The semiconductor industry has been able to improve the performance of electronic systems for more than four decades by making ever-smaller devices. However, this approach will soon encounter both scientific and technical limits, which is why the industry is exploring a number of alternative device technologies. Here we review the progress that has been made with carbon nanotubes and, more recently, graphene layers and nanoribbons. Field-effect transistors based on semiconductor nanotubes and graphene nanoribbons have already been demonstrated, and metallic nanotubes could be used as high-performance interconnects. Moreover, owing to the excellent optical properties of nanotubes it could be possible to make both electronic and optoelectronic devices from the same material.

Carbon-based electronics.

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 shortand 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.

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Electronic and transport properties of nanotubes

Carbon nanotubes possess unique properties that make them potentially useful in many applications in optoelectronics. This review describes the fundamental optical behaviour of carbon nanotubes as well as their opportunities for light generation and detection, and photovoltaic energy generation.

Carbon-nanotube photonics and optoelectronics

Polymer composites are one of the most attractive near-term means to exploit the unique properties of carbon nanotubes and graphene. This is particularly true for composites aimed at electronics and photonics, where a number of promising applications have already been demonstrated. One such example is nanotube-based saturable absorbers. These can be used as all-optical switches, optical amplifier noise suppressors, or mode-lockers to generate ultrashort laser pulses. Here, we review various aspects of fabrication, characterization, device implementation and operation of nanotube-polymer composites to be used in photonic applications. We also summarize recent results on graphene-based saturable absorbers for ultrafast lasers.

Nanotube–Polymer Composites for Ultrafast Photonics

Scientists resolve the long-debated issue of the nature and value of the bandgap in hexagonal boron nitride by providing evidence for an indirect bandgap at 5.955 eV and an exciton binding energy of about 130 meV by means of optical spectroscopy.

Hexagonal boron nitride is an indirect bandgap semiconductor

Excitonic effects in the linear and nonlinear optical properties of single-walled carbon nanotubes are manifested by photoluminescence excitation experiments and ab initio calculations. One- and two-photon spectra showed a series of exciton states; their energy splitting is the fingerprint of excitonic interactions in carbon nanotubes. By ab initio calculations we determine the energies, wave functions, and symmetries of the excitonic states. Combining experiment and theory we find binding energies of $0.3\char21{}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for nanotubes with diameters between 6.8 and $9.0\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.

Exciton binding energies in carbon nanotubes from two-photon photoluminescence

We present two-photon excitation luminescence experiments on carbon nanotubes which show the excitonic origin of the optical excitations. The two-photon allowed exciton state, which has even parity under rotation about the U-axis, is roughly 300 meV above the one-photon active, odd-parity state. This indicates exciton binding energies on the order of 400 meV for nanotubes with diameters around 8 A. Ab-initio calculations of the exciton wavefunctions and energies are in good agreement with our experimental results, confirming the predictions on the symmetry of the exciton states.

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Excitons in carbon nanotubes

We compare experimental one- and two-photon luminescence excitation spectra of single-walled carbon nanotubes at room temperature to ab initio calculations. The experimental spectra reveal a Rydberg-like series of excitonic states. The energy splitting between these states is a clear fingerprint of excitonic correlations in carbon nanotubes. From those spectra, we derive exciton binding energies of 0.3-0.4 eV for nanotubes with diameters between 6.8 A and 9.0 A. These energies are in quantitative agreement with our theoretical calculations, which predict the symmetries of the relevant excitonic wave functions and indicate that a low-lying optically dark excitonic state may be responsible for the low luminescence quantum yields in nanotubes.

E. Chang

Papers

Exciton binding energies in carbon nanotubes from two-photon photoluminescence

Excitons in carbon nanotubes

Two-photon photoluminescence and exciton binding energies in single-walled carbon nanotubes