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Conduction in Carbon Nanotube Networks pp 25–37Cite as

Mesoscopic Current and Ballistic Conductance

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Abstract

In this chapter we introduce the methodology used throughout this dissertation for computing the conductance of carbon nanotubes.

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Notes

  1. 1.

    In this dissertation, we will focus only on current flow in the steady-state at zero frequency.

  2. 2.

    The conductance also behaves classically when the coherence length is very short compared to any other length scale. Due to a rapid loss of phase coherence, the effect of coherent interference at each scattering event can be neglected and Ohm’s law can be recovered [4].

  3. 3.

    We note for completeness that a recent study [6] has questioned the observation of ballistic conductance as reported in Ref. [3] (Fig. 3.1) and similar studies. It has been suggested that nanoscale contacts directly between the probe and mercury may have been mistaken for ballistic-conductor CNTs. Nevertheless, extremely large electron scattering lengths have been inferred in CNTs using independent methods as shown in Table 3.1.

  4. 4.

    This was in fact the picture first proposed by Drude in 1900, which pre-dates quantum theory [33, 34].

  5. 5.

    The lead region that connects the reservoirs to the device is assumed to do so adiabatically, and therefore does not introduce any additional scattering. Scattering at this location is referred to as contact resistance [4]. In addition, we have assumed time-reversal symmetry so that the transmission is not dependent on the direction of travel of the electrons. Such an assumption is broken in the presence of a magnetic field [4].

  6. 6.

    The Fermi energy may be modified through a gate voltage or through doping; the effect of charge doping in CNTs due to water is the focus of Chap. 8.

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  1. Cavendish Laboratory, Theory of Condensed Matter Group, University of Cambridge, Cambridge, UK

    Robert A. Bell

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Bell, R.A. (2015). Mesoscopic Current and Ballistic Conductance. In: Conduction in Carbon Nanotube Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-19965-8_3

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