Peculiar Band Gap Structure of Graphene Nanoribbons
Motohiko Ezawa
备注：
8 pages, 7 figures: Presented at 14th International Conference on Superlattices, Nano-Structures and Nano-Devices, Istanbul, July 30-August 4 (2006); Cover picture of the proceeding
Graphene nanoribbons are quasi-one-dimensional meterials with finite width. Characterizing a wide class of nanoribbons by edge shape and width, we make a systematic analysis of their electronic properties. The band gap structure of nanoribbons is shown to exhibit a valley structure with stream-like sequences of metallic or almost metallic nanoribbons. Among them, all zigzag nanoribbons are metallic, and armchair nanoribbons are metallic by period of 3. We find that these stream-like sequences correspond to equi-width curves, and that the band gap of chiral and armchair nanoribbons oscillate as a function of the width. Furthermore a possible application of nanoribbons to nanoelectronics is discussed.
Nanoribbons (nanographite ribbons) are carbon systems analogous to carbon nanotubes. We characterize a wide class of nanoribbons by a set of two integers $<p,q>$, and then define the width $w$ in terms of $p$ and $q$. Electronic properties are explored for this class of nanoribbons. Zigzag (armchair) nanoribbons have similar electronic properties to armchair (zigzag) nanotubes. The band gap structure of nanoribbons exhibits a valley structure with stream-like sequences of metallic or almost metallic nanoribbons. These sequences correspond to equi-width curves indexed by $w$. We reveal a peculi…
Graphene nanoribbon (GNR) field-effect transistors (FETs) with widths down to 12 nm have been fabricated by electron beam lithography using a wafer-scale chemical vapor deposition (CVD) process to form the graphene. The GNR FETs show drain-current modulation of approximately 10 at 300 K, increasing to nearly 106 at 4 K. The strong temperature dependence of the minimum current indicates the opening of a bandgap for CVD-grown GNR-FETs. The extracted bandgap is estimated to be around 0.1 eV by differential conductance methods. This work highlights the development of CVD-grown large-area graphene …
We study electronic properties of graphene derivatives which have closed edges. They are finite-length graphene nanoribbons and graphene nanodisks. No metallic states are found in finite-length zigzag nanoribbons though all infinite-length zigzag nanoribbons are metallic. We also study hexagonal, parallelogrammic and trigonal nanodisks with zigzag or armchair edges. No metallic states are found in these nanodisks either except trigonal zigzag nanodisks. It is interesting that we can design the degeneracy of the metallic states arbitrarily in trigonal zigzag nanodisks by changing the size.
The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half-metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at K (K') near the Fermi level. The present results demonstrate that the unique combination of…
We investigate theoretically resonant tunneling through double-bended graphene nanoribbon structures, i.e., armchair-edged graphene nanoribbons (AGNRs) in between two semi-infinite zigzag graphene nanoribbon (ZGNR) leads. Our numerical results demonstrate that the resonant tunneling can be tuned dramatically by the Fermi energy and the length and/or widths of the AGNR for both the metallic and semiconductor-like AGNRs. The structure can also be use to control the valley polarization of the tunneling currents and could be useful for potential application in valleytronics devices.
We report the experimental observation of conductance quantization in graphene nanoribbons, where 1D transport subbands are formed due to the lateral quantum confinement. We show that this quantization in graphene nanoribbons can be observed at temperatures as high as 80 K and channel lengths as long as 1.7 $μ$m. The observed quantization is in agreement with that predicted by theoretical calculations.
