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Electron and Phonon Transport in Graphene in and out of the Bulk

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Physics of Graphene

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Abstract

Carbon atoms have the unique capability of associating with each other in different ways at the macro- and nanoscopic scales to form various architectures, some of them being unique. Following the discovery of fullerenes, these last twenty-five years witnessed the discovery of some new forms of carbon atom associations leading to a large diversity of nanocarbons with fascinating properties. As regards bulk carbons, the decade preceding the discovery of fullerenes paved the way for finding some physical properties which were found later to be displayed in these new nano entities. This mainly concerns the semiclassical and, more particularly, the quantum aspects of two-dimensional (2D) electronic transport and the behavior of phonons in low-dimensional materials. These effects are discussed here in relation to the electrical and thermal conductivities of various nano-carbon based materials. This chapter also reflects the obvious similarities and differences observed in the transport properties of an isolated single layer graphene out of the bulk (SLG), or a few layers of graphene out of the bulk (FLG), supported or suspended, and those of a single (stage-1) or more (stage-n, where n=2,3,…) of these carbon layer planes sandwiched between planes formed by other chemical species, as is the case for macroscopic graphite intercalation compounds (GICs), and more particularly quasi 2D acceptor compounds (GACs), or even, in some cases, pristine highly oriented pyrolytic graphite (HOPG).

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Notes

  1. 1.

    Note that HOPG is not a single crystal but instead could be considered as a 2D polycrystalline material with a crystallite size of about 10 micrometers when heat treated above 3,000 °C.

  2. 2.

    One should note that the term “graphene” was already used in 1987 by Mouras et al. (Ref. [2]) to describe the single graphite sheets, which together with the intercalate species, constitute the graphite intercalation compounds (GICs).

  3. 3.

    See also Ref. [5].

  4. 4.

    See, for example Refs. [12, 19] and [23].

  5. 5.

    Actually the density of carriers at 0 K varies from one semimetal to another. If we consider the group V semimetals, the density at 0 K is very small in bismuth and is comparable to that of pristine graphite, it is larger in antimony and much larger in arsenic, where the electron gas is still degenerate at room temperature.

  6. 6.

    The word “doping” commonly attributed to intercalation—as it is for conducting polymers—is not correct in this context. Solid state physicists introduced this concept initially to define the introduction of a small amount of foreign atoms which increases the charge carrier density without modifying the band structure which is considered according to the rigid band model. This is far from being the case in GICs or in electroactive polymers.

  7. 7.

    The mobility concept holds for a diffusive regime.

  8. 8.

    Note that k F ζ≫1 is also the condition for transport in the Boltzmann approximation.

  9. 9.

    The common reference to copper, which is justified when we speak about practical applications, is meaningless when we consider the physics: one is comparing a material with the highest electronic thermal conductivity (copper) to the family of carbon materials with a low carrier density (diamond, HOPG, VDF, …). Solid state physicists know that pure covalent materials have the highest lattice conductivities, which are often higher than the highest electronic conductivities. Also diamond and HOPG in-plane are known to be the best bulk thermal conductors. This high thermal conductivity might be understood qualitatively using a naïve mechanical picture: strong covalent bonding and light atoms favor the transmission of lattice vibrations.

  10. 10.

    Note that I c varies slightly with the stage of the compound, but the effect is too small to be taken into consideration in this context.

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Authors and Affiliations

  1. CERMIN, Université Catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Jean-Paul Issi

  2. Department of Electrical Engineering and Computer Sciences, Massachusetts Institute of Technology, Cambridge, MA, 02139-4307, USA

    Paulo T. Araujo & Mildred S. Dresselhaus

  3. Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL, 35487-0324, USA

    Paulo T. Araujo

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139-4307, USA

    Mildred S. Dresselhaus

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Editors and Affiliations

  1. Faculty of Science Department of Physics, University of Tokyo, Tokyo, Japan

    Hideo Aoki

  2. Physics and Electrical Eng. Dept., Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Mildred S. Dresselhaus

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Issi, JP., Araujo, P.T., Dresselhaus, M.S. (2014). Electron and Phonon Transport in Graphene in and out of the Bulk. In: Aoki, H., S. Dresselhaus, M. (eds) Physics of Graphene. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02633-6_3

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