We present a systematic study of electron backscattering phenomena during conduction for graphene nanoribbons with single-vacancy scatterers and dimensions within the capabilities of modern lithographic techniques. Our analysis builds upon an \textit{ab initio} parameterized semiempirical model that breaks electron-hole symmetry and nonequilibrium Green's function methods for the calculation of the conductance distribution $g$. The underlying mechanism is based on wavefunction localizations and perturbations that in the case of the first $π-π^*$ plateau can give rise to impurity-like pseudogaps with both donor and acceptor characteristics. Confinement and geometry are crucial for the manifestation of such effects. Self-consistent quantum transport calculations characterize vacancies as local charging centers that can induce electrostatic inhomogeneities on the ribbon topology.
The coherent electron transport along zigzag and metallic armchair graphene nanoribbons in the presence of one or two vacancies is investigated. Having in mind atomic scale tunability of the conductance fingerprints, the primary focus is on the effect of the distance to the edges and inter vacancies spacing. An involved interplay of vacancies sublattice location and nanoribbon edge termination, together with the spacing parameters lead to a wide conductance resonance line shape modification. Turning on a magnetic field introduces a new length scale that unveils counter-intuitive aspects of the…
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…
The graphene and phosphorene nanostructures have a big potential application in a large area of actuals research in physics. However, their methods of synthesis still do not allow the production of perfect materials with an intact molecular structure. In this paper, the occurrence of atomic vacancies was considered in the edge structure of the zigzag phosphorene and graphene nanoribbons. For different concentrations of these edge vacancies, their influence on the metallic properties was investigated. The calculations were performed for different sizes of the unit cell. Furthermore, for a small…
We present first-principles calculations of quantum transport in chemically doped graphene nanoribbons with a width of up to 4 nm. The presence of boron and nitrogen impurities is shown to yield resonant backscattering, whose features are strongly dependent on the symmetry and the width of the ribbon, as well as the position of the dopants. Full suppression of backscattering is obtained on the pi-pi* plateau when the impurity preserves the mirror symmetry of armchair ribbons. Further, an unusual acceptor-donor transition is observed in zig-zag ribbons. These unconventional doping effects could…
Using first-principles plane wave calculations we predict that electronic and magnetic properties of graphene nanoribbons can be affected by defect-induced itinerant states. The band gaps of armchair nanoribbons can be modified by hydrogen saturated holes. Defects due to periodically repeating vacancy or divacancies induce metallization, as well as magnetization in non-magnetic semiconducting nanoribbons due to the spin-polarization of local defect states. Antiferromagnetic ground state of semiconducting zigzag ribbons can change to ferrimagnetic state upon creation of vacancy defects, which r…
The robustness of topological materials against disorder and defects is presumed but has not been demonstrated explicitly in realistic systems. In this work, we use state-of-the-art density functional theory and recursive nonequilibrium Green's functions methods to study the effect of disorder in the electronic transport of long nanoribbons, up to 157 nm, as a function of vacancy concentration. In narrow nanoribbons, even for small vacancy concentrations, defect-like localized states give rise to hybridization between the edge states erasing topological protection and enabling backscattering e…
We study the crystal reconstruction in the presence of monovacancies (MVs), divacancies (DVs) and linear vacancies (LVs) in a zigzag silicene nanoribbon (ZSiNR) with transversal symmetry. Their influence on the electric and thermoelectric properties is assessed by the density functional theory combined with the nonequilibrium Green's functions. In particular, we focus on the spin resolved conductance, magnetoresistance and current-voltage curves. A 5-atom-ring is formed in MVs, a 5-8-5 ring structure in DVs, and a 8-4-8-4 ring structure in LVs. The linear conductance becomes strongly spin depe…
We report a first-principles based study of mesoscopic quantum transport in chemically doped graphene nanoribbons with a width up to 10 nm. The occurrence of quasibound states related to boron impurities results in mobility gaps as large as 1 eV, driven by strong electron-hole asymmetrical backscattering phenomena. This phenomenon opens new ways to overcome current limitations of graphene-based devices through the fabrication of chemically-doped graphene nanoribbons with sizes within the reach of conventional lithography.
