quantum wire.
Molybdenum disulfide nanoribbons with zigzag edges show ferromagnetic and metallic properties based on previous \emph{ab-initio} calculations. The investigation of the role of disorder on the magnetic properties is, however, still lacking due to the computational costs of these methods. In this work we fill this gap by studying the magnetic and electronic properties of several nanometer long MoS$_2$ zigzag nanoribbons using tight-binding and Hubbard Hamiltonians. Our results reveal that proper tight-binding parameters for the edge atoms are crucial to obtain quantitatively the metallic states …
We present the analytical solution of the wavefunction and energy dispersion of armchair graphene nanoribbons (GNRs) based on the tight-binding approximation. By imposing hard-wall boundary condition, we find that the wavevector in the confined direction is discretized. This discrete wavevector serves as the index of different subbands. Our analytical solutions of wavefunction and associated energy dispersion reproduce the numerical tight-binding results and the solutions based on the k*p approximation. In addition, we also find that all armchair GNRs with edge deformation have energy gaps, wh…
We theoretically show that an interlayer bias voltage in the AB-stacked bilayer graphene nanoribbons with armchair edges induces an electric polarization along the ribbon. Both tight-binding and ab initio calculations consistently indicate that when the bias voltage is weak, the polarization shows opposite signs depending on the ribbon width modulo three. This nontrivial dependence is explained using a two-band effective model. A strong limit of the bias voltage in the tight-binding model shows either one-third or zero polarization, which agrees with topological argument.
In this study, we analyze the band structure, the state characterization, and electronic transport of monolayer black phosphorus (phosphorene) zigzag nanoribbons (zPNRs) and armchair nanoribbons (aPNRs), using five-parameter tight-binding (TB) approximation. In zPNRs, the ratio of the two dominant hopping parameters indicates the possibility of a relativistic dispersion relation and the existence of a pair of separate quasi-flat bands at the Fermi level. Moreover, the corresponding states are edge localized if their bands are well separated from the valence and conduction bands. We also invest…
Accurate modeling of the pi-bands of armchair graphene nanoribbons (AGNRs) requires correctly reproducing asymmetries in the bulk graphene bands as well as providing a realistic model for hydrogen passivation of the edge atoms. The commonly used single-pz orbital approach fails on both these counts. To overcome these failures we introduce a nearest-neighbor, three orbital per atom p/d tight-binding model for graphene. The parameters of the model are fit to first-principles density-functional theory (DFT) - based calculations as well as to those based on the many-body Green's function and scree…
We study the properties of flat-bands that appear in a heterostructure composed of strands of different widths of graphene armchair nanoribbons. One of the flat-bands is reminiscent of the one that appears in pristine armchair nanoribbons and has its origin in a quantum mechanical destructive interference effect, dubbed `Wannier orbital states' by Lin et al. in Phys. Rev. B 79, 035405 (2009). The additional flat-bands found in these heterostructures, some reasonably closer to the Fermi level, seem to be generated by a similar interference process. After doing a thorough tight-binding analysis …
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 eigen-states and eigen-energies. We write down exact expressions for the Coulomb interactions among edge states and introduce a Hubbard-dimer model to analyse the emergence and featu…
We investigate the bending properties of carbon nanoribbons by combining continuum elasticity theory and tight-binding atomistic simulations. First, we develop a complete analysis of a given bended configuration through continuum mechanics. Then, we provide by tight-binding calculations the value of the bending rigidity in good agreement with recent literature. We discuss the emergence of a stretching field induced by the full atomic-scale relaxation of the nanoribbon architecture. We further prove that such an in-plane strain field can be decomposed into a first contribution due to the actual…
Using a tight binding model, we theoretically study the electronic properties of zigzag boron-carbon-nitride (BCN) nanoribbons where the outermost C atoms of zigzag graphene nanoribbons are replaced with B and N atoms. We show that the flat bands and edge states appear at the Fermi level when the number of B and N atoms are equal except the case of six times supercell. To investigate the origin of the edge states in BCN nanoribbons, we consider the semi-infinite graphene sheet with zigzag edge where outermost C atoms are replaced with B and N atoms. We analytically demonstrate the presence of …
The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half-metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at K (K') near the Fermi level. The present results demonstrate that the unique combination of…
