Analytical Tight-binding Approach for Ballistic Transport through Armchair Graphene Ribbons: Exact Solutions for Propagation through Step-like and Barrier-like Potentials
Based on a tight-binding approximation, we present analytical solutions for the wavefunction and propagation velocity of an electron in armchair graphene ribbons. The derived expressions are used for computing the transmission coefficients through step-like and barrier-like potentials. Our analytical solutions predict a new kind of transmission resonances for one-mode propagation in semiconducting ribbons. Contrary to the Klein paradox in graphene, this approach shows that backscattering for gapless mode is possible. In consistence with a higher order $\bf{k\cdot p}$ method, the backscattering probabilities vary with the square of the applied potential in the low-energy limit. We also demonstrate that gapless-mode propagation through a potential step in armchair ribbons can be described by the same through-step relation as that for an undimerized 1D chain of identical atoms.
We address electron transport in honeycomb lattice ribbons with armchair edges attached to two semi-infinite one-dimensional metallic electrodes within the tight-binding framework. Here we present numerically the conductance-energy and current-voltage characteristics as functions of the length and width of the ribbons. Our theoretical results predict that for a ribbon with much smaller length and width, so-called a nanoribbon, a gap in the conductance spectrum appears across the energy E=0. While, this gap decreases gradually with the increase of the size of the ribbon, and eventually it almos…
Interlayer Conductance in the Armchair Nanotube -- Zigzag Graphene Ribbon Parallel Contact: Theoretical Proposal of Detection of Wavefunction Growing from the Edge to the Center in the Graphene Ribbon
In semiconducting armchair graphene ribbons a chiral lattice deformation can induce pairs of topological gap states with opposite energies. Near the critical value of the deformation potential these kink and antikink states become almost degenerate with zero energy and have a fractional charge one-half. Such a semiconducting armchair ribbon represents a one-dimensional topological insulator with nearly zero energy end states. Using data collapse of numerical results we find that the shape of the kink displays an anomalous power-law dependence on the width of the local lattice deformation. We s…
We investigate the effects of external electric fields on the electronic properties of bilayer armchair graphene nano-ribbons. Using atomistic simulations with Tight Binding calculations and the Non-equilibrium Green function formalism, we demonstrate that (i) in semi-metallic structures, vertical fields impact more effectively than transverse fields in terms of opening larger bandgap, showing a contrary phenomenon compared to that demonstrated in previous studies in bilayer zigzag graphene nano-ribbons; (ii) in some semiconducting structures, if transverse fields just show usual effects as in…
We consider the end states of a half-filled rectangular armchair graphene ribbon (RAGR) in a staggered potential. Taking electron-electron interactions into account we find that, as the strength of the staggered potential varies, three types of couplings between the end states can occur: antiferromagnetic without or with spin splitting, and paramagnetic without spin-splitting. We find that a spin-splitting is present only in the staggered potential region $0<Δ<Δ_c$. The transition from the antiferromagnetic state at $Δ=0$ to the paramagnetic state goes through an intermediate spin-split antife…
We explore the electronic structure, orbital character and topological aspect of a monolayer MoS$_2$ nanoribbon using tight-binding (TB) and low-energy (${\bm k}\cdot{\bm p} $) models. We obtain a mid-gap edge mode in the zigzag ribbon of monolayer MoS$_2$, which can be traced back to the topological properties of the bulk band structure. Monolayer MoS$_2$ can be considered as a valley Hall insulator. The boundary conditions at armchair edges mix the valleys on the edges, and a gap is induced in the edge modes. The spin-orbit coupling in the valence band reduces the hybridization of the bulk s…
