States Of Graphene Nanoribbons Research Articles

Enhancement of laser pulse induced photocurrents by topological states in graphene nanoribbons

Enhancement of laser pulse induced photocurrents by topological states in graphene nanoribbons

Detecting the spin-polarization of edge states in graphene nanoribbons

Low dimensional carbon-based materials can show intrinsic magnetism associated to p-electrons in open-shell π-conjugated systems. Chemical design provides atomically precise control of the π-electron cloud, which makes them promising for nanoscale magnetic devices. However, direct verification of their spatially resolved spin-moment remains elusive. Here, we report the spin-polarization of chiral graphene nanoribbons (one-dimensional strips of graphene with alternating zig-zag and arm-chair boundaries), obtained by means of spin-polarized scanning tunnelling microscopy. We extract the energy-dependent spin-moment distribution of spatially extended edge states with π-orbital character, thus beyond localized magnetic moments at radical or defective carbon sites. Guided by mean-field Hubbard calculations, we demonstrate that electron correlations are responsible for the spin-splitting of the electronic structure. Our versatile platform utilizes a ferromagnetic substrate that stabilizes the organic magnetic moments against thermal and quantum fluctuations, while being fully compatible with on-surface synthesis of the rapidly growing class of nanographenes.

Reverse strain-induced snake states in graphene nanoribbons

Strain can tailor the band structures and properties of graphene nanoribbons (GNRs) with the well-known emergent pseudo-magnetic fields and the corresponding pseudo-Landau levels (pLLs). We design one type of the zigzag GNR (ZGNR) with reverse strains, producing pseudo-magnetic fields with opposite signs in the lower and upper half planes. Therefore, electrons propagate along the interface as "snake states", experiencing opposite Lorentz forces as they cross the zero field border line. By using the Landauer-Buttiker formalism combined with the nonequilibrium Green's function method, the existence and robustness of the reverse strain-induced snake states are further studied. Furthermore, the realization of long-thought pure valley currents in monolayer graphene systems is also proposed in our device.

Inducing metallicity in graphene nanoribbons via zero-mode superlattices.

The design and fabrication of robust metallic states in graphene nanoribbons (GNRs) are challenging because lateral quantum confinement and many-electron interactions induce electronic band gaps when graphene is patterned at nanometer length scales. Recent developments in bottom-up synthesis have enabled the design and characterization of atomically precise GNRs, but strategies for realizing GNR metallicity have been elusive. Here we demonstrate a general technique for inducing metallicity in GNRs by inserting a symmetric superlattice of zero-energy modes into otherwise semiconducting GNRs. We verify the resulting metallicity using scanning tunneling spectroscopy as well as first-principles density-functional theory and tight-binding calculations. Our results reveal that the metallic bandwidth in GNRs can be tuned over a wide range by controlling the overlap of zero-mode wave functions through intentional sublattice symmetry breaking.

Time Evolution of Floquet States in Graphene

Based on a solution of the Floquet Hamiltonian we have studied the time evolution of electronic states in graphene nanoribbons driven out of equilibrium by time-dependent electromagnetic fields in different regimes of intensity, polarization, and frequency. We show that the time-dependent band structure contains many unconventional features that are not captured by considering the Floquet eigenvalues alone. By analyzing the evolution in time of the state population we have identified regimes for the emergence of time-dependent edge states responsible for charge oscillations across the ribbon.

Quantum Transport by Spin‐Polarized Edge States in Graphene Nanoribbons in the Quantum Spin Hall and Quantum Anomalous Hall Regimes

Using the non‐equilibrium Green's function method and the Keldysh formalism, we study the effects of spin–orbit interactions and time‐reversal symmetry breaking exchange fields on non‐equilibrium quantum transport in graphene armchair nanoribbons. We identify signatures of the quantum spin Hall (QSH) and the quantum anomalous Hall (QAH) phases in non‐equilibrium edge transport by calculating the spin‐resolved real space charge density and local currents at the nanoribbon edges. We find that the QSH phase, which is realized in a system with intrinsic spin–orbit coupling, is characterized by chiral counter‐propagating local spin currents summing up to a net charge flow with opposite spin polarization at the edges. In the QAH phase, emerging in the presence of Rashba spin–orbit coupling and a ferromagnetic exchange field, two chiral edge channels with opposite spins propagate in the same direction at each edge, generating an unpolarized charge current and a quantized Hall conductance G = 2e2/h. Increasing the intrinsic spin–orbit coupling causes a transition from the QAH to the QSH phase, evinced by characteristic changes in the non‐equilibrium edge transport. In contrast, an antiferromagnetic exchange field can coexist with a QSH phase, but can never induce a QAH phase due to a symmetry that combines time‐reversal and sublattice translational symmetry.