In this paper, we develop an analytical approach to predict the field-induced alignment of cantilevered graphene nanoribbons. This approach is validated through molecular simulations using a constitutive atomic electrostatic model. Our results reveal that graphene's field-oriented bending angle is roughly proportional to the square of field strength or the graphene length for small deformations, while is roughly independent of graphene width. The effective bending stiffness and the longitudinal polarizability are also found to be approximately proportional to the square of graphene length. Com…
In contrast to the well recognized transverse-electric-field-induced half-metallicity in zigzag graphene nanoribbons, here we demonstrate by first-principles calculations that zigzag graphene nanoribbons sandwiched between hexagonal boron nitride nanoribbons or sheets can be tuned into half-metal simply by a bias voltage or a moderate compressive strain. The half-metallicity is attributed to an enhanced coupling effect of spontaneous polarization and asymmetrical exchange correlation along the ribbon width. The findings should open a viable route for efficient spin-resolved band engineering in…
The fabrication of atomically precise structures with designer electronic properties is one of the emerging topics in condensed matter physics. The required level of structural control can either be reached through atomic manipulation using the tip of a scanning tunneling microscope (STM) or by bottom-up chemical synthesis. In this review, we focus on recent progress in constructing novel, atomically precise artificial materials: artificial lattices built through atom manipulation and graphene nanoribbons (GNRs) realized by on-surface synthesis. We summarize the required theoretical background…
The atomic structure, stacking sequences and electronic structure of folded graphene nanoribbons (FGNRs) are investigated by first-principles calculations. It reveals that the common configurations of all FGNRs are racket-like structures including a nanotube-like edge and two flat nanoribbons. Interestingly, the two flat nanoribbons can form new stacking styles instead of the most stable AB-stacking sequences for bilayer nanoribbons. The stability of the FGNRs are associated with several factors of initial structures, such as interlayer distance of two nanoribbons, stacking sequences, edge sty…
A simple one-stage solution-based method was developed to produce graphene nanoribbons by sonicating graphite powder in organic solutions with polymer surfactant. The graphene nanoribbons were deposited on silicon substrate, and characterized by Raman spectroscopy and atomic force microscopy. Single-layer and few-layer graphene nanoribbons with a width ranging from sub-10 nm to tens of nm and length ranging from hundreds of nm to 1 μm were routinely observed. Electrical transport properties of individual graphene nanoribbons were measured in both the back-gate and polymer-electrolyte top-gate …
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.
We derive analytical expressions for the Young's modulus and the Poisson's ratio of the graphene nanoribbon, in which free edges are warped by the compressive edge stress. Our analytical formulas explicitly illustrate the reduction of the Young's modulus by the warped free edges, leading to the obvious width dependence for the Young's modulus of the graphene nanoribbon. The Poisson's ratio is also reduced by the warped free edges, and negative Poisson's ratio can be achieved in the graphene nanoribbon with an ultra-narrow width. These results are comparable with previous theoretical works.
The universality of $k$-dependent electron-photon and electron-phonon matrix elements is discussed for graphene nanoribbons and carbon nanotubes. An electron undergoes a change in wavevector in the direction of broken translational symmetry, depending on the light polarization direction. We suggest that this phenomenon originates from a microscopic feature of chirality.
Graphene nanoribbons are widely regarded as promising building blocks for next-generation carbon-based devices. A critical issue to their prospective applications is whether and to what degree their electronic structure can be externally controlled. Here, we combine simple model Hamiltonians with extensive first-principles calculations to investigate the response of armchair graphene nanoribbons to transverse electric fields. Such fields can be achieved either upon laterally gating the nanoribbon or incorporating ambipolar chemical co-dopants along the edges. We reveal that the field induces a…
Graphene nanoribbons present diverse electronic properties ranging from semiconducting to half-metallic, depending on their geometry, dimensions and chemical composition. Here we present a route to control these properties via externally applied mechanical deformations. Using state-of-the-art density functional theory calculations combined with classical elasticity theory considerations, we find a remarkable Young's modulus value of ~7 TPa for ultra-narrow graphene strips and a pronounced electromechanical response towards bending and torsional deformations. Given the current advances in the s…
We report energy estimated to dissociate a C-C bond of a graphene sheet to form nanoribbons of armchair and zigzag configurations using first principles calculations. For the ground state energy calculations, the configurations considered are with spin, and without spin polarization. It is observed that the energy required to dissociate a C-C bond of a graphene sheet to form zigzag configuration is higher than that of armchair configuration for both spin polarized state, as well as non-spin polarized state. Therefore, formation of smooth edged graphene nanoribbons along the crystallographic di…
The successful fabrication of single layer graphene has greatly stimulated the progress of the research on graphene. In this article, focusing on the basic electronic and transport properties of graphene nanoribbons (GNRs), we review the recent progress of experimental fabrication of GNRs, and the theoretical and experimental investigations of physical properties and device applications of GNRs. We also briefly discuss the research efforts on the spin polarization of GNRs in relation to the edge states.