We have investigated, using effective mass approach (EMA), magnetic properties of a one-dimensional electron gas in graphene armchair ribbons when the electrons of occupy only the lowest conduction subband. We find that magnetic properties of the one-dimensional electron gas may depend sensitively on the width of the ribbon. For ribbon widths $L_x=3Ma_0$, a critical point separates ferromagnetic and paramagnetic states while for $L_x=(3M+1)a_0$ paramagnetic state is stable ($M$ is an integer and $a_{0}$ is the length of the unit cell). These width-dependent properties are a consequence of eige…
We study quantum transport in honeycomb lattice ribbons with either armchair or zigzag edges. The ribbons are coupled to semi-infinite linear chains serving as the input and output leads and we use a tight-binding Hamiltonian with nearest-neighbor hops. For narrow ribbons we find transmission gaps for both types of edges. The center of the gap is at the middle of the band in ribbons with armchair edges. This symmetry is due to a property satisfied by the matrices in the resulting linear problem. In ribbons with zigzag edges the gap center is displaced to the right of the middle of the band. We…
Characterized by zigzag and armchair boundaries, the narrow ribbons display the very different characteristics in Hall conductivities. It is shown that the multi-band-crossings occur in the energy spectrum for armchair ribbons, and the number of them depends on the width of ribbons. Theoretically, it is predicated that the conductivities exhibit drastic sign reversals for narrow ribbons as the Fermi energy sweep over the band-crossings. A new classification of armchair ribbons is suggested based on the emergence of a flat band in the energy spectrum only for odd armchair ribbons. The evolution…
We study the conductance of graphene nanoribbons with long-range disorder. Due to the absence of intervalley scattering from the disorder potential, time-reversal symmetry (TRS) can be effectively broken even without a magnetic field, depending on the type of ribbon edge. Even though armchair edges generally mix valleys, we show that metallic armchair nanoribbons possess a hidden pseudovalley structure and effectively broken TRS. In contrast, semiconducting armchair nanoribbons inevitably mix valleys and restore TRS. As a result, in strong disorder metallic armchair ribbons exhibit a perfectly…
A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-ribbon is in the quantum spin Hall (QSH) state, then there must be helical edge states. By folding a graphene ribbon to a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furt…
On the basis of first principles calculations, we report energy estimated to cut a graphene sheet into nanoribbons of armchair and zigzag configurations. Our calculations show that the energy required to cut a graphene sheet into zigzag configuration is higher than that of armchair configuration by an order of 0.174 eV. Thus, a control over the threshold energy might be helpful in designing an experiment for cutting a graphene sheet into smooth edged armchair or zigzag configurations.
We combine density-functional theory and the nonequilibrium Green's function method to study the thermal conductance of graphene nanoribbons with armchair and zigzag edges. Zigzag ribbons have higher thermal conductance than armchair ribbons of comparable widths due to an anisotropy in phonon dispersion for graphene nanoribbons: low-frequency bands in zigzag ribbons are more dispersive than those in armchair ribbons. The edges with and without hydrogen-passivation modify the atomic structure and ultimately influence the phonon thermal transport differently for the two ribbon types.