Vacancies in graphene lead to the appearance of localized electronic states with non-vanishing spin moments. Using a mean-field Hubbard model and an effective double-quantum dot description we investigate the influence of strain on localization and magnetic properties of the vacancy-induced states in semiconducting armchair nanoribbons. We find that the exchange splitting of a single vacancy and the singlet-triplet splitting for two vacancies can be widely tuned by applying uniaxial strain, which is crucial for spintronic applications.
Transport of the edge-state electrons along zigzag phosphorene nanoribbons in presence of two impurities/vacancies is analytically investigated. Considering the places of the defects, a number of different situations are examined. When both defects are placed on the edge zigzag chain, as is expected, with changing the energy of the traveling electrons the electrical conductance exhibits a resonance behavior. In this case, for two vacancies the observed resonant peaks become extremely sharp. An amazing behavior is seen when the second vacancy is located along an armchair chain while the first i…
Graphane and graphene are both two-dimensional materials but of different bonding configurations, which can result in distinct thermal conduction properties. We simulate thermal conduction in graphane nanoribbons (GANRs) using the nonequilibrium Green's function method. It is found that GANRs have lower ballistic thermal conductance and stronger thermal conductance anisotropy than the graphene counterparts. Furthermore, hydrogen vacancies of GANRs considerably suppress thermal conduction, accompanied by enhanced thermal conductance anisotropy. The tunable thermal conduction, realized by contro…
We present numerical studies of conduction in graphene nanoribbons with reconstructed edges based on the standard tight-binding model of the graphene and the extended Huckel model of the reconstructed defects. We performed atomic geometry relaxation of individual defects using density functional theory and then explicitly calculated the tight-binding parameters used to model electron transport in graphene with reconstructed edges. The calculated conductances reveal strong backscattering and electron-hole asymmetry depending on the edge and defect type. This is related to an additional defect-i…
Thermoelectric properties of graphene nanoribbons with periodic edge vacancies and antidot lattice are investigated. The electron-phonon interaction is taken into account in the framework of the Hubbard-Holstein model with the use of the Lang-Firsov unitary transformation scheme. The electron transmission function, the thermopower and the thermoelectric figure of merit are calculated. We have found that the electron-phonon interaction causes a decrease in the peak values of the thermoelectric figure of merit and the shift of the peak positions closer to the center of the bandgap. The effects a…
Thermoelectrics as a way to use waste heat, is essential in electronic industries, but its low performance at operational temperatures makes it inappropriate in practical applications. Tailoring graphene can change its properties. In this work, we are interested in studying the transport properties of S-shape graphene structures with the single vacancy (SV) and double vacancy (DV) models. The structures are composed of a chiral part, which is an armchair graphene nanoribbon, and two zigzag graphene ribbons. We investigate the changes in the figure of merit by means of the Seebeck coefficient, …
Quantum thermal transport in armchair and zig-zag graphene nanoribbons are investigated in the presence of single atomic vacancies and subject to different boundary conditions. We start with a full comparison of the phonon polarizations and energy dispersions as given by a fifth-nearest-neighbor force-constant model (5NNFCM) and by elasticity theory of continuum membranes (ETCM). For free-edges ribbons we discuss the behavior of an additional acoustic edge-localized flexural mode, known as fourth acoustic branch (4ZA), which has a small gap when it is obtained by the 5NNFCM. Then, we show that…
Armchair phosphorene nanoribbons (APNRs) are known to be semiconductors with an indirect bandgap. Here, we propose to introduce new states in the gap of APNRs by creating a periodic structure of vacancies (antidots). Based on the tight-binding model, we show that a periodic array of vacancies or nanopores leads to the formation of an impurity band inside the gap region. We first present an analytical expression for the dispersion relation of an impurity band induced by hybridization of bound states associated with each single vacancy defect. Then, we increase the size of vacancy defects to inc…
We report on (magneto)-transport experiments in chemically derived narrow graphene nanoribbons under high magnetic fields (up to 60 Tesla). Evidences of field-dependent electronic confinement features are given, and allow estimating the possible ribbon edge symmetry. Besides, the measured large positive magnetoconductance indicates a strong suppression of backscattering induced by the magnetic field. Such scenario is supported by quantum simulations which consider different types of underlying disorders (smooth edge disorder and long range Coulomb scatters).
