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...

We present a new class of boron sheets, composed of triangular and hexagonal motifs, that are more stable than structures considered to date and thus are more likely to be the precusors of boron nanotubes. We describe a simple and clear picture of electronic bonding in boron sheets and highlight the importance of three-center bonding and its competition with two-center bonding, which can also explain the stability of recently discovered boron fullerenes. Our findings call for reconsideration of the literature on boron sheets, nanotubes and clusters.PACS numbers: 73.63.Fg All boron nanotubes (BNT), regardless of diameter or chirality, are predicted to be metallic and have large densities of states (DOS) at their Fermi energies (E F ) [1]. In contrast, carbon nanotubes (CNT) can be semiconductors or metals with small DOS at their E F . Metallic CNT are used widely to study one-dimensional (1D) electronics [2,3] and are superconducting at low temperatures [4,5]. Due to the larger DOS, BNT should be better metallic systems for 1D electronics and may have higher superconducting temperatures than CNT.Recent experiments have fabricated boron nanotubular structures both as small clusters [6] and long, 1D geometries [7]. Understanding the properties of BNT is crucial for realizing their applications. For CNT, it has been fruitful to study two-dimensional (2D) graphene: e.g., many properties of CNT are derived directly from graphene [8,9]. For boron, however, no 2D planar structure exists in its crystals which are built from B 12 icosahedra [10]. Researchers have proposed several 2D boron sheets (BS). The hexagonal graphitic BS was found to be unstable [11,18]. Based on extensive theoretical studies of boron clusters [11,12,13,14,15], an Aufbau principle was proposed whereby the most stable structures should be composed of buckled triangular motifs [12] . Experiments on small clusters of 10-15 atoms support this view [16]. A recent study of many possible sheet structures found, again, the buckled triangular arrangement to be most favorable [17]. Hence, 2D triangular BS have been studied and used to construct BNT [18,19,20].In this Letter, we present a class of boron sheets that are more stable than the currently accepted ones. We describe their structures, energetics, electronic states, and provide a clear picture of the nature of their bonding that clarifies their stability. We also show that clusters with these structures are competitive with or more favorable than those considered to date. Our findings have important consequences for understanding and interpreting the properties of these systems. For example, the unusual stability of B 80 fullerenes [21] can be explained by our bonding picture. Hence, in our view, it is necessary to reconsider previous work in this general field.We use Density Functional Theory [22,23] within the ab initio supercell planewave pseudopotential total energy approach [24]. Calculations are done by PARATEC [25]. We use both the local density approximation (LDA) [23,26] and the generalize...

We present a theoretical analysis and first-principles calculation of the radiative lifetime of excitons in semiconducting carbon nanotubes. An intrinsic lifetime of the order of 10 ps is computed for the lowest optically active bright excitons. The intrinsic lifetime is, however, a rapid increasing function of the exciton momentum. Moreover, the electronic structure of the nanotubes dictates the existence of dark excitons near in energy to each bright exciton. Both effects strongly influence measured lifetime. Assuming a thermal occupation of bright and dark exciton bands, we find an effective lifetime of the order of 10 ns at room temperature, in good accord with recent experiments.