Excitonic Effects and Optical Spectra of Single-Walled Carbon Nanotubes

Abstract

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...

Photophysics of Individual Single-Walled Carbon Nanotubes

“…However, due to strong 1D confinement in SWNTs, the electrostatic electron-hole interaction energy (i.e., exciton binding energy) is very large, on the order of 300-500 meV, relative to an energy gap of ~1 eV. [111][112][113][114] As a result of this strong eh attraction, it is generally accepted that the photoexcited state of an SWNT is excitonic. In SWNTs, the electron orbits the heavier hole at a characteristic eh separation (Bohr radius) of approximately 2.5 nm.…”

“…In SWNTs, the electron orbits the heavier hole at a characteristic eh separation (Bohr radius) of approximately 2.5 nm. 111,113,115 The exciton is a mobile quasiparticle that travels along the SWNT with an average diffusion length of ~90 nm before relaxing to the ground state. 116 Both the HOMO (highest occupied molecular orbital) and LUMO (lowest …”

Field-Effect Transistors Assembled from Functionalized Carbon Nanotubes

“…1). After annealing at 600 • C for 120 s in N2 (ramp 5 • /s) a broad adsorption band around 1650 nm appears, associated with the first dipole active exciton (E11) [29,30,31]. The broad shape of the absorption peak is due to the presence of a distribution of nanotubes in the sample, with diameters ranging from 0.8 to 1.2 nm [32].…”

Exciton Ionization, Franz−Keldysh, and Stark Effects in Carbon Nanotubes

“…Large Stark shifts were observed in fields directed perpendicular to the 2D planes. In 1D carbon nanotubes, excitons were predicted to have large binding energies [6] and to dominate the absorption spectra [7,8], a fact which was verified experimentally by two-photon spectroscopy [9,10] and from the observation of the phonon sidebands in photoconductivity spectra [11]. The exciton binding energies in carbon nanotubes have interesting scaling properties [8] and they can be as small as those in 2D structures and as large as 30% of their bandgap depending on both the nanotube structure and the environment.…”