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincare index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum py of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.

Effects of edge magnetism on the Kohn anomalies of zigzag graphene nanoribbons

The effects of edge magnetism on the Kohn anomaly (KA) of the G-band phonons of zigzag graphene nanoribbons (ZGNRs) are studied using a combination of the tight-binding and mean-field Hubbard models. We show that the opening of an energy gap, induced by magnetic ordering, significantly changes the KA effects, particularly for narrow ribbons in which the gap is larger than the phonon energy. Therefore, the G-band phonon frequency and lifetime are altered for a magnetically-ordered edge state with respect to an unpolarized edge state. The effects of temperature, ZGNR width, doping and transverse electric fields are systematically investigated. We propose using this effect to probe the magnetic order of edge states in graphene nanoribbons using Raman spectroscopy.

Transport properties and localization of electronic states in graphene nanoribbons with edge absorptions

We study the effect of edge methylene on transport properties in graphene nanoribbons (GNRs) using the recursive green’s function method. The concentration of methylene (w) is defined as the substituted probability of edge dangling bonds. Due to the antiresonance of quasilocalized states, some conductance dips are found when single absorption (w = 0.005 in this work) sits on the edge. Localization analyses of wave functions also confirm this. With w increasing, the conductance is suppressed significantly and transport gap develops near E = 0.0 eV. Conductance suppression is induced by antiresonances between edge scattering centers. Meanwhile, these scattering centers prevent the formation of edge extended states which play an important role in the electronic transport at low energy and consequently the transport gaps develop. We found that a stable gap can be obtained at w = 0.3 and it becomes small as the width of the GNRs increases. An interesting oscillation at transport gaps for armchair edge GNRs is observed and it relates to the geometric symmetry of sample. The physical mechanisms behind the novel phenomenon are still unclear.

Structural and Electronic Properties of Zigzag Graphene Nanoribbons on Si(001) Substrates

We study the adsorption of zigzag graphene nanoribbons (GNRs) on Si(001) substrates using the first-principles density functional theory, exploring the effects of the interface interaction on the structural and electronic properties of both GNRs and the substrate. By comparing the adsorption structures predicted by the local density approximation, the generalized gradient approximation, and the DFT-D2 approach, we confirm that both edge and inner C atoms of GNRs can form covalent bonds with the substrate. The GNR/substrate interaction destroys the antiferromagnetic coupling of the edge states in GNRs. The charge transfer from the substrate to GNRs exhibits a complicated pattern and is mainly localized near the C–Si bonds. We also observe a strong perturbation of the surface states and a surface reconstruction transition induced by the GNR adsorption.

Lanczos transformation for quantum impurity problems ind-dimensional lattices: Application to graphene nanoribbons

We present a completely unbiased and controlled numerical method to solve quantum impurity problems in d-dimensional lattices. This approach is based on a canonical transformation, of the Lanczos form, where the complete lattice Hamiltonian is exactly mapped onto an equivalent one dimensional system, in the same spirit as Wilson's numerical renormalization. The method is particularly suited to study systems that are inhomogeneous, and/or have a boundary. As a proof of concept, we use the density matrix renormalization group to solve the equivalent one-dimensional problem. The resulting dimensional reduction translates into a reduction of the scaling of the entanglement entropy by a factor $L^{d-1}$, where L is the linear dimension of the original d-dimensional lattice. This allows one to calculate the ground state of a magnetic impurity attached to an LxL square lattice and an LxLxL cubic lattice with L up to 140 sites. We also study the localized edge states in graphene nanoribbons by attaching a magnetic impurity to the edge or the center of the system. For armchair metallic nanoribbons we find a slow decay of the spin correlations as a consequence of the delocalized metallic states. In the case of zigzag ribbons, the decay of the spin correlations depends on the position of the impurity. If the impurity is situated in the bulk of the ribbon, the decay is slow as in the metallic case. On the other hand, if the adatom is attached to the edge, the decay is fast, within few sites of the impurity, as a consequence of the localized edge states, and the short correlation length. The mapping can be combined with ab-initio band structure calculations to model the system, and to understand correlation effects in quantum impurity problems from first principles.