We theoretically study current dynamics of graphene nanoribbons subject to bias dc and ac driven fields. We showed that graphene nanoribbons exhibit negative high-harmonic differential conductivity. Negative differential conductivity appears when bias electric filed is in the neighborhood of applied ac filed amplitude. We also observe both even and odd high-harmonic negative differential conductivity at wave mixing of two commensurate frequencies. The even harmonics are more pronounced than the odd harmonics. A possible use of the present method for generating terahertz frequencies at even har…
Using a continuum Dirac theory, we study the density and spin response of zigzag edge terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g. width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of…
We investigate electron and phonon transport through edge disordered zigzag graphene nanoribbons based on the same methodological tool of nonequilibrium Green functions. We show that edge disorder dramatically reduces phonon thermal transport while being only weakly detrimental to electronic conduction. The behavior of the electronic and phononic elastic mean free paths points to the possibility of realizing an electron-crystal coexisting with a phonon-glass. The calculated thermoelectric figure of merit (ZT) values qualify zigzag graphene nanoribbons as a very promising material for thermoele…
Chiral graphene nanoribbons are extremely interesting structures due to their low bandgaps and potential development of spin-polarized edge states. Here, we study their band structure on low work function silver surfaces and assess the effect of charge transfer on their properties.
An analytical device model for a graphene nanoribbon phototransistor (GNR-PT) is presented. GNR-PT is based on an array of graphene nanoribbons with the side source and drain contacts, which is sandwiched between the highly conducting substrate and the top gate. Using the developed model, we derive the explicit analytical relationships for the source-drain current as a function of the intensity and frequency of the incident radiation and find the detector responsivity. It is shown that GNR-PTs can be rather effective photodetectors in infrared and terahertz ranges of spectrum.
The anchoring of benzene molecules on lithium adsorption sites at the surface of graphene and nanoribbons thereof are investigated. The effects of adsorbate densities, specific adsorption locations, and spin states on the structural stability and electronic properties of the underlying graphene derivatives are revealed. At sufficiently high densities, bare lithium adsorption turns armchair graphene nanoribbons metallic and their zigzag counterparts half-metallic due to charge transfer from the adatom to the π electronic system. Upon benzene adsorption, the lithium cation encounters two π syste…
It is known that there is a wide class of quasi-two-dimensional graphenelike nanomaterials which in many respects can outperform graphene. So, here in addition to graphene, the attention is directed to stanene (buckled honeycomb structure) and phosphorene (puckered honeycomb structure). It is shown that, depending on the doping, these materials can have magnetically ordered edges. Computed diagrams of magnetic phases illustrate that, on the one hand, n-type doped narrow zigzag nanoribbons of graphene and stanene have antiferromagnetically aligned magnetic moments between the edges. On the othe…
We analyze the collective mode spectrum of graphene nanoribbons within the random phase approximation. In the undoped case, only metallic armchair nanoribbons support a propagating plasmon mode. Landau damping of this mode is shown to be suppressed through the chirality of the single particle wavefunctions. We argue that undoped zigzag nanoribbons should not support plasmon excitations because of a broad continuum of particle-hole excitations associated with surface states, into which collective modes may decay. Doped nanoribbons have properties similar to those of semiconductor nanowires, inc…
A theory of electron states for graphene nanoribbons with a smoothly varying width is developed. It is demonstrated that the standard adiabatic approximation allowing to neglect the mixing of different standing waves is more restrictive for the massless Dirac fermions in graphene than for the conventional electron gas. For the case of zigzag boundary conditions, one can expect a well-pronounced conductance quantization only for highly excited states. This difference is related to the relativistic Zitterbewegung effect in graphene.