Zigzag edges of neutral armchair-oriented Graphene Nano-Ribbons show states strongly localized at those edges. They behave as free radicals that can capture electrons during processing, increasing ribbon's stability. Thus, charging and its consequences should be investigated.Total energy calculations of finite ribbons using spin polarized Density Functional Theory (DFT) show that ribbon's charging is feasible. Energies for Pariser-Parr-Pople (PPP) model Hamiltonian are compatible with DFT allowing the study of larger systems. Results for neutral ribbons indicate: i) the fundamental gap of spin…
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…
Based on atomistic simulations, the nonlinear elastic properties of monolayer graphene nanoribbons under quasistatic uniaxial tension are predicted, emphasizing the effect of edge structures (armchair and zigzag, without and with hydrogen passivation). The results of atomistic simulations are interpreted within a theoretical framework of thermodynamics, which enables determination of the nonlinear functions for the strain-dependent edge energy and the hydrogen adsorption energy, for both zigzag and armchair edges. Due to the edge effects, the initial Young's modulus of graphene nanoribbons und…
Zig-zag edge graphene ribbons grown on 6H-SiC facets are ballistic conductors. It has been assumed that zig-zag graphene ribbons grown on 4H-SiC would also be ballistic. However, in this work we show that SiC polytype matters; ballistic graphene ribbons only grow on 6H SiC. 4H and 4H-passivated ribbons are diffusive conductors. Detailed photoemmision and microscopy studies show that 6H-SiC sidewalls zig-zag ribbons are metallic with a pair of n-doped edge states associated with asymmetric edge terminations, In contrast, 4H-SiC zig-zag ribbons are strongly bonded to the SiC; severely distorting…
Boundary conditions for the two-dimensional fermions in ribbons of the hexagonal lattice are studied in the dice model whose energy spectrum in infinite system consists of three bands with one completely flat band of zero energy. Like in graphene the regular lattice terminations are of the armchair and zigzag types. However, there are four possible zigzag edge terminations in contrast to graphene where only one type of zigzag termination is possible. Determining the boundary conditions for these lattice terminations, the energy spectra of pseudospin-1 fermions in dice model ribbons with zigzag…
We calculate the band structure and the conductance of periodic corrugated graphene nanoribbons within the framework of the tight-binding $p$-orbital model. We consider corrugated structures based on host ribbons with armchair and zigzag edges and three different types of corrugations (armchair edges, zigzag edges as well as a rectangular corrugation). We demonstrate that for armchair host ribbons, depending on the type of corrugation, a band gap or low-velocity minibands appear near the charge neutrality point. For higher energies the allowed Bloch state bands become separated by mini-stopban…
Quantum size effects in armchair graphene nano-ribbons (AGNR) with hydrogen termination are investigated via density functional theory (DFT) in Kohn-Sham formulation. "Selection rules" will be formulated, that allow to extract (approximately) the electronic structure of the AGNR bands starting from the four graphene dispersion sheets. In analogy with the case of carbon nanotubes, a threefold periodicity of the excitation gap with the ribbon width (N, number of carbon atoms per carbon slice) is predicted that is confirmed by ab initio results. While traditionally such a periodicity would be obs…
Controlling the forbidden gap of graphene nano-ribbons (GNR) is a major challenge that has to be attained if this attractive material has to be used in micro- and nano-electronics. Using an unambiguous notation {m,n}-GNR, where m (n) is the number of six carbon rings in the arm-chair (zig-zag) directions, we investigate how varies the HOMO-LUMO gap when the size of the GNR is varied by increasing either m or n, while keeping the other variable fixed. It is shown that no matter whether charge- or spin-density-waves solutions are considered, the gap varies smoothly when n is kept fixed whereas i…
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 present an analytical investigation of the exciton optical absorption in a narrow armchair graphene nanoribbon (AGNR) in the presence of a longitudinal external electric field directed parallel to the ribbon axis. The two-body 2D Dirac equation for the massless electron and hole subject to the ribbon confinement, Coulomb interaction and electric field is employed. The ribbon confinement is assumed to be much stronger than the internal exciton electric field which in turn considerably exceeds the external electric field. This justifies an adiabatic approximation implying a slow longitudinal …
