The expression for the screened Coulomb potential V͑z , ; R͒ reported on p. 3 of our paper and in the related auxiliary material ͑see Ref. 31 of our paper͒ is incorrect. The correct Hamiltonian in a.u. reads:where ⑀ is the dielectric constant, D is the diameter of the tube, and ͑z , ͒ the relative coordinates of the electron and the hole on the tube surface. The exciton binding energies are calculated following the procedure described in the manuscript, and the new values are reported in the last column of Table I. The effective masses m * are computed within a tight-binding approach; 1 the dielectric constant ⑀, which is our fitting parameter, is 4.4± 0.3.These results for the exciton binding energies differ very little from the published ones ͑Ͻ0.05 eV͒, and the differences are well below the accuracy expected for these model calculations. We confirm our estimate for the exciton binding energies to be 0.3-0.4 eV for nanotubes with diameters between 6.8 Å and 9.0 Å.The main results of the paper, i.e., the experiments and the ab initio calculations, are not affected by this erratum. All conclusions remain valid.

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 0.3–0.4 eV for nanotubes with diameters between 6.8 and 9.0 Å

The optical absorption spectrum of the carbon (4, 2) nanotube is computed using an ab initio many-body approach which takes into account excitonic effects. We develop a new method involving a local basis set which is symmetric with respect to the screw symmetry of the tube. Such a method has the advantages of scaling faster than plane-wave methods and allowing for a precise determination of the symmetry character of the single particle states, two-particle excitations, and selection rules. The binding energy of the lowest, optically active states is approximately 0.8 eV. The corresponding exciton wavefunctions are delocalized along the circumference of the tube and localized in the direction of the tube axis.A wealth of extraordinary results concerning the mechanical and electrical properties of carbon nanotubes (NTs) have been reported in the last few years [1]. Until recently, however, their optical properties have not received the same attention: experimental work has often been hindered by low emission efficiency, and the interpretation has been complicated by the fact that tubes of different species and orientation are normally mixed together in the same sample, making it difficult to assign the measured spectra to a single NT species.Very recent experiments have indicated that these limitations can be overcome. Improved optical efficiency has been obtained by isolating NTs in porous materials [2], in solution [3], or on patterned substrates [4]. It was possible to assign optical spectra to specific NTs via their characteristic vibrations in resonant Raman [5] or in near-field experiments [6]. The observation of electrically induced optical emission from a carbon NT FET [7] has paved the way for a new class of single-molecule experiments and devices. These advances therefore establish optical spectroscopies as powerful characterization tools for NTs. Nanotubes also hold great promise for novel nanoscale opto-electronic and photonic applications [7], because the optical gap of NTs spans a very large frequency range which overlaps with the range of interest in the field of telecommunications.In spite of such fervent interest in this subject, the fundamental nature of optical excitations of NTs is not yet understood. The possible relevance of excitonic effects in these systems was pointed out in a pioneering paper by Ando [8]. In general, it is well known that the electronhole interaction plays a crucial role in one-dimensional systems, not only in the ideal case [9], but also in realistic systems such as semiconductor quantum wires [10] or polymer chains [11] where excitons dominate the optical spectra. The binding energies are however very sensitive to the spatial extent of the single-particle wavefunctions and to the (anisotropic) dielectric screening [12]. In the case of NTs, one might expect these quantities to be sensitive to size and geometry. Moreover, given the peculiar nature of the electronic states, even the smaller diameter NTs cannot be regarded as pure one-dimensional systems. It is therefore ex...

Narrow graphene nanoribbons exhibit substantial electronic bandgaps and optical properties fundamentally different from those of graphene. Unlike graphene-which shows a wavelength-independent absorbance for visible light-the electronic bandgap, and therefore the optical response, of graphene nanoribbons changes with ribbon width. Here we report on the optical properties of armchair graphene nanoribbons of width N ¼ 7 grown on metal surfaces. Reflectance difference spectroscopy in combination with ab initio calculations show that ultranarrow graphene nanoribbons have fully anisotropic optical properties dominated by excitonic effects that sensitively depend on the exact atomic structure. For N ¼ 7 armchair graphene nanoribbons, the optical response is dominated by absorption features at 2.1, 2.3 and 4.2 eV, in excellent agreement with ab initio calculations, which also reveal an absorbance of more than twice the one of graphene for linearly polarized light in the visible range of wavelengths.