A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of the conductance steps towards higher energies. The magnetic barrier also induces Fabry-Perot type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevent confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbon…
We demonstrate anisotropic etching of single-layer graphene by thermally-activated nickel nanoparticles. Using this technique, we obtain sub-10nm nanoribbons and other graphene nanostructures with edges aligned along a single crystallographic direction. We observe a new catalytic channeling behavior, whereby etched cuts do not intersect, resulting in continuously connected geometries. Raman spectroscopy and electronic measurements show that the quality of the graphene is resilient under the etching conditions, indicating that this method may serve as a powerful technique to produce graphene na…
We report on the possibility for a spin valve effect driven by edge defect engineering of zigzag graphene nanoribbons. Based on a mean-field spin unrestricted Hubbard model, electronic band structures and conductance profiles are derived, using a self-consistent scheme to include gate-induced charge density. The use of an external gate is found to trigger a semiconductor-metal transition in clean zigzag graphene nanoribbons, whereas it yields a closure of the spin-split bandgap in the presence of Klein edge defects. These features could be exploited to make novel charge and spin based switches…
The hybrid graphene - hexagonal boron nitride (G-hBN) systems offer new routes in the design of nanoscale electronic devices. Using {\it ab initio} density functional theory calculations we investigate the dynamics of zig-zag nanoribbons a few interatomic distances wide. Several structures are analyzed, namely pristine graphene, hBN and G-hBN systems. By passivating the nanoribbon edges with hydrogen and different halogen atoms, one may tune the electronic and mechanical properties, like the band gap energies and the natural frequencies of vibration.
Using a tight binding model, we theoretically study the electronic properties of zigzag boron-carbon-nitride (BCN) nanoribbons where the outermost C atoms of zigzag graphene nanoribbons are replaced with B and N atoms. We show that the flat bands and edge states appear at the Fermi level when the number of B and N atoms are equal except the case of six times supercell. To investigate the origin of the edge states in BCN nanoribbons, we consider the semi-infinite graphene sheet with zigzag edge where outermost C atoms are replaced with B and N atoms. We analytically demonstrate the presence of …
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 used a complete tight-binding band structure of graphene nanoribbon to obtain, for the first time, analytical techniques for observing photon assisted transport, and dynamic localization of electrons in the graphene nanoribbons. When the ribbons are subject to a multi-frequency dc-ac field, photon assisted replicas show up at rather strong drive force. The strong dependence of the photon peaks on ac amplitudes allow for high-harmonic dynamic oscillations at these amplitudes. We identified regions of positive differential conductivity where a nanoelectronic graphene device may be operated as…
Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.
Graphene nanoribbons with perfect edges are predicted to exhibit interesting electronic and spintronic properties, notably quantum-confined bandgaps and magnetic edge states. However, graphene nanoribbons produced by lithography have, to date, exhibited rough edges and low-temperature transport characteristics dominated by defects, mainly variable range hopping between localized states in a transport gap near the Dirac point. Here, we report that one- and two-layer nanoribbons quantum dots made by unzipping carbon nanotubes10 exhibit well-defined quantum transport phenomena, including Coulomb …
Spin-dependent electronic transport properties of Fe-terminated zig-zag graphene nanoribbons (zGNR) have been studied using first-principles transport simulations. The spin configuration of proposed zGNR junction can be controlled with external magnetic field, and the tunneling junction show MR>1000 at small bias and is a perfect spin-filter by applying uniform external magnetic filed at small bias.
We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a non-equilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find \emph{perfect reflection} of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.
We have fabricated suspended few layer (1-3 layers) graphene nanoribbon field effect transistors from unzipped multiwall carbon nanotubes. Electrical transport measurements show that current-annealing effectively removes the impurities on the suspended graphene nanoribbons, uncovering the intrinsic ambipolar transfer characteristic of graphene. Further increasing the annealing current creates a narrow constriction in the ribbon, leading to the formation of a large band-gap and subsequent high on/off ratio (which can exceed 104). Such fabricated devices are thermally and mechanically stable: re…
Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and $\textit{ab initio}$ calculations. We focus on a specific set of nanoribbons of width $n = 3p+2$, where $n$ is the number of carbon atoms across the nanoribbon axis and $p$ is a positive integer. We demonstrate that the energy-gap opening in these nanoribbons originates from the breaking of a previously unidentified hidden symmetry by long-ranged hopping of $π$-electrons and structural dist…
We unveil the nature of the structural disorder in bottom-up zigzag graphene nanoribbons along with its effect on the magnetism and electronic transport on the basis of scanning probe microscopies and first-principles calculations. We find that edge-missing m-xylene units emerging during the cyclodehydrogenation step of the on-surface synthesis are the most common point defects. These "bite'' defects act as spin-1 paramagnetic centers, severely disrupt the conductance spectrum around the band extrema, and give rise to spin-polarized charge transport. We further show that the electronic conduct…