In graphene nanoribbons (GNRs), the lateral confinement of charge carriers opens a band gap, the key feature to enable novel graphene-based electronics. Successful synthesis of GNRs has triggered efforts to realize field-effect transistors (FETs) based on single ribbons. Despite great progress, reliable and reproducible fabrication of single-ribbon FETs is still a challenge that impedes applications and the understanding of the charge transport. Here, we present reproducible fabrication of armchair GNR-FETs based on a network of nanoribbons and analyze the charge transport mechanism using nine…
We study the effects of the long-range disorder potential and warping on the conductivity and mobility of graphene ribbons using the Landauer formalism and the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of the structure increases the system undergoes a transition from the ballistic to the diffusive regime. This is reflected in the calculated electron density dependencies of the conductivity and the mobility. In particular, we show that the mobility of graphene ribbons varies as mu(n) n^(-lambda), with 0<lambda<0.5. The exponent lambda depends on the length of the sy…
Strain fold-like deformations on armchair graphene nanoribbons (AGNRs) can be properly engineered in experimental setups, and could lead to a new controlling tool for gaps and transport properties. Here, we analyze the electronic properties of folded AGNRs relating the electronic responses and the mechanical deformation. An important and universal parameter for the gap engineering is the ribbon percent width variation, i.e., the difference between the deformed and undeformed ribbon widths. AGNRs bandgap can be tuned mechanically in a well defined bounded range of energy values, eventually lead…
We present an analytical investigation of the quasi-Coulomb impurity states in a narrow gapped armchair graphene nanoribbon (GNR) in the presence of a uniform external electric field directed parallel to the ribbon axis. The effect of the ribbon confinement is taken to be much greater than that of the impurity electric field, which in turn considerably exceeds the external electric field. Under these conditions we employ the adiabatic approximation assuming that the motion parallel ("slow") and perpendicular ("fast") to the ribbon axis are separated adiabatically. In the approximation of the i…
We present a theoretical study on narrow armchair graphene nanoribbons (AGNRs) with hydroxyl functionalized edges. Although this kind of passivation strongly affects the structure of the ribbon, a high degree of edge functionalization proves to be particularly stable. An important consequence of the geometric deviations is a severe reduction of the band-gap of the investigated 7-AGNR. This shift follows a linear dependence on the number of added hydroxyl groups per unit cell and thus offers the prospect of a tunable band-gap by edge functionalization. We furthermore cover the behavior of chara…
We show that near an armchair edge of a wide graphene channel, and in the presence of a smooth step-like electrostatic lateral confining potential, the chirality, spectrum, spatial structure, and number of the fundamental edge magnetoplasmons (EMPs), in the $ν=2$ regime of the quantum Hall effect, depend strongly on the position of the Fermi level $E_{F}$. (i) When $E_{F}$ is small enough and intersects four degenerate states of the zero Landau level (LL) at one location and two degenerate states of this level at a different one, two fundamental, counter propagating EMPs exist with opposite ch…
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 study the optical response of nanoribbons made from the $α-T_3$ lattice under a weak magnetic field in the terahertz to far-infrared regime. It is found that the magnetic field can open a gap in the band structure and induce a new absorption peak with much reduced frequency in metallic armchair ribbons and a class of zigzag ribbons with particular boundaries. This tunable magneto-optical modulation effect is attributed to the interband transitions between the flat band and the propagating bands. By contrast, this magnetic modulation of gap opening and optical conductance is much weaker in m…
We study the energy spectra and wavefunctions of graphene rings formed from metallic armchair ribbons, near zero energy, to search for properties which may be identified with "effective broken time reversal symmetry" (EBTRS). Appropriately chosen corner junctions are shown to impose phase shifts in the wavefunctions that at low energies have the same effect as effective flux tubes passing near the ribbon surface. Closing the ribbon into a ring captures this flux and yields properties that may be understood as signatures of EBTRS. These include a gap in the spectrum around zero energy, which ca…
The conductivity of armchair graphene nanoribbons in the presence of short-range impurities and edge roughness is studied theoretically using the Boltzmann transport equation for quasi-one-dimensional systems. As the number of occupied subbands increases, the conductivity due to short-range impurities converges towards the two-dimensional case. Calculations of the magnetoconductivity confirm the edge-roughness-induced dips at cyclotron radii close to the ribbon width suggested by the recent quantum simulations.