We report results on the Young's modulus (YM) of defect-free and defective silicene nanoribbons (SNRs) as a function of length and temperature. In this study, we perform molecular dynamics simulations using the Environment-Dependent Interatomic Potential (EDIP) to describe the interaction of the Si atoms. We find that the Young's modulus of pristine and defective SNRs increases with the ribbon length in both chirality directions. It is shown that the Young's modulus of defective SNRs exhibit a complex dependence on the combinations of vacancies. With respect to temperature, we find that YM for…
Graphene nanoribbons can be folded into a double layer system keeping the two layers decoupled. In the Quantum Hall regime folds behave as a new type of Hall bar edge. We show that the symmetry properties of the zero Landau level in metallic nanoribbons dictate that the zero energy edge states traversing a fold are perfectly transmitted onto the opposite layer. This result is valid irrespective of fold geometry, magnetic field strength and crystallographic orientation of the nanoribbon. Backscattering suppression on the N=0 Hall plateau is ultimately due to the orthogonality of forward and bac…
Quantum-mechanical calculations of electron magneto-transport in ideal graphene nanoribbons are presented. In noninteracting theory, it is predicted that an ideal ribbon that is attached to wide leads should reveal Fabry-Perot conductance oscillations in magnetic field. In the theory with Coulomb interaction taken into account, the oscillation pattern should rather be determined by the Aharonov-Bohm interference effect. Both of these theories predict the formation of quasi-bound states, albeit of different structures, inside the ribbon because of strong electron scattering on the interfaces be…
We calculate the local current density in pristine armchair graphene nanoribbons (AGNRs) with varying width, $N_\mathrm{C}$, employing a density-functional-theory-based ab initio transport formalism. We observe very pronounced current patterns (streamlines) with threefold periodicity in $N_\mathrm{C}$. They arise as a consequence of quantum confinement in the transverse flow direction. Neighboring streamlines are separated by stripes of almost vanishing flow. As a consequence, the response of the current to functionalizing adsorbates is very sensitive to their placement: adsorbates located wit…
The effects of electron interaction on the magnetoconductance of graphene nanoribbons (GNRs) are studied within the Hartree approximation. We find that a perpendicular magnetic field leads to a suppression instead of an expected improvement of the quantization. This suppression is traced back to interaction-induced modifications of the band structure leading to the formation of compressible strips in the middle of GNRs. It is also shown that the hard wall confinement combined with electron interaction generates overlaps between forward and backward propagating states, which may significantly e…
Numerical calculations based on the recursive Green's functions method in the tight-binding approximation are performed to calculate the dimensionless conductance $g$ in disordered graphene nanoribbons with Gaussian scatterers. The influence of the transition from short- to long-ranged disorder on $g$ is studied as well as its effects on the formation of a perfectly conducting channel. We also investigate the dependence of electronic energy on the perfectly conducting channel. We propose and calculate a backscattering estimative in order to establish the connection between the perfectly conduc…
Backscattering of delocalized electrons has been recently established [Phys. Rev. A 105, L041101 (2022)] as a mechanism to enhance high-order harmonic generation (HHG) in periodic systems with broken translational symmetry. Here we study this effect for a variable spatial gap in an atomic chain. Propagating the many-electron dynamics numerically, we find enhanced HHG and identify its origin in two mechanisms, depending on the gap size, either backscattering or enhanced tunneling from an impurity state. Since the gapped atomic chain exhibits both impurities and vacancies in a unified setting, i…
An intense laser field in the high-frequency regime drives carriers in graphene nanoribbons (GNRs) out of equilibrium and creates topologically-protected edge states. Using Floquet theory on driven GNRs, we calculate the time evolution of local excitations of these edge states and show that they exhibit a robust dynamics also in the presence of very localized lattice defects (atomic vacancies), which is characteristic of topologically non-trivial behavior. We show how it is possible to control them by a modulated electrostatic potential: They can be fully transmitted on the same edge, reflecte…