With nonequilibrium Green's function approach combined with density functional theory, we perform an ab initio calculation to investigate transport properties of graphene nanoribbon junctions self-consistently. Tight-binding approximation is applied to model the zigzag graphene nanoribbon (ZGNR) electrodes, and its validity is confirmed by comparison with GAUSSIAN03 PBC calculation of the same system. The origin of abnormal jump points usually appearing in the transmission spectrum is explained with the detailed tight-binding ZGNR band structure. Transport property of an edge defect ZGNR junct…
We report electronic structure and electric field modulation calculations in the width direction for armchair graphene nanoribbons (acGNRs) using a semi-empirical extended Huckel theory. Important band structure parameters are computed, e.g. effectives masses, velocities and bandgaps. For the three types of acGNRs, the pz orbital tight-binding parameters are extracted if feasible. Furthermore, the effect of electric field in the width direction on acGNRs dispersion is explored. It is shown that for the two types of semiconducting acGNRs, an external electric field can reduce the bandgap to a f…
We used a complete tight-binding band structure of graphene nanoribbon to obtain, for the first time, analytical techniques for observing photon assisted transport, and dynamic localization of electrons in the graphene nanoribbons. When the ribbons are subject to a multi-frequency dc-ac field, photon assisted replicas show up at rather strong drive force. The strong dependence of the photon peaks on ac amplitudes allow for high-harmonic dynamic oscillations at these amplitudes. We identified regions of positive differential conductivity where a nanoelectronic graphene device may be operated as…
Since graphene nanoribbons are thin and flimsy, they need support. Support gives firm ground for applications, and adhesion holds ribbons flat, although not necessarily straight: ribbons with high aspect ratio are prone to bend. The effects of bending on ribbons' electronic properties, however, are unknown. Therefore, this article examines the electromechanics of planar and gently bent graphene nanoribbons. Simulations with density-functional tight-binding and revised periodic boundary conditions show that gentle bends in armchair ribbons can cause significant widening or narrowing of energy g…
By applying tight binding model, we investigate the electronic and transport properties of randomly distributed Stone-Wales (SW) defects on an armchair graphene nanoribbon (AGNR). We use four different functions, as distribution functions, to generate our SW defected nanoribbons. It is found that defect density can have a major effect on the conductance of our defected system, whilst other configurations such as defect orientation will contribute less. In our investigations. some special geometries are found, which shows interesting electronic and transport properties. These special cases alon…
We theoretically investigate the electron transport in armchair and zigzag graphene nanoribbons (GNRs) chemically functionalized with p-polyphenyl and polyacene groups of increasing length. Our nearest-neighbor tight-binding calculations indicate that, depending on whether the number of aromatic rings in the functional group is even or odd, the resulting conductance at energies matching the energy levels of the corresponding isolated molecule are either unaffected or reduced by exactly one quantum as compared to the pristine GNR, respectively. Such an even-odd effect is shown to originate from…
Using a continuum Dirac theory, we study the density and spin response of zigzag edge terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g. width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of…
One of severe limits of graphene nanoribbons (GNRs) in future applications is that zigzag GNRs (ZGNRs) are gapless, so cannot be used in field effect transistors (FETs). In this paper, using tight-binding approach and first principles method, we derived and proved a general edge (boundary) condition for the opening of a significant bandgap in ZGNRs with defective edge structures. The proposed semiconducting GNRs have some interesting properties including the one that they can be embedded and integrated in a large piece of graphene without the need of completely cutting them out. We also demons…
The influence of periodic edge vacancies and antidot arrays on the thermoelectric properties of zigzag graphene nanoribbons is investigated. Using the Green's function method, the tight-binding approximation for the electron Hamiltonian and the 4th nearest neighbor approximation for the phonon dynamical matrix, we calculate the Seebeck coefficient and the thermoelectric figure of merit. It is found that, at a certain periodic arrangement of vacancies on both edges of zigzag nanoribbon, a finite band gap opens and almost twofold degenerate energy levels appear. As a result, a marked increase in…
By using analytical solution of a tight-binding model for armchair nanoribbons, it is confirmed that the solution represents the standing wave formed by intervalley scattering and that pseudospin is invariant under the scattering. The phase space of armchair nanoribbon which includes a single Dirac singularity is specified. By examining the effects of boundary perturbations on the wave function, we suggest that the existance of a strong boundary potential is inconsistent with the observation in a recent scanning tunneling microscopy. Some of the possible electron-density superstructure pattern…
