Electronic spectra, topological states, and impurity effects in graphene nanoribbons (original) (raw)
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Electronic states of zigzag graphene nanoribbons with edges reconstructed with topological defects
Physica B: Condensed Matter
The energy spectrum and electronic density of states (DOS) of zigzag graphene nanoribbons with edges reconstructed with topological defects are investigated within the tight-binding method. In case of the Stone-Wales zz (57) edge the low-energy spectrum is markedly changed in comparison to the pristine zz edge. We found that the electronic DOS at the Fermi level is different from zero at any width of graphene nanoribbons. In contrast, for ribbons with heptagons only at one side and pentagons at another one the energy gap at the Fermi level is open and the DOS is equal to zero. The reason is the influence of uncompensated topological charges on the localized edge states, which are topological in nature. This behavior is similar to that found for the structured external electric potentials along the edges.
Interplay between edge states and simple bulk defects in graphene nanoribbons
The European Physical Journal B, 2013
We study the interplay between the edge states and a single impurity in a zigzag graphene nanoribbon. We use tight-binding exact diagonalization techniques, as well as density functional theory calculations to obtain the eigenvalue spectrum, the eigenfunctions, as well the dependence of the local density of states (LDOS) on energy and position. We note that roughly half of the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize with the impurity state, and the corresponding eigenvalues are shifted with respect to their unperturbed values. The maximum shift and hybridization occur for a state whose energy is inverse proportional to the impurity potential; this energy is that of the impurity peak in the DOS spectrum. We find that the interference between the impurity and the edge gives rise to peculiar modifications of the LDOS of the nanoribbon, in particular to oscillations of the edge LDOS. These effects depend on the size of the system, and decay with the distance between the edge and the impurity.
Edge disorder and localization regimes in bilayer graphene nanoribbons
Physical Review B, 2009
A theoretical study of the magnetoelectronic properties of zigzag and armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive Green's function method, we study the band structure of BGNs in uniform perpendicular magnetic fields and discuss the zero-temperature conductance for the corresponding clean systems. The conductance quantized as 2(n + 1)G0 for the zigzag edges and nG0 for the armchair edges with G0 = 2e 2 /h being the conductance unit and n an integer. Special attention is paid to the effects of edge disorder. As in the case of monolayer graphene nanoribbons (GNR), a small degree of edge disorder is already sufficient to induce a transport gap around the neutrality point. We further perform comparative studies of the transport gap Eg and the localization length ξ in bilayer and monolayer nanoribbons. While for the GNRs E GNR g ∼ 1/W , the corresponding transport gap E BGN g for the bilayer ribbons shows a more rapid decrease as the ribbon width W is increased. We also demonstrate that the evolution of localization lengths with the Fermi energy shows two distinct regimes. Inside the transport gap, ξ is essentially independent on energy and the states in the BGNs are significantly less localized than those in the corresponding GNRs. Outside the transport gap ξ grows rapidly as the Fermi energy increases and becomes very similar for BGNs and GNRs.
Electronic states in finite graphene nanoribbons: Effect of charging and defects
Physical Review B, 2013
We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length. Doping also quenches the antiferromagnetic coupling between the end-localized states leading to a spin-split gap in neutral ribbons. By comparing dI/dV maps calculated using the many-body Hubbard model, its mean-field approximation and density-functional theory, we show that the use of a single-particle description is justified for graphene π states. Furthermore, we study the effect of structural defects in the ribbons on their electronic structure. Defects at one ribbon termini do not significantly modify the electronic states localized at the intact end. This provides further evidence for the interpretation of a multi-peaked structure in a recent scanning tunneling spectroscopy (STS) experiment resulting from inelastic tunneling processes [J. van der Lit et al., Nature Commun., in press (2013)]. Finally, we show that the hydrogen termination at the flake edges leaves identifiable fingerprints on the positive bias side of STS measurements, thus possibly aiding the experimental identification of graphene structures.
Topological band engineering of graphene nanoribbons
Nature, 2018
Topological insulators are an emerging class of materials that host highly robust in-gap surface or interface states while maintaining an insulating bulk. Most advances in this field have focused on topological insulators and related topological crystalline insulators in two dimensions and three dimensions, but more recent theoretical work has predicted the existence of one-dimensional symmetry-protected topological phases in graphene nanoribbons (GNRs). The topological phase of these laterally confined, semiconducting strips of graphene is determined by their width, edge shape and terminating crystallographic unit cell and is characterized by a [Formula: see text] invariant (that is, an index of either 0 or 1, indicating two topological classes-similar to quasi-one-dimensional solitonic systems). Interfaces between topologically distinct GNRs characterized by different values of [Formula: see text] are predicted to support half-filled, in-gap localized electronic states that could,...