We investigate the combined influence of structural defects and uniaxial longitudinal strain on the electronic transport properties of armchair graphene nanoribbons using the numerical approach based on the semiempirical tight-binding model, the Landauer formalism, and the recursion method for Green functions. We calculate the conductance of graphene nanoribbons in the quantum coherent regime with different types and concentrations of defects. Further, we apply uniform planar tension to the nonideal graphene ribbons with randomly distributed and oriented single and double vacancies and Stone-W…
We have used molecular dynamics to calculate the thermal conductivity of symmetric and asymmetric graphene nanoribbons (GNRs) of several nanometers in size (up to ~4 nm wide and ~10 nm long). For symmetric nanoribbons, the calculated thermal conductivity (e.g. ~2000 W/m-K @400K for a 1.5 nm {\times} 5.7 nm zigzag GNR) is on the similar order of magnitude of the experimentally measured value for graphene. We have investigated the effects of edge chirality and found that nanoribbons with zigzag edges have appreciably larger thermal conductivity than nanoribbons with armchair edges. For asymmetri…
In this work we present a study on the negative differential resistance behavior and the impact of various deformations {like ripples, twist, wrap} and defects like vacancies and edge roughness on the electronic properties of short-channel MoS2 armchair nanoribbon MOSFETs. The effect of deformation {3 to 7 degree twist or wrap and 0.3 to 0.7 Ang rippling amplitude} and defects on a 10 nm MoS2 ANR FET is evaluated by the density functional tight binding theory and the non-equilibrium Green`s function approach. We study the channel density of states, transmission spectra and the ID VD characteri…
We study the size effects on the transport properties in topological Anderson insulators by means of the Landauer-Büttiker formalism combined with the nonequilibrium Green function method. Conductances calculated for serval different widths of the nanoribbons reveal that there is no longer quantized plateaus for narrow nanoribbons. The local spin-resolved current distribution demonstrates that the edge states on the two sides can be coupled, leading to enhancement of backscattering as the width of the nanoribbon decreases, thus destroying the perfect quantization phenomena in the topological A…
Motivated by recent scanning tunneling microscopy/spectroscopy experiments on probing single vacancies in black phosphorus, we present a theory for Fano antiresonances induced by coupling between vacancy states and edge states of zigzag phosphorene nanoribbons (zPNRs). To this end, in the first step, using the tight-binding Hamiltonian, we obtain an analytic solution on the lattice for the state associated to a single vacancy located in the bulk phosphorene which shows a highly anisotropic localization in real space. For a finite zigzag ribbon, in the absence of particle-hole symmetry, the loc…
Based on the investigation of the multi-terminal conductance of a system composed of two graphene nanoribbons, in which one is on top of the other and rotated by 60 degrees, we propose a setup for a 50/50 electronic beam splitter that neither requires large magnetic fields nor ultra low temperatures. Our findings are based on an atomistic tight-binding description of the system and on the Green's function method to compute the Landauer conductance. We demonstrate that this system acts as a perfect 50/50 electronic beam splitter, in which its operation can be switched on and off by varying the …
We provide a theoretical study of the conductance response of systems based on graphene nanoribbon to the potential of a scanning probe. The study is based on the Landauer approach for the tight-binding Hamiltonian with an implementation of the quantum transmitting boundary method and covers homogenous nanoribbons, their asymmetric narrowing and quantum point contacts of various profiles. The response maps at low Fermi energies resolve formation of n-p junctions induced by the probe potential and a presence of zigzag-armchair segments of the edges for inhomogeneous ribbons. For an asymmetric n…
We study scanning gate microscopy (SGM) conductance mapping of a $\mathrm{MoS}_2$ zigzag ribbon exploiting tight-binding and continuum models. We show that, even though the edge modes of a pristine nanoribbon are robust to backscattering on the potential induced by the tip, the conductance mapping reveals presence of both the edge modes and the quantized spin- and valley-current carrying modes. By inspecting the electron flow from a split gate quantum point contact (QPC) we find that the mapped current flow allows to determine the nature of the quantization in the QPC as spin-orbit coupling st…
