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Register a new userChaotic dynamics of graphene and graphene nanoribbons
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We study the chaotic dynamics of graphene structures, considering both a periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of various widths. By numerically calculating the maximum Lyapunov exponent, we quantify the chaoticity for a spectrum of energies in both systems. We find that for all cases, the chaotic strength increases with the energy density, and that the onset of chaos in graphene is slow, becoming evident after more than $10^4$ natural oscillations of the system. For the GNRs, we also investigate the impact of the width and chirality (armchair or zigzag edges) on their chaotic behavior. Our results suggest that due to the free edges the chaoticity of GNRs is stronger than the periodic graphene sheet, and decreases by increasing width, tending asymptotically to the bulk value. In addition, the chaotic strength of armchair GNRs is higher than a zigzag ribbon of the same width. Further, we show that the composition of ${}^{12}C$ and ${}^{13}C$ carbon isotopes in graphene has a minor impact on its chaotic strength.
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It is now possible to produce graphene nanoribbons (GNRs) with atomically defined widths. GNRs offer many opportunities for electronic devices and composites, if it is possible to establish the link between edge structure and functionalisation, and resultant GNR properties. Switching hydrogen edge termination to larger more complex functional groups such as hydroxyls or thiols induces strain at the ribbon edge. However we show that this strain is then relieved via the formation of static out-of-plane ripples. The resultant ribbons have a significantly reduced Youngs Modulus which varies as a function of ribbon width, modified band gaps, as well as heterogeneous chemical reactivity along the edge. Rather than being the exception, such static edge ripples are likely on the majority of functionalized graphene ribbon edges.
Matrix elements of electron-light interactions for armchair and zigzag graphene nanoribbons are constructed analytically using a tight-binding model. The changes in wavenumber ($Delta n$) and pseudospin are the necessary elements if we are to understand the optical selection rule. It is shown that an incident light with a specific polarization and energy, induces an indirect transition ($Delta n=pm1$), which results in a characteristic peak in absorption spectra. Such a peak provides evidence that the electron standing wave is formed by multiple reflections at both edges of a ribbon. It is also suggested that the absorption of low-energy light is sensitive to the position of the Fermi energy, direction of light polarization, and irregularities in the edge. The effect of depolarization on the absorption peak is briefly discussed.
Transport measurements on an etched graphene nanoribbon are presented. It is shown that two distinct voltage scales can be experimentally extracted that characterize the parameter region of suppressed conductance at low charge density in the ribbon. One of them is related to the charging energy of localized states, the other to the strength of the disorder potential. The lever arms of gates vary by up to 30% for different localized states which must therefore be spread in position along the ribbon. A single-electron transistor is used to prove the addition of individual electrons to the localized states. In our sample the characteristic charging energy is of the order of 10 meV, the characteristic strength of the disorder potential of the order of 100 meV.
A recent experimental study showed that an induced folded flap of graphene can spontaneously drive itself its tearing and peeling off a substrate, thus producing long, micrometer sized, regular trapezoidal-shaped folded graphene nanoribbons. As long as the size of the graphene flaps is above a threshold value, the tug of war between the forces of adhesion of graphene-graphene and graphene-substrate, flexural strain of folded region and carbon-carbon (C-C) covalent bonds favor the self-tearing and self-peeling off process. As the detailed information regarding the atomic scale mechanism involved in the process remains not fully understood, we carried out atomistic reactive molecular dynamics simulations to address some features of the process. We show that large thermal fluctuations can prevent the process by increasing the probability of chemical reactions between carbon dangling bonds of adjacent graphene layers. The effects of the strength of attraction between graphene and the substrate on the ribbon growth velocities at the early stages of the phenomenon were also investigated. Structures with initial armchair crack-edges were observed to form more uniform cuts than those having initial zigzag ones. Our results are of importance to help set up new experiments on this phenomenon, especially with samples with nanoscale sized cuts.
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 semiconductor-to-semimetal transition, with the semimetallic phase featuring zero-energy Dirac fermions that propagate along the armchair edges. The transition occurs at critical fields that scale inversely with the width of the nanoribbons. These findings are universal to group-IV honeycomb lattices, including silicene and germanene nanoribbons, irrespective of the type of edge termination. Overall, our results create new opportunities to electrically engineer Dirac fermions in otherwise semiconducting graphene-like nanoribbons.
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