Many-electron effects often dramatically modify the properties of reduced dimensional systems. We report calculations, based on an ab initio many-electron Green's function approach, of electronhole interaction effects on the optical spectra of small-diameter single-walled carbon nanotubes. Excitonic effects qualitatively alter the optical spectra of both semiconducting and metallic tubes. Excitons are bound by ∼ 1 eV in the semiconducting (8,0) tube and by ∼ 100 meV in the metallic (3,3) tube. These large many-electron effects explain the discrepancies between previous theories and experiments.Synthesis and observation of single-walled carbon nanotubes (SWCNT) have advanced greatly in recent years, making possible the experimental study of the optical properties of individual SWCNTs [1,2]. If well understood, the optical response of SWCNTs may be used to characterize these nanotubes, to monitor and guide their separation by type [3], and can be employed in device applications [4]. However, measured optical transition frequencies deviate substantially from theoretical predictions based on one-particle interband theories. This deviation is not unexpected since many-body interactions should play a vital role in reduced dimensions [5]. Our ab initio results show that, indeed, many-electron effects can change qualitatively the optical spectra of SWCNTs. Strongly bound exictons are predicted in small diameter semiconducting nanotubes and even in some metallic tubes, and they dominate the optical response.Below, motivated by recent experiments [1, 3], we compute the optical absorption spectra of the three smalldiameter SWCNTs: (3,3), (5,0), and (8,0). We use a recently developed approach in which electron-hole excitations and optical spectra of real materials are calculated from first principles in three stages [6]: (i) we treat the electronic ground-state with ab initio pseudopotential density-functional theory (DFT) [7], (ii) we obtain the quasiparticle energies E nk within the GW approximation for the electron self-energy Σ [8] by solving the Dyson equation:and (iii) we calculate the coupled electron-hole excitation energies Ω S and spectrum by solving the Bethe-Salpeter equation of the two-particle Green's function [6,9]:where A S vck is the exciton amplitude, K eh is the electronhole interaction kernel, and |ck and |vk are the quasielectron and quasihole states, respectively. We obtain the DFT wavefunctions and eigenvalues by solving the Kohn-Sham equations within the local density approximation (LDA) [7] using a plane-wave basis with an energy cutoff of 60 Ry. We use ab initio Troullier-Martins pseudopotentials [10] in the Kleinmann-Bylander form [11] (r c = 1.4 a.u.). To compare with experiments in which 4Å diameter SWCNTs are grown inside zeolites [1], we study the (3,3) and (5,0) tubes in the experimental geometry with a dielectric background of AlP O 4 [12]. For the (8,0) tube, we work in a supercell with an intertube separation of at least 9.7Å to mimic experiments on isolated tubes [2,3]. In supercells, due...

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.

Introduction of pentagon-heptagon pair defects into the hexagonal network of a single carbon nanotube can change the helicity of the tube and alter its electronic structure. Using a tight-binding method to calculate the electronic structure of such systems we show that they behave as nanoscale metal/semiconductor or semiconductor/semiconductor junctions. These junctions could be the building blocks of nanoscale electronic devices made entirely of carbon.

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