This contribution reports on comparative studies on giant magnetoresistance (GMR) in carbon nanotubes (CNTs) and graphene nanoribbons of similar aspect ratios (i.e perimeter/length and width/length ratios, for the former and the latter, respectively). The problem is solved at zero temperature in the ballistic transport regime, by means of the Green's functions technique within the tight-binding model and with the so-called wide band approximation for electrodes. The GMR effect in graphene is comparable to that of CNTs, it depends strongly on the chirality and only slightly on the aspect ratio.…
In this work, using self-consistent tight-binding calculations, for the first time, we show that a direct to indirect bandgap transition is possible in an armchair graphene nanoribbon by the application of an external bias along the width of the ribbon, opening up the possibility of new device applications. With the help of Dirac equation, we qualitatively explain this bandgap transition using the asymmetry in the spatial distribution of the perturbation potential produced inside the nanoribbon by the external bias. This is followed by the verification of the bandgap trends with a numerical te…
A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width $W_{L}$, the middle part is a GNR of width $W_{M}$, and the right part is a GNR of width $W_{R}$. We assume that the left and right parts of the GNR heterojunction interact with the middle part only. Under this approxi…
This paper presents electronic spectra of zigzag and armchair graphene nanoribbons calculated within the tight-binding model for pi-electrons. Zigzag and armchair nanoribbons of different edge geometries are considered, with surface perturbation taken into account. The properties of surface states are discussed on the basis of their classification into Tamm states and Shockley states. In armchair nanoribbons surface states are shown to close the energy gap at the Dirac point for certain edge geometries.
We have performed density functional calculations as well as employed a tight-binding theory, to study the effect of passivation of zigzag graphene nanoribbons (ZGNR) by Hydrogen. We show that each edge C atom bonded with 2 H atoms open up a gap and destroys magnetism for small widths of the nanoribbon. However, a re-entrant magnetism accompanied by a metallic electronic structure is observed from 8 rows and thicker nanoribbons. The electronic structure and magnetic state are quite complex for this type of termination, with sp$^3$ bonded edge atoms being non-magnetic, whereas the nearest neigh…
The energy spectrum and eigenstates of single-layer black phosphorous nanoribbons in the presence of perpendicular magnetic field and in-plane transverse electric field are investigated by means of a tight-binding method and the effect of different types of edges is analytically examined. A description based on a new continuous model is proposed by expansion of the tight-binding model in the long-wavelength approximation. The wavefunctions corresponding to the flatband part of the spectrum are obtained analytically and are shown to approach agree well with the numerical results from the tight-…
On the basis of many-body {\it ab-initio} calculations, using single-shot G$_0$W$_0$ method and Bethe-Salpeter equation, we study phosphorene nanoribbons (PNRs) in the two typical zigzag and armchair directions. The electronic structure, optical absorption, electron-hole (exciton) binding energy, exciton exchange splitting, and exciton wave functions are calculated for different size of PNRs. The typically strong splitting between singlet and triplet excitonic states make PNRs favorable systems for application in optoelectronic. Quantum confinement occurs in both kinds of PNRs, and it is stron…
We study analytically, based on the tight-binding model, the electronic band structure of armchair AA-stacked bilayer graphene nanoribbons (BLGNRs) in several regimes. We apply hard-wall boundary conditions to determine the discretion dominating on the Bloch wavefunctions in the confined direction. First we consider an ideal case, perfect nanoribbons without any edge deformation, and show that their electronic properties are strongly size-dependent. We find that the narrow armchair AA-stacked BLGNRs (similar to single-layer graphene nanoribbons) may be metallic or semiconducting depending on t…
We argue that twisted graphene nanoribbons subjected to a transverse electric field can operate as a variety of nanoelectronic devices, such as tunable tunnel diodes with current-voltage characteristics controlled by the transverse field. Using the density-functional tight-binding method to address the effects of mechanical strain induced by the twisting, we show that the electronic transport properties remain almost unaffected by the strain in relevant cases and propose a simplified tight-binding model which gives reliable results. The transverse electric field creates a periodic electrostati…