A study of the effect of unscreened Coulomb interactions on the quantum spin Hall (QSH) phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit interaction (I-SO), exact expressions for band-structures and edge-states wavefunctions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wavefunctions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb int…
The ab initio band structure of 2D graphene sheet is well reproduced by the third nearest neighbor tight binding model proposed by Reich et al [Phys. Rev. B 66, 035412]. For ribbon structures, the existing sets of tight binding parameters can successfully explain semi-conducting behavior of all armchair ribbon structures. However, they are still failing in describing accurately the slope of the bands while this feature is directly associated to the group velocity and the effective mass of electrons. In this work, both density functional theory and tight binding calculations were performed and …
We show strong effects of a weak and smooth, on the magnetic length, superlattice potential upon edge magnetoplasmons (EMPs) at the armchair edge, with a smooth steplike electrostatic lateral confining potential, of a wide graphene channel in the $ν=2$ quantum Hall effect regime. The superlattice potential leads to essential enlargement of a number of EMPs, descend from two fundamental EMPs in the absence of superlattice. For the wave vector $k_{x}$ within the first Brillouin zone, the EMPs show as the regions of acoustical or quasi-acoustical dispersion, with a finite value of group velocity,…
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…
In this study, we investigate the electronic and magnetic properties of graphane nanoribbons. We find that zigzag and armchair graphane nanoribbons with H-passivated edges are nonmagnetic semiconductors. While bare armchair ribbons are also nonmagnetic, adjacent dangling bonds of bare zigzag ribbons have antiferromagnetic ordering at the same edge. Band gaps of the H-passivated zigzag and armchair nanoribbons exponentially depend on their width. Detailed analysis of adsorption of C, O, Si, Pt, Ti, V and Fe atoms on the graphane ribbon surface reveal that functionalization of graphane ribbons i…
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 appro…
A graphene nanoribbon is a good candidate for a $(1+1)$ Chern-Simons topological insulator since it obeys particle-hole symmetry. We show that in a finite semiconducting armchair ribbon, which has two zigzag edges and two armchair edges, a $(1+1)$ Chern-Simons topological insulator is indeed realized as the length of the armchair edges becomes large in comparison to that of the zigzag edges. But only a quasi-topological insulator is formed in a metallic armchair ribbon with a pseudogap. In such systems a zigzag edge acts like a domain wall, through which the polarization changes from $0$ to $e…
Describing by a Hubbard type of model a thin armchair graphene ribbon in the armchair hexagon chain limit, one shows in exact terms, that even if the system does not have flat bands at all, at low concentration a mesoscopic sample can have ferromagnetic ground state, being metallic in the same time. The mechanism is connected to a common effect of correlations and confinement.
We consider theoretically a wide graphene ribbon, that on both ends is attached to electronic reservoirs which generally have different temperatures. The graphene ribbon is assumed to be deposited on a substrate, that leads to a spin-orbit coupling of Rashba type. We calculate the thermally induced charge current in the ballistic transport regime as well as the thermoelectric voltage (Seebeck effect). Apart from this, we also consider thermally induced spin current and spin polarization of the graphene ribbon. The spin currents are shown to have generally two components; one parallel to the te…
Quantum-dot states in graphene nanoribbons (GNR) were calculated using density-functional theory, considering the effect of the electric field of gate electrodes. The field is parallel to the GNR plane and was generated by an inhomogeneous charge sheet placed atop the ribbon. Varying the electric field allowed to observe the development of the GNR states and the formation of localized, quantum-dot-like states in the band gap. The calculation has been performed for armchair GNRs and for armchair ribbons with a zigzag section. For the armchair GNR a static dielectric constant of ε approx. 4 coul…
Explicit expressions of the band spectrum near the neutrality point for armchair and zigzag graphene ribbons and carbon nanotubes were derived based on a tight-binding macromolecule model of graphene. The obtained dispersion relations are used to determine and compare the conductance ladders of these structures and are beneficial for many other applications. Our results are different in many respects from previously reported data. This new information forms a solid reliable basis for evaluation of the potential of graphene nanoelectronic devices.