Impurity effects on Dirac modes in graphene armchair nanoribbons
Physical Review B
We consider finite ribbons of graphene with armchair orientation of their edges to study in detail impurity effects on specific Dirac-like modes. In the framework of Anderson hybrid model of impurity perturbation, a possibility for Mott localization and for opening of a mobility gap under local impurity perturbations is found and analyzed in function of this model parameters: the impurity energy level, its hybridization with the host Dirac modes, and the impurity concentration. Possible electronic phase states in such disordered system and subsequent phase transitions between them are discussed.
Scientific Reports, 2019
We theoretically address the electronic structure of mono-and simple bi-layer armchair graphene nanoribbons (AGNRs) when they are infected by extrinsic charged dilute impurity. This is done with the aid of the modified tight-binding method considering the edge effects and the Green's function approach. Also, the interplay of host and guest electrons are studied within the full self-consistent Born approximation. Given that the main basic electronic features can be captured from the electronic density of states (DOS), we focus on the perturbed DOS of lattices corresponding to the different widths. The modified model says that there is no metallic phase due to the edge states. We found that the impurity effects lead to the emergence of midgap states in DOS of both systems so that a semiconductor-to-semimetal phase transition occurs at strong enough impurity concentrations and/ or impurity scattering potentials. The intensity of semiconductor-to-semimetal phase transition in monolayer (bilayer) ultra-narrow (realistic) ribbons is sharper than bilayers (monolayers). In both lattices, electron-hole symmetry breaks down as a result of induced-impurity states. The findings of this research would provide a base for future experimental studies and improve the applications of AGNRs in logic semiconductor devices in industry.
Electronic properties of armchair graphene nanoribbons
2009
We investigate the electronic band structure of an undoped graphene armchair nanoribbon. We demonstrate that such nanoribbon always has a gap in its electronic spectrum. Indeed, even in the situations where simple single-electron calculations predict a metallic dispersion, the system is unstable with respect to the deformation of the carbon-carbon bonds dangling at the edges of the armchair nanoribbon. The edge bonds' deformation couples electron and hole states with equal momentum. This coupling opens a gap at the Fermi level. In a realistic sample, however, it is unlikely that this instability could be observed in its pure form. Namely, since chemical properties of the dangling carbon atoms are different from chemical properties of the atoms inside the sample (for example, the atoms at the edge have only two neighbours, besides additional non-carbon atoms might be attached to passivate unpaired covalent carbon bonds), it is very probable that the bonds at the edge are deformed due to chemical interactions. This chemically-induced modification of the nanoribbon's edges can be viewed as an effective field biasing our predicted instability in a particular direction. Yet by disordering this field (e.g., through random substitution of the radicals attached to the edges) we may tune the system back to the critical regime and vary the electronic properties of the system. For example, we show that electrical transport through a nanoribbon is strongly affected by such disorder.
Edge states and flat bands in graphene nanoribbons with arbitrary geometries
Physical Review B, 2011
We prescribe general rules to predict the existence of edge states and zero-energy flat bands in graphene nanoribbons and graphene edges of arbitrary shape. No calculations are needed. For the so-called minimal edges, the projection of the edge translation vector into the zigzag direction of graphene uniquely determines the edge bands. By adding extra nodes to minimal edges, arbitrary modified edges can be obtained. The edge bands of modified graphene edges can be found by applying hybridization rules of the extra atoms with the ones belonging to the original edge. Our prescription correctly predicts the localization and degeneracy of the zero-energy bands at one of the graphene sublattices, confirmed by tight-binding and first-principle calculations. It also allows us to qualitatively predict the existence of E = 0 bands appearing in the energy gap of certain edges and nanoribbons.
Edge States and Flat Bands of Graphene Nanoribbons with Edge Modification
Journal of The Physical Society of Japan, 2010
We study the electronic states of graphene nanoribbons with modified edge structures by attaching Klein's bearded bonds as a minimal model of edge modification. The partial attachment of Klein's bearded bonds to graphene nanoribbons gives rise to the partial flat bands at zero-energy even under the condition of jN A À N B j ¼ 0, where N A ðN B Þ is the number of A ðBÞ-sublattice sites. Using transfer matrix method, we successfully derive the analytic representation of edge states for modified zigzag edge. The modification of armchair edges causes the complete flat bands, where the wavefunction has the character of valley polarization. We also applied the density functional theory to optimize the lattice structure and estimate the spin density. Our results indicate that the chemical and structural modification of graphene edge will serve to design and stabilize the spin polarized edge states.