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Register a new userTopological gap states of semiconducting armchair graphene ribbons
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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 suggest that these gap states may be probed in optical measurements. However, metallic armchair graphene ribbons with a gap induced by many-electron interactions have no gap states and are not topological insulators.
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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 leading to a metallic system. This characteristic provides a new controllable degree of freedom that allows manipulation of electronic currents. We show that the numerical results are analytically predicted by solving the Dirac equation for the strained system.
We study the effects of the structural corrugation or rippling on the electronic properties of undoped armchair graphene nanoribbons (AGNR). First, reanalyzing the single corrugated graphene layer we find that the two inequivalent Dirac points (DP), move away one from the other. Otherwise, the Fermi velocity decrease by increasing rippling. Regarding the AGNRs, whose metallic behavior depends on their width, we analyze in particular the case of the zero gap band-structure AGNRs. By solving the Dirac equation with the adequate boundary condition we show that due to the shifting of the DP a gap opens in the spectra. This gap scale with the square of the rate between the high and the wavelength of the deformation. We confirm this prediction by exact numerical solution of the finite width rippled AGNR. Moreover, we find that the quantum conductance, calculated by the non equilibrium Greens function technique vanish when the gap open. The main conclusion of our results is that a conductance gap should appear for all undoped corrugated AGNR independent of their width.
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 it oscillates when the opposite is done, posing serious difficulties to the control of the gap. It is argued that the origin of this behavior is the fact that excess or defect charges or magnetic moments are mostly localized at zig-zag edges.
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 ribbons stability. Thus, charging and its consequences should be investigated.Total energy calculations of finite ribbons using spin polarized Density Functional Theory (DFT) show that ribbons 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 polarized (non polarized) solutions is larger (smaller) than experimental data, ii) the ground state is spin polarized, a characteristic still not observed experimentally. Total energy of GNRs decreases with the number of captured electrons reaching a minimum for a number that mainly depends on zigzag edges size. The following changes with respect to neutral GNRs are noted: i) the ground state is not spin polarized, ii) fundamental gap is in-between that of spin polarized and non polarized solutions of neutral ribbons, iii) while in neutral ribbons valence and conduction band onsets vs. the fundamental gap, linearly and symmetrically approach mid-gap with slope 0.5, charging induces Fermi level pinning, i.e., the slopes of the valence and conduction bands being about 0.1 and 0.9, in agreement with experiment.
We extensively characterize the electronic structure of ultra-narrow graphene nanoribbons (GNRs) with armchair edges and zig-zag termini that have 5 carbon atoms across their width (5-AGNRs), as synthesised on Au(111). Scanning tunnelling spectroscopy measurements on the ribbons, recorded on both the metallic substrate and a decoupling NaCl layer, show well-defined dispersive bands and in-gap states. In combination with theoretical calculations, we show how these in-gap states are topological in nature and localised at the zig-zag termini of the nanoribbons. Besides rationalising the driving force behind the topological class selection of 5-AGNRs, we also uncover the length-dependent behaviour of these end states which transition from singly occupied spin-split states to a closed-shell form as the ribbons become shorter. Finally, we demonstrate the magnetic character of the end states via transport experiments in a model two-terminal device structure in which the ribbons are suspended between the scanning probe and the substrate that both act as leads.
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