We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient and…
We investigate higher-order plasmons in graphene nanoribbons, and present how electronic edge states and wavefunction fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ri…
We study the effects of uniaxial strains on the transport properties of the graphene nanoribbons(GNRs) connected with two metallic leads in heterojunctions, using the transfer matrix method. Two typical GNRs with zigzag and armchair boundaries are considered, and the tension is applied either parallel or perpendicular to the ribbon axis. It turns out that the electron-hole symmetry is missing in the gate voltage dependence of the conductance data of the armchair GNRs, while it persists in the zigzag ribbons under any strains. For an armchair GNR with a vertical tension applied, a sharp drop of…
Heat flow in nanomaterials is an important area of study, with both fundamental and technological implications. However, little is known about heat flow in two-dimensional (2D) devices or interconnects with dimensions comparable to the phonon mean free path (mfp). Here, we find that short, quarter-micron graphene samples reach ~35% of the ballistic heat conductance limit up to room temperature, enabled by the relatively large phonon mfp (~100 nm) in substrate-supported graphene. In contrast, patterning similar samples into nanoribbons (GNRs) leads to a diffusive heat flow regime that is contro…
We theoretically study the magnetoresistance of single wall carbon nanotubes (SWCNTs) in the ballistic transport regime, using a standard tight-binding approach. The main attention is directed to spin-polarized electrical transport in the presence of either axial or perpendicular magnetic field. The method takes into account both Zeeman splitting as well as size and chirality effects. These factors (along with a broadening of energy levels due to a strong nanotube/electrode coupling) lead, in ultra small SWCNTs, to serious modifications in profile of the Aharonov-Bohm oscillations. Other notew…
Graphene nanoribbons (GNRs) are one-dimensional (1D) structures that exhibit a rich variety of electronic properties1-17. Therefore, they are predicted to be the building blocks in next-generation nanoelectronic devices. Theoretically, it has been demonstrated that armchair GNRs can be divided into three families, i.e., Na = 3p, Na = 3p + 1, and Na = 3p + 2 (here Na is the number of dimer lines across the ribbon width and p is an integer), according to their electronic structures, and the energy gaps for the three families are quite different even with the same p1,3-6. However, a systematic ex…
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.
Adiabatic quantum charge pumping in graphene nanoribbon double barrier structures with armchair and zigzag edges in the resonant transmission regime is analyzed. Using recursive Green's function method we numerically calculate the pumped charge for pumping contours encircling a resonance. We find that for armchair ribbons the whole resonance line contributes to the pumping of a single electron (ignoring double spin degeneracy) per cycle through the device. The case of zigzag ribbons is more interesting due to zero-conductance resonances. These resonances separate the whole resonance line into …
We present a microscopic theory for interacting graphene armchair nanoribbon quantum dots. Long range interaction processes are responsible for Coulomb blockade and spin-charge separation. Short range ones, arising from the underlying honeycomb lattice of graphene, smear the spin-charge separation and induce exchange correlations between bulk electrons - delocalized on the ribbon - and single electrons localized at the two ends. As a consequence, entangled end-bulk states where the bulk spin is no longer a conserved quantity occur. Entanglement's signature is the occurrence of negative differe…
Graphene electronics has motivated much of graphene science for the past decade. A primary goal was to develop high mobility semiconducting graphene with a band gap that is large enough for high performance applications. Graphene ribbons were thought to be semiconductors with these properties, however efforts to produce ribbons with useful bandgaps and high mobility has had limited success. We show here that high quality epitaxial graphene nanoribbons 40 nm in width, with annealed edges, grown on sidewall SiC are not semiconductors, but single channel room temperature ballistic conductors for …
Based on the nearest-neighbor tight-binding model, we present analytical description of low-energy electron transport through a symmetrical junction of two semimetal armchair ribbons. The results obtained demonstrate the transmission suppression in the vicinity of the neutrality point except for the junction of the ribbons consisting of 3p-1 and 3p+5 dimer lines, p/2 is odd. Unlike other interconnections, these compounds are shown to be free of even local levels arising at the junction interface and exhibit electron backscattering to be inversely as the square of p+1.