The discovery of unusual heat conduction properties of graphene has led to a surge of theoretical and experimental studies of phonon transport in two-dimensional material systems. The rapidly developing graphene thermal field spans from theoretical physics to practical engineering applications. In this invited review we outline different theoretical approaches developed for describing phonon transport in graphene and provide comparison with available experimental thermal conductivity data. A special attention is given to analysis of the recent theoretical results for the phonon thermal conduct…
By applying tight binding model, we investigate the electronic and transport properties of randomly distributed Stone-Wales (SW) defects on an armchair graphene nanoribbon (AGNR). We use four different functions, as distribution functions, to generate our SW defected nanoribbons. It is found that defect density can have a major effect on the conductance of our defected system, whilst other configurations such as defect orientation will contribute less. In our investigations. some special geometries are found, which shows interesting electronic and transport properties. These special cases alon…
Hydrogenated graphene, graphane, is studied on oxygen-terminated silicon dioxide substrate using ab initio calculations. A structure with hydrogenation only on one side of the graphene layer is found stable and its hydrogen configurations are presented. Additionally, we form zigzag graphene nanoribbons by selectively removing hydrogens from the epitaxial graphane layer. In these ribbons, the spin degeneracy of the freestanding antiferromagnetic zigzag ribbons is broken, and band gaps of different magnitude emerge for the opposite spin species. This degeneracy breaking is due to a charge imbala…
Since graphene nanoribbons are thin and flimsy, they need support. Support gives firm ground for applications, and adhesion holds ribbons flat, although not necessarily straight: ribbons with high aspect ratio are prone to bend. The effects of bending on ribbons' electronic properties, however, are unknown. Therefore, this article examines the electromechanics of planar and gently bent graphene nanoribbons. Simulations with density-functional tight-binding and revised periodic boundary conditions show that gentle bends in armchair ribbons can cause significant widening or narrowing of energy g…
We present electronic structure calculations of few-layer epitaxial graphene nanoribbons on SiC(0001). Trough an atomistic description of the graphene layers and the substrate within the extended Hückel Theory and real/momentum space projections we argue that the role of the heterostructure's interface becomes crucial for the conducting capacity of the studied systems. The key issue arising from this interaction is a Fermi level pinning effect introduced by dangling interface bonds. Such phenomenon is independent from the width of the considered nanostructures, compromising the importance of c…
The quantum corrections to the energies of the $Γ$ point optical phonon modes (Kohn anomalies) in graphene nanoribbons are investigated. We show theoretically that the longitudinal optical modes undergo a Kohn anomaly effect, while the transverse optical modes do not. In relation to Raman spectroscopy, we show that the longitudinal modes are not Raman active near the zigzag edge, while the transverse optical modes are not Raman active near the armchair edge. These results are useful for identifying the orientation of the edge of graphene nanoribbons by G band Raman spectroscopy, as is demonstr…
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…
We will present brief overview on the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering. The low-energy electronic states of graphene have two non-equivalent massless Dirac spectrum. The relative distance between these two Dirac points in the momentum space and edge states due to the existence of the zigzag type graphene edges are decisive to the electronic and transport properties of graphene nanoribbons. In graphene nanoribbons with zigzag edges, two valleys related to each Dirac spectrum are well separated in momentum s…
A novel type of spaser with the net amplification of surface plasmons (SPs) in doped graphene nanoribbon is proposed. The plasmons in THz region can be generated in a dopped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon is obtained. The dependence of the minimal population inversion on the surface plasmon wavevector, graphene nanoribbon width, doping and damping parameters necessary for the ampli…
Using a model Hamiltonian approach including electron-electron interactions, we systematically investigate the electronic structure and magnetic properties of chiral graphene nanoribbons. We show that the presence of magnetic edge states is an intrinsic feature of smooth graphene nanoribbons with chiral edges, and discover a number of structure-property relations. Specifically, we study the dependence of magnetic moments and edge-state energy splittings on the nanoribbon width and chiral angle as well as the role of environmental screening effects. Our results address a recent experimental obs…
In contrast with carbon nanotubes, the absence of translational symmetry (or periodical boundary condition) in the restricted direction of zigzag graphene nanoribbon removes the selection rule of subband number conservation. However, zigzag graphene nanoribbons with even dimers do have the inversion symmetry. We, therefore, propose a selection rule of parity conservation for electron-phonon interactions. The electron-phonon scattering matrix in zigzag graphene nanoribbons is developed using the tight-binging model within the deformation potential approximation.