Matrix elements of electron-light interactions for armchair and zigzag graphene nanoribbons are constructed analytically using a tight-binding model. The changes in wavenumber ($Δn$) and pseudospin are the necessary elements if we are to understand the optical selection rule. It is shown that an incident light with a specific polarization and energy, induces an indirect transition ($Δn=\pm1$), which results in a characteristic peak in absorption spectra. Such a peak provides evidence that the electron standing wave is formed by multiple reflections at both edges of a ribbon. It is also suggest…
A form of an indirect Ruderman-Kittel-Kasuya-Yosida (RKKY)-like coupling between magnetic on-site impurities in armchair graphene nanoribbons is studied theoretically. The calculations are based on a tight-binding model for a finite nanoribbon system with periodic boundary conditions. A pronounced Friedel-oscillation-like dependence of the coupling magnitude on the impurity position within the nanoribbon resulting from quantum size effects is found and investigated. In particular, the distance dependence of coupling is analysed. For semiconducting nanoribbons, this dependence is exponential-li…
Carbon-based nanostructures and graphene, in particular, evoke a lot of interest as new promising materials for nanoelectronics and spintronics. One of the most important issue in this context is the impact of external electrodes on electronic properties of graphene nanoribbons (GNR). The present theoretical method is based on the tight-binding model and a modified recursive procedure for Green's functions. The results show that within the ballistic transport regime, the so called end-contacted geometry (of minimal GNR/electrode interface area), is usually more advantageous for practical appli…
We present the Tight-Binding Studio (TBStudio) software package for calculating tight-binding Hamiltonian from a set of Bloch energy bands obtained from first principle theories such as density functional theory, Hartree-Fock calculations or Semi-empirical band structure theory. This will be helpful for scientists who are interested in studying the electronic properties of structures using Green's function theory in tight-binding approximation. TBStudio is a cross-platform application written in C++ with a graphical user interface design that is user-friendly and easy to work with. This softwa…
We investigate the energy spectrum of single layer black phosphorene nanoribbons (BPN) by means of a low-energy expansion of a recently proposed tight-binding model that describes electron and hole bands close to the Fermi energy level. Using the continuum approach, we propose boundary conditions based on sublattice symmetries for BPN with zigzag and armchair edges and show that our results for the energy spectra exhibit good agreement with those obtained by using the five-parameter tight-binding model. We also explore the behaviour of the energy gap versus the nanoribbon width $W$. Our findin…
Graphene nanoribbons are the flimsiest material systems in the world, and they get readily distorted. Distortion by twisting, for one, is important because it couples to ribbon's electronic properties. In this Letter, using simulations with density-functional tight-binding and revised periodic boundary conditions, I show that twisting appears almost equivalent to stretching; electronic structures in a given nanoribbon either upon twisting or upon certain stretching are quantitatively similar. This simple equivalence will provide a valuable guideline for interpreting and designing experiments w…
A systematic study of the electronic properties of single layer Sb (antimonene) nanoribbons is presented. By using a 6-orbital tight-binding Hamiltonian, we study the electronic band structure of finite ribbons with zigzag or armchair termination. We show that there is good agreement between ab initio calculations and the tight-binding model. We study how the size of the gap can be controlled by applying an external bias potential. An electric field applied perpendicular to the antimonene layer is found to increase the band gap, while a transverse bias potential leads to a position dependent r…
Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width $3m+2$ with integer $m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atom…
Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our {\it ab initio} calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges.…
In this paper we propose an analytical method to calculate the band structures of graphene-like nanoribbons of the armchair type with arbitrary line defects or uniaxial strains. The model is based on the tight-binding model and the standing wave assumption for the armchair nanoribbons. It gives accurate band results for large supercell systems. Within this method, we analyze different local states near the line defect in the graphene and boron-nitride nanoribbons. We also derive the analytical expression for the local states in a semi-infinite graphene nanoribbon by this method and the transfe…
The characteristics of energy band spectrum of armchair graphene nanoribbons in presence of line defect are analyzed within a simple non-interacting tight-binding framework. In metallic nanoribbons an energy gap may or may not appear in the band spectrum depending on the location of the defect line, while in semiconducting ribbons the gaps are customized, yielding the potential applicabilities of graphene nanoribbons in nanoscale electronic devices. With a more general model, we also investigate two-terminal electron transport using Green's function formalism.
