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 antiferromagnetic state, and this spin-splitting disappears suddenly at $Δ_c$. For small and large values of $Δ$ the end charge of a RAGR can be connected to the Zak phase of the periodic armchair graphene ribbon (PARG) with the same width, and it varies continuously as the strength of the potential changes.
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
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 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 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.
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 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…
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…
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 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…
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…
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…
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…
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…
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…
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…
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…
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…
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.
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 …
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…
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…
We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k), which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum k at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one dimensional toy model as well as for graphene ribbons with zigzag edges. The range of k for which edge states exist in a graphene ribbon is then…
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…
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.
Using density functional theory, we predict half-metallicity in edge hydrogenated armchair boron nitride nanoribbons (ABNNRs). The predicted spin polarization is analyzed in detail by calculating electronic and magnetic properties of these hydrogenated ABNNRs by means of first-principles calculations within the local spin-density approximation (LSDA). ABNNRs with only edge B atoms passivated by H atoms are found to be half-metallic (regardless of their width) with a half-metal gap of 0.26 eV. Upto 100% spin polarized charge transport is predicted across the Fermi level owing to the giant spin …
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…
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…
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 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…
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 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…
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…
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,…
We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are computed self-consistently in the Hartree approximation. We compute the average density of extra carriers, $n_{2D}$, the number of occupied subbands and the density profiles as a function of the gate potential $V_g$. We discuss quantum corrections to the classical capacitance and we calculate the threshold $V_g$ above which semiconducting armchair ribbons c…
Quantum spin Hall insulator/metal interfaces are formed in graphene ribbons with intrinsic spin-orbit coupling by selectively doping two regions creating a potential step. For a clean graphene ribbon, the transmission of the topological edge states through a n-n or p-p junction is perfect irrespective of the ribbon termination, width, and potential step parameters due to the orthogonality of incoming and outgoing edge channels. This is shown numerically for an arbitrary crystallographic orientation of the ribbon and proven analytically for zigzag and metallic armchair boundary conditions. In d…
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.
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…
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 …
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…
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…
The list of textbook tunneling formulas is extended by deriving exact expressions for the transmission coefficient in graphene ribbons with armchair edges and the step-like and barrier-like profiles of site energies along the ribbon. These expressions are obtained by matching wave functions at the interfaces between the regions, where quasiparticles have constant but different potential energies. It is shown that for an $U_0$ high barrier and low-energy electrons and holes, the mode transmission of charge carriers in this type of ribbons is described by the textbook formula, where the constant…
We calculate the polarization function of Dirac fermions in metallic armchair graphene nanoribbons for an arbitrary temperature and doping. We find that at finite temperatures due to the phase space redistribution among inter-band and intra-band electronic transitions in the conduction and valence bands, the full polarization function becomes independent of the temperature and the position of the chemical potential. As a result, for a given width of nanoribbons there exists a single plasmon mode, with the energy dispersion determined by the graphene's fine structure constant. In Coulomb-couple…
Non-equilibrium two-parameter pumping transport through graphene ribbons, attached to reservoirs is described. A tight-binding model is solved using Keldysh formalism, and the crossover between adiabatic and non-adiabatic regimes is studied. Pumped dc currents through armchair ribbons show properties common in two-dimensional systems. The width-dependent dc current in zigzag ribbons, reveals that edge states akin to those in two-dimensional topological insulators, do not contribute to pumped transport in the adiabatic regime. The interplay between propagating and evanescent modes is discussed.
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…
Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanori…
By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall ferromagnetism (QHF) gaps and dynamically generated Dirac-like masses. The analysis is done for graphene ribbons with both zigzag and armchair edges. The characteristic features of the spectrum of the edge states in both these cases are described. In particular, the conditions for the existence of the gapless edge states are established. Implications of these results for…
