This article reviews the electronic and transport properties of carbon nanotubes. The focus is mainly theoretical, but when appropriate the relation with experimental results is mentioned. While simple band-folding arguments will be invoked to rationalize how the metallic or semiconducting character of nanotubes is inferred from their topological structure, more sophisticated tight-binding and ab initio treatments will be introduced to discuss more subtle physical effects, such as those induced by curvature, tube-tube interactions, or topological defects. The same approach will be followed for transport properties. The fundamental aspects of conduction regimes and transport length scales will be presented using simple models of disorder, with the derivation of a few analytic results concerning specific situations of short-and long-range static perturbations. Further, the latest developments in semiempirical or ab initio simulations aimed at exploring the effect of realistic static scatterers ͑chemical impurities, adsorbed molecules, etc.͒ or inelastic electron-phonon interactions will be emphasized. Finally, specific issues, going beyond the noninteracting electron model, will be addressed, including excitonic effects in optical experiments, the Coulomb-blockade regime, and the Luttinger liquid, charge density waves, or superconducting transition.

New models of fluid transport are expected to emerge from the confinement of liquids at the nanoscale, with potential applications in ultrafiltration, desalination and energy conversion. Nevertheless, advancing our fundamental understanding of fluid transport on the smallest scales requires mass and ion dynamics to be ultimately characterized across an individual channel to avoid averaging over many pores. A major challenge for nanofluidics thus lies in building distinct and well-controlled nanochannels, amenable to the systematic exploration of their properties. Here we describe the fabrication and use of a hierarchical nanofluidic device made of a boron nitride nanotube that pierces an ultrathin membrane and connects two fluid reservoirs. Such a transmembrane geometry allows the detailed study of fluidic transport through a single nanotube under diverse forces, including electric fields, pressure drops and chemical gradients. Using this device, we discover very large, osmotically induced electric currents generated by salinity gradients, exceeding by two orders of magnitude their pressure-driven counterpart. We show that this result originates in the anomalously high surface charge carried by the nanotube's internal surface in water at large pH, which we independently quantify in conductance measurements. The nano-assembly route using nanostructures as building blocks opens the way to studying fluid, ionic and molecule transport on the nanoscale, and may lead to biomimetic functionalities. Our results furthermore suggest that boron nitride nanotubes could be used as membranes for osmotic power harvesting under salinity gradients.

Extensive LDA and quasi-particle calculations have been performed on boron nitride (BN) single-wall and multi-wall nanotubes. Strain energies are found to be smaller for BN nanotubes than for carbon nanotubes of the same radius, owing to a buckling effect which stabilizes the BN tubular structure. For tubes larger than 9.5A in diameter, the lowest conduction band is predicted to be freeelectron-like with electronic charge density localized inside the tube. For these tubes, this band is at constant energy above the top of the valence band. Consequently, contrarily to carbon nanotubes, single-and multi-wall BN nanotubes are constant-band-gap materials, independent of their radius and helicity. In addition, we expect them to exhibit remarkable properties under n-type doping.

Hybridization of the o* and x* states of the graphene network is shown to be as important as bandfolding eAects in determining the metallicity of small radius carbon nanotubes. Using detailed planewave ab initio pseudopotential local density functional (LDA) calculations, we find that the electronic properties of small tubes are significantly altered from those obtained in previous tight-binding calculations. Strongly modified low-lying conduction band states are introduced into the band gap of insulating tubes because of strong a*-n* hybridization. As a result, the LDA gaps of some tubes are lowered by more than 50%, and a tube previously predicted to be semiconducting is shown to be metallic.

Nitrogen doped carbon nanotubes have been synthesized using pyrolysis and characterized by Scanning Tunneling Spectroscopy and transmission electron microscopy. The doped nanotubes are all metallic and exhibit strong electron donor states near the Fermi level. Using tight-binding and ab initio calculations, we observe that pyridine-like N structures are responsible for the metallic behavior and the prominent features near the Fermi level. These electron rich structures are the first example of n-type nanotubes, which could pave the way to real molecular hetero-junction devices.

The quasiparticle band structure of bulk hexagonal boron nitride is studied within the GTV approximation for the self-energy operator. The inBuence of the interlayer distance on the band structure is investigated both within the local density approximation and the quasiparticle approach, and the importance of an interlayer state in determining the gap is demonstrated. Also, the quasiparticle band structure for an isolated sheet of boron nitride is calculated. We show that the equivalent of the interlayer state in the case of the isolated boron nitride sheet plays the same role as in the bulk case in determining the band gap.

We report on a numerical study of electronic transport in chemically doped 2D graphene materials. By using ab initio calculations, a self-consistent scattering potential is derived for boron and nitrogen substitutions, and a fully quantum-mechanical Kubo-Greenwood approach is used to evaluate the resulting charge mobilities and conductivities of systems with impurity concentration ranging within [0.5, 4.0]%. Even for a doping concentration as large as 4.0%, the conduction is marginally affected by quantum interference effects, preserving therefore remarkable transport properties, even down to the zero temperature limit. As a result of the chemical doping, electron-hole mobilities and conductivities are shown to become asymmetric with respect to the Dirac point.

We perform benchmark calculations of the Bethe–Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe–Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average −0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe–Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe–Salpeter implementation may differ significantly for states implying a large multiple excitation character.