High-quality BN-Graphene-BN nanoribbon capacitors with double side-gates of graphene are experimentally realized. Graphene electronic properties can be significantly modulated by the double side-gates. The modulation effects are very obvious and followed the metallic electrode behavior of numerical simulations, while the theoretically predicted negative quantum capacitance was not observed, possibility due to the over-estimated or weakened interactions between the graphene nanoribbon and side-gate electrodes.
Graphene plasmonics is a rapidly growing field with multiple potential applications. One of the standard ways to study plasmons in graphene is by fabricating an array of graphene nanoribbons where nanoribbon edges provide the efficient photon-plasmon coupling. We systematically analyze the problem of optical plasmonic response in such systems and demonstrate the purely geometric nature of the size quantization condition for graphene plasmons. Accurate numerical calculations allowed us to tabulate the universal geometric parameters of plasmon size quantization, which is expected to become usefu…
We have experimentally investigated quantum interference corrections to the conductivity of graphene nanoribbons at temperatures down to 20 mK studying both weak localization (WL) and universal conductance fluctuations (UCF). Since in individual nanoribbons at millikelvin temperatures the UCFs strongly mask the weak localization feature we employ both gate averaging and ensemble averaging to suppress the UCFs. This allows us to extract the phase coherence length from both WL and UCF at all temperatures. Above 1 K, the phase coherence length is suppressed due to Nyquist scattering whereas at lo…
We present symmetry properties of the lattice vibrations of graphene nanoribbons with pure armchair (AGNR) and zigzag edges (ZGNR). In non-symmorphic nanoribbons the phonon modes at the edge of the Brillouin zone are twofold degenerate, whereas the phonon modes in symmorphic nanoribbons are non-degenerate. We identified the Raman-active and infrared-active modes. We predict 3N and 3(N+1) Raman-active modes for N-ZGNRs and N-AGNRs, respectively (N is the number of dimers per unit cell). These modes can be used for the experimental characterization of graphene nanoribbons. Calculations based on …
We present electronic transport measurements on etched graphene nanoribbons on silicon dioxide before and after a short hydrouoric acid (HF) treatment. We report on changes in the transport properties, in particular, in terms of a decreasing transport gap and a reduced doping level after HF dipping. Interestingly, the effective energy gap is nearly unaffected by the HF treatment. Additional measurements on a graphene nanoribbon with lateral graphene gates support strong indications that the HF significantly modifies the edges of the investigated nanoribbons leading to a significantly reduced d…
The electronic and magnetic properties of zigzag graphene nanoribbons with asymmetric notches along their edges are investigated by first principle density functional theory calculations. It is found that the electronic and magnetic properties of the asymmetrically-notched graphene nanoribbons are closely related with the depth of notches, but weekly dependent on the length of notches. As the relative depth of notch increases, the energy level of spin-up and spin-down becomes greatly shifted, associated with the gradual increase of magnetic momentum. The asymmetric band shift allows the asymme…
We study vibrational states localized at the edges of graphene nanoribbons. Such surface oscillations can be considered as a phonon analog of Tamm states well known in the electronic theory. We consider both armchair and zigzag graphene stripes and demonstrate that surface modes correspond to phonons localized at the edges of the graphene nanoribbon, and they can be classified as in-plane and out-of-plane modes. In addition, in armchair nanoribbons anharmonic edge modes can experience longitudinal localization in the form of self-localized nonlinear modes, or surface breather solitons.
In this paper we propose an analytical method to calculate the band structures of graphene-like nanoribbons of the armchair type with arbitrary line defects or uniaxial strains. The model is based on the tight-binding model and the standing wave assumption for the armchair nanoribbons. It gives accurate band results for large supercell systems. Within this method, we analyze different local states near the line defect in the graphene and boron-nitride nanoribbons. We also derive the analytical expression for the local states in a semi-infinite graphene nanoribbon by this method and the transfe…