We employ the formalism of bond currents, expressed in terms of the nonequilibrium Green functions, to image the charge flow between two sites of the honeycomb lattice of graphene ribbons of few nanometers width. In sharp contrast to nonrelativistic electrons, current density profiles of quantum transport at energies close to the Dirac point in clean zigzag graphene nanoribbons (ZGNR) differs markedly from the profiles of charge density peaked at the edges due to zero-energy localized edge states. For transport through the lowest propagating mode induced by these edge states, edge vacancies do…
Here, we report the performance of vacancy affected supercell of a hybrid Graphene-Boron Nitride embedded armchair nanoribbon (a-GNR-BN) based n-MOSFET at its ballistic transport limit using Non Equilibrium Green's Function (NEGF) methodology. A supercell is made of the 3p configuration of armchair nanoribbon that is doped on the either side with 6 BN atoms and is also H-passivated. The type of vacancies studied are mono (B removal), di (B and N atom removal) and hole (removal of 6 atoms) formed all at the interface of carbon and BN atoms. Density Functional Theory (DFT) is employed to evaluat…
We developed a unified mesoscopic transport model for graphene nanoribbons, which combines the non-equilibrium Green's function (NEGF) formalism with the real-space π-orbital model. Based on this model, we probe the spatial distributions of electrons under a magnetic field, in order to obtain insights into the various signature Hall effects in disordered armchair graphene nanoribbons (AGNR). In the presence of a uniform perpendicular magnetic field (B\perp-field), a perfect AGNR shows three distinct spatial current profiles at equilibrium, depending on its width. Under non-equilibrium conditio…
We numerically investigate the electronic transport properties of graphene nanoribbons and carbon nanotubes with inter-valley coupling, e.g., in \sqrt{3}N \times \sqrt{3}N and 3N \times 3N superlattices. By taking the \sqrt{3} \times \sqrt{3} graphene superlattice as an example, we show that tailoring the bulk graphene superlattice results in rich structural configurations of nanoribbons and nanotubes. After studying the electronic characteristics of the corresponding armchair and zigzag nanoribbon geometries, we find that the linear bands of carbon nanotubes can lead to the Klein tunnelling-l…
Previously, graphene nanoribbons set in lateral heterostructures with hexagonal boron nitride were predicted to support topologically protected states at low energy. We investigate how robust the transport properties of these states are against lattice disorder. We find that forms of disorder that do not couple the two valleys of the zigzag graphene nanoribbon do not impact the transport properties at low bias, indicating that these lateral heterostructures are very promising candidates for chip-scale conducting interconnects. Forms of disorder that do couple the two valleys, such as vacancies…
We present numerical studies of conduction in graphene nanoribbons with different types of disorder. We find that even when defect scattering depresses the conductance to values two orders of magnitude lower than 2e^2/h, equally spaced conductance plateaus occur at moderately low temperatures due to enhanced electron backscattering near subband edge energies if bulk vacancies are present in the ribbon. This work accounts quantitatively for the surprising conductance quantization observed by Lin et al. [Phys. Rev. B 78, 161409 (2008)] in ribbons with such low conductances.
The thermoelectric properties of in plane heterostructures made of Graphene and hexagonal Boron Nitride (BN) have been investigated by means of atomistic simulation. The heterostructures consist in armchair graphene nanoribbons to the sides of which BN flakes are periodically attached. This arrangement generates a strong mismatch of phonon modes between the different sections of the ribbons, which leads to a very small phonon conductance, while the electron transmission is weakly affected. In combination with the large Seebeck coefficient resulting from the BN-induced bandgap opening or broade…
Vacancies in graphene have been proposed to give rise to $π$-like magnetism in carbon materials, a conjecture which has been supported by recent experimental evidence. A key element in this "vacancy magnetism" is the formation of magnetic moments in vacancy-induced electronic states. In this work we compute the charging energy $U$ of a single-vacancy generated localized state for bulk graphene and graphene ribbons. We use a tight-binding model to calculate the dependency of the charging energy $U$ on the amplitudes of the localized wave function on the graphene lattice sites. We show that for …