Metal-to-Insulator Transition and Electron-Hole Puddle Formation in Disordered Graphene Nanoribbons

The experimentally observed metal-to-insulator transition in hydrogenated graphene is numerically confirmed for actual sized graphene samples and realistic impurity concentrations. The eigenstates of our tight-binding model with substitutional disorder corroborate the formation of electron-holepuddles with characteristic length scales comparable to the ones found in experiments. The puddles cause charge inhomogeneities and tend to suppress Anderson localization. Even though, monitoring the charge carrier quantum dynamics and performing a finite-size scaling of the local density of states distribution, we find strong evidence for the existence of localized states in graphene nanoribbons with short-range but also correlated long-range disorder.

Accurate Prediction of the Electronic Properties of Low-Dimensional Graphene Derivatives Using a Screened Hybrid Density Functional

Over the last several years, low-dimensional graphene derivatives, such as carbon nanotubes and graphene nanoribbons, have played a central role in the pursuit of a plausible carbon-based nanotechnology. Their electronic properties can be either metallic or semiconducting depending purely on morphology, but predicting their electronic behavior has proven challenging. The combination of experimental efforts with modeling of these nanometer-scale structures has been instrumental in gaining insight into their physical and chemical properties and the processes involved at these scales. Particularly, approximations based on density functional theory have emerged as a successful computational tool for predicting the electronic structure of these materials. In this Account, we review our efforts in modeling graphitic nanostructures from first principles with hybrid density functionals, namely the Heyd-Scuseria-Ernzerhof (HSE) screened exchange hybrid and the hybrid meta-generalized functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh). These functionals provide a powerful tool for quantitatively studying structure-property relations and the effects of external perturbations such as chemical substitutions, electric and magnetic fields, and mechanical deformations on the electronic and magnetic properties of these low-dimensional carbon materials. We show how HSE and TPSSh successfully predict the electronic properties of these materials, providing a good description of their band structure and density of states, their work function, and their magnetic ordering in the cases in which magnetism arises. Moreover, these approximations are capable of successfully predicting optical transitions (first and higher order) in both metallic and semiconducting single-walled carbon nanotubes of various chiralities and diameters with impressive accuracy. This versatility includes the correct prediction of the trigonal warping splitting in metallic nanotubes. The results predicted by HSE and TPSSh provide excellent agreement with existing photoluminescence and Rayleigh scattering spectroscopy experiments and Green's function-based methods for carbon nanotubes. This same methodology was utilized to predict the properties of other carbon nanomaterials, such as graphene nanoribbons. Graphene nanoribbons may be viewed as unrolled (and passivated) carbon nanotubes. However, the emergence of edges has a crucial impact on the electronic properties of graphene nanoribbons. Our calculations have shown that armchair nanoribbons are predicted to be nonmagnetic semiconductors with a band gap that oscillates with their width. In contrast, zigzag graphene nanoribbons are semiconducting with an electronic ground state that exhibits spin polarization localized at the edges of the carbon nanoribbon. The spatial symmetry of these magnetic states in graphene nanoribbons can give rise to a half-metallic behavior when a transverse external electric field is applied. Our work shows that these properties are enhanced upon different types of oxidation of the edges. We also discuss the properties of rectangular graphene flakes, which present spin polarization localized at the zigzag edges.

Simple and efficient modeling of the E–k relationship and low-field mobility in Graphene Nano-Ribbons

This paper proposes a simple analytical formulation for the dispersion relationship of extended electronic states in Graphene Nano-Ribbons (GNRs). The model has been validated by comparison with Tight-Binding calculation of GNRs in the presence of edge disorder. The model is suited for inclusion in semiclassical models for GNRs featuring widths down to approximately 2 nm. Monte-Carlo simulations accounting for phonons and edge roughness scattering are then used to understand the ribbon width of the low-field mobility. The mechanisms responsible for the low mobility values measured in narrow ribbons compared to graphene sheets are the increased phonon scattering rate and mobility effective mass due to the strong band structure modification induced by the reduced lateral dimensions and the increased scattering with the edges. However, scattering with phonons and with edges is not sufficient to reproduce the experimental mobility on insulating substrates, suggesting that the effect of remote polar phonons originating in the substrate can be significant in graphene based devices.