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Exploring Quantum Transport in Graphene Ribbons with Lattice Defects and Adsorbates

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Graphene Nanoelectronics

Part of the book series: NanoScience and Technology ((NANO))

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Abstract

The reader is introduced to the Landauer theory of quantum transport in the context of graphene nanoribbons as well as to the geometries and electronic structures of and ballistic quantum transport in ideal ribbons. Imperfections present in ribbons that are realized in the laboratory, including carbon atom vacancies, edge disorder, long-ranged defect potentials and covalently bonded adsorbates including H, F, O, and OH and their roles in quantum transport in the ribbons are then considered. Quantum transport simulations for ribbons with these defects show that carbon atom vacancies and adsorbates can give rise to quantized conductance steps such as those observed experimentally in samples with conductances much smaller than the conductance quantum 2e 2 ∕ h. Adsorbate-induced scattering resonances in graphene are discussed from the perspective of extended Hückel-based tight binding models and T-matrix theory and the effects of the adsorbate-induced rehybridization of the graphene from sp 2 to sp 3 bonding on these resonances are examined. Transport gaps are shown to open in the conductances of graphene ribbons with adsorbed H, F, O, and OH for electron Fermi energies in the vicinities of these resonances.

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Notes

  1. 1.

    Very recently S. Ihnatsenka and G. Kirczenow have demonstrated similar ballistic conductance quantization theoretically in a tight binding model of graphene constrictions with mesoscopically smooth but atomically stepped boundaries by means of million-atom quantum transport calculations.

  2. 2.

    A bottom-up method of fabricating very narrow graphene ribbons by self-assembly has been demonstrated [16] but transport measurements on the ribbons produced in this way have not as yet been reported.

  3. 3.

    In general the EMOs ψα are not orthogonal to the 2p z orbitals ϕ j of carbon atom(s) to which the adsorbate bonds. We allow for this in our T-matrix calculations [55] by making the substitution γαj  → γαj  − εσαj where σαj  = ⟨ψα | ϕ j ⟩ as is discussed in [126,  127].

  4. 4.

    For the relationship between the Fermi energy and experimental gate voltages see Fig. 13.9.

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  1. Department of Physics, Simon Fraser University, Burnaby, BC, Canada

    George Kirczenow & Siarhei Ihnatsenka

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  1. George Kirczenow
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    Hassan Raza

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Kirczenow, G., Ihnatsenka, S. (2011). Exploring Quantum Transport in Graphene Ribbons with Lattice Defects and Adsorbates. In: Raza, H. (eds) Graphene Nanoelectronics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22984-8_13

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