In this work the tight binding model calculations are carried out for AA-Bilayer Graphene nanoribbons as an example of bilayer systems. The effects of edges, NNN hopping, and impurities of a single layer are introduced numerically as a change in the elements of the relevant block diagonal matrix appearing in the direct diagonalization method. The direct interlayer hopping between the top and the bottom single layers is constructed in the generalized direct diagonalization method by the off-diagonal block matrices in which the strength of the interlayer hopping is included.
In contrast with carbon nanotubes, the absence of translational symmetry (or periodical boundary condition) in the restricted direction of zigzag graphene nanoribbon removes the selection rule of subband number conservation. However, zigzag graphene nanoribbons with even dimers do have the inversion symmetry. We, therefore, propose a selection rule of parity conservation for electron-phonon interactions. The electron-phonon scattering matrix in zigzag graphene nanoribbons is developed using the tight-binging model within the deformation potential approximation.
We have investigated electronic transport in graphene nanoribbon devices with additional bar-shaped extensions ("wings") at each side of the device. We find that the Coulomb-blockade dominated transport found in conventional ribbons is strongly modified by the presence of the extensions. States localized far away from the central ribbon contribute significantly to transport. We discuss these findings within the picture of multiple coupled quantum dots. Finally, we compare the experimental results with tight-binding simulations which reproduce the experiment both qualitatively and quantitativel…
We present an atomistic three-dimensional simulation of graphene nanoribbon field effect transistors (GNR-FETs), based on the self-consistent solution of the 3D Poisson and Schroedinger equation with open boundary conditions within the non-equilibrium Green's Function formalism and a tight-binding hamiltonian. With respect to carbon nanotube FETs, GNR-FETs exhibit comparable performance, reduced sensitivity on the variability of channel chirality, and similar leakage problems due to band-to-band tunneling. Acceptable transistor performance requires effective nanoribbon width of 1-2 nm, that co…
In this paper, we present a mode space method for atomistic non-equilibrium Green's function simulations of armchair graphene nanoribbon FETs that includes electron-phonon scattering. With reference to both conventional and tunnel FET structures, we show that, in the ideal case of a smooth electrostatic potential, the modes can be decoupled in different groups without any loss of accuracy. Thus, inter-subband scattering due to electron-phonon interactions is properly accounted for, while the overall simulation time considerably improves with respect to real-space, with a speed-up factor of 40 …
We present a first-principles and tight-binding model study of silicane and germanane, the hydrogenated derivatives of two-dimensional silicene and germanene. We find that the materials are stable in freestanding form, analyse the orbital composition, and derive a tight-binding model using first-principles calculations to fit the parameters.
In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal π-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene.
