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First-Principles Electronic Transport

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Conduction in Carbon Nanotube Networks

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In the previous chapter, we showed how the Hamiltonian that describes the electronic structure of a system can be computed using the density functional theory formalism to map the many-body problem onto an effective single-body problem of non-interacting electrons.

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Notes

  1. 1.

    Chapter 7 presents a more detailed study of conduction between end-terminated CNTs.

  2. 2.

    See the derivation presented in Appendix A.

  3. 3.

    For principle layers containing multiple primitive lead unit cells, the band structure for a single primitive lead unit cell can be obtained by replacing the principle layer matrix blocks by equivalent primitive unit cell matrix blocks, and modifying Eq. (5.7a–c) to include contributions from non-adjacent primitive unit cells, e.g. introducing \(\varvec{h}_{02}\), \(\varvec{s}_{02}\) etc.

  4. 4.

    The calculation uses the same pseudopotentials and, as far as possible, parameter set. During the self-consistent field calculation of the ground state, the Brillouin zone was sampled at 8 equally spaced points along the periodic direction.

  5. 5.

    Plane-wave eigenstates were calculated using the Quantum Espresso package [40] using the same pseudopotentials and, as far as possible, calculation parameters. A set of 102 MLWFs were extracted from lowest 170 bands resulting in 68 MLWFs localised in the bonding region between species, 32 \(p_z\) type orbitals centred on carbon atoms, and two additional MLWFs on the nitrogen lone pairs.

  6. 6.

    We note that as a consequence of the connection between the leads across the periodic boundary, the auxiliary simulation geometry in Fig. 5.6 can only study conductance between CNTs of the same chirality. The results presented in Chap. 7 use an alternative geometry consisting of finite CNT fragments that allows for the study of conduction between CNTs of different chirality.

  7. 7.

    The variation in the real-space integral as atoms are shifted a fraction of a grid-spacing is known as the egg-box effect [42].

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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). First-Principles Electronic Transport. In: Conduction in Carbon Nanotube Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-19965-8_5

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