We analyze electronic and phononic quantum transport through zigzag or chiral graphene nanoribbons (GNRs) perforated with an array of nanopores. Since local charge current profiles in these GNRs are peaked around their edges, drilling nanopores in their interior does not affect such edge charge currents while drastically reducing heat current carried by phonons in sufficiently long wires. The combination of these two effects can yield highly efficient thermoelectric devices with maximum $ZT \simeq 11$ at liquid nitrogen temperature and $ZT \simeq 4$ at room temperature achieved in $\sim 1$ $μ$…
We study narrow zigzag graphene nanoribbons (ZGNRs), employing density functional theory (DFT) simulations and the tight-binding (TB) method. The main result of these calculations is the braiding of the conduction and valence bands, generating Dirac cones for non-commensurate wave vectors $\vec{k}$. Employing a TB Hamiltonian, we show that the braiding is generated by the third-neighbor hopping (N3). We calculate the band structure, the density of states and the conductance, new conductance channels are opened, and the conductance at the Fermi energy assumes integer multiples of the quantum co…
We investigate the electronic transport properties of a folded graphene nanoribbon with monolayer nanoribbon contacts. We consider two possible foldings: either the nanoribbon can be folded onto itself in the shape of a hairpin with the nanoribbon leads at a $0^\circ$ angle, or the monolayer contacts have different directions, forming a $60^\circ$ angle. The system is described by a single $π$-band nearest-neighbor tight-binding Hamiltonian taking into account curvature effects. We have found that for the case of a nanoribbon folded over itself the conductance oscillates from almost zero and a…
We present an analytical description of pi electrons of a finite size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.
Random fluctuations of the shot-noise power in disordered graphene nanoribbons are studied. In particular, we calculate the distribution of the shot noise of nanoribbons with zigzag and armchair edge terminations. We show that the shot noise statistics is different for each type of these two graphene structures, which is a consequence of presence of different electron localizations: while in zigzag nanoribbons electronic edge states are Anderson localized, in armchair nanoribbons edge states are absent, but electrons are anomalously localized. Our analytical results are verified by tight bindi…
Armchair graphene nanoribbons, when forming a superlattice, can be classified in different topological phases, with or without edge states. By means of tight-binding and classical molecular dynamics (MD) simulations, we studied the electronic and mechanical properties of some of these superlattices. MD shows that fracture in modulated superlattices is brittle, as for unmodulated ribbons, and that occurs at the thinner regions, with staggered superlattices achieving a larger fracture strain. We found a general mechanism to induce a topological transition with strain, related to the electronic p…
We study the electronic and transport properties of heterostructures formed by armchair graphene nanoribbons with intersections of finite length. We describe the system by a tight-binding model and calculate the density of states and the conductance within the Green's function formalism based on real-space renormalization techniques. We show the apparition of interface states and bound states in the continuum which present a strong dependence of the heterostructure geometry. We investigate the effects on the conductance of an external perturbation applied on the edges atoms of the intersection…
The effects of substrate on the electronic properties of Graphene remains unclear. Many theoretical and experimental efforts have been done to clarify this discrepancy. In this work, we studied the electronic transport in armchair Graphene nanoribbons (AGNR) in the presence of substrate's disorder. The three main substrate's disorders -- surface roughness, charged impurity and surface optical phonon -- are investigated. Non-Equilibrium Green's function along with the tight-binding model is employed to investigate the electronic properties of Graphene Nanoribbons. The effects of these disorders…
Band gap control by an external field is useful in various optical, infrared and THz applications. However, widely tunable band gaps are still not practical due to variety of reasons. Using the orthogonal tight-binding method for $π$-electrons, we have investigated the effect of the external electric field on a subclass of monolayer chevron-type graphene nanoribbons that can be referred to as jagged graphene nanoribbons. A classification of such ribbons was proposed and band gaps for applied fields up to the SiO$_2$ breakdown strength ($1$ V/nm) were calculated. According to the tight-binding …
It is shown that apart from well-known factors, like temperature, substrate, and edge reconstruction effects, also the presence of external contacts is destructive for the formation of magnetic moments at the edges of graphene nanoribbons. The edge magnetism gradually decreases when graphene/electrode interfaces become more and more transparent for electrons. In addition to the graphene/electrode coupling strength, also the aspect ratio parameter, i.e. a width/length ratio of the graphene nanoribbon, is crucial for the suppression of edge magnetism. The present theory uses a tight-binding meth…
The effect of the uniaxial strain on the current-voltage characteristic of a typical armchair graphene-nanoribbon-hBN heterostructure device is simulated numerically by employing the nearest-neighbor tight-binding model and the non-equilibrium Green's function formalism. Simulations clearly reveal the following notable dependencies: (i) the strain invariably reduces the current; (ii) the strain applied in the armchair direction markedly widens the main peak of the current over a larger region of the bias voltage compared with the unstrained state; (iii) the current decreases faster when the st…
