Biexciton Stability in Carbon Nanotubes

Physica E: Low-dimensional Systems and Nanostructures, 2008

We performed quantum Monte Carlo (QMC) calculations for a model system of excitons and biexcitons in carbon nanotubes (CNTs) and compared the results with those of a variational approach [T.G. Pedersen, K. Pedersen, H.D. Cornean, P. Duclos, Nano Lett. 5 ]. Due to their geometric properties, the shape of a hollow cylinder, CNTs can be treated as 2D objects. With decreasing diameter one expects them even to exhibit quasi-1D properties. In the present study the biexciton in its ground state is found to be more strongly bound than estimated before. Biexcitonic complexes are predicted to remain stable for all diameters even at room temperature. The binding energy grows significantly with decreasing diameter, showing indeed a transition from a quasi-2D system to a quasi-1D system. r

Physical Review B, 2005

One-and two-photon luminescence excitation spectroscopy showed a series of distinct excitonic states in single-walled carbon nanotubes. The energy splitting between one-and two-photon-active exciton states of different wavefunction symmetry is the fingerprint of excitonic interactions in carbon nanotubes. We determine exciton binding energies of 0.3 − 0.4 eV for different nanotubes with diameters between 6.8Å and 9.0Å. Our results, which are supported by ab-initio calculations of the linear and non-linear optical spectra, prove that the elementary optical excitations of carbon nanotubes are strongly Coulomb-correlated, quasi-one dimensionally confined electron-hole pairs, stable even at room temperature. This alters our microscopic understanding of both the electronic structure and the Coulomb interactions in carbon nanotubes, and has direct impact on the optical and transport properties of novel nanotube devices.

Physical Review B, 2006

We calculate the diameter and chirality dependences of the binding energies, sizes, and bright-dark splittings of excitons in semiconducting single-wall carbon nanotubes (SWNTs). Using results and insights from ab initio calculations, we employ a symmetry-based, variational method based on the effective-mass and envelope-function approximations using tight-binding wavefunctions. Binding energies and spatial extents show a leading dependence with diameter as 1/d and d, respectively, with chirality corrections providing a spread of roughly 20% with a strong family behavior. Brightdark exciton splittings show a 1/d 2 leading dependence. We provide analytical expressions for the binding energies, sizes, and splittings that should be useful to guide future experiments.

Physical Review B, 2006

One-and two-photon luminescence excitation spectroscopy showed a series of distinct excitonic states in single-walled carbon nanotubes. The energy splitting between one-and two-photon-active exciton states of different wavefunction symmetry is the fingerprint of excitonic interactions in carbon nanotubes. We determine exciton binding energies of 0.3 − 0.4 eV for different nanotubes with diameters between 6.8Å and 9.0Å. Our results, which are supported by ab-initio calculations of the linear and non-linear optical spectra, prove that the elementary optical excitations of carbon nanotubes are strongly Coulomb-correlated, quasi-one dimensionally confined electron-hole pairs, stable even at room temperature. This alters our microscopic understanding of both the electronic structure and the Coulomb interactions in carbon nanotubes, and has direct impact on the optical and transport properties of novel nanotube devices.

2007

Single wall carbon nanotube SWNT structures can be characterized by two integers n, m with 2n+m= 3p+r, where p is an integer and r= 0, 1, 2 define metallic M, semiconducting type I SI, and type II SII SWNTs, respectively. 1–3 The synthesis and observation of the properties of SWNTs have advanced greatly in recent years, making possible the experimental study of the optical properties of individual SWNTs.

Physica E: Low-dimensional Systems and Nanostructures, 2008

We develop a scaling relationship between the exciton binding energy and the external dielectric function in carbon nanotubes. We show that the electron-electron and electron-hole interaction energies are strongly affected by screening yet largely counteract each other, resulting in much smaller changes in the optical transition energy. The model indicates that the relevant particle interaction energies are reduced by as much as 50 percent upon screening by water and that the unscreened electron-electron interaction energy is larger than the unscreened electron-hole interaction energy, in agreement with explanations of the "ratio problem." We apply the model to measurements of the changes in the optical transistion energies in single, suspended carbon nanotubes as the external dielectric environment is altered.

Physical Review B, 2013

We present a study of free carrier photogeneration and multicarrier bound states, such as biexcitons and trions (charged excitons), in semiconducting single-walled carbon nanotubes. Pump-and-probe measurements performed with fs pulses reveal the effects of strong Coulomb interactions between carriers on their dynamics. Biexciton formation by optical transition from exciton population results in an induced absorption line (binding energy 130 meV). Exciton-exciton annihilation process is shown to evolve at high densities towards an Auger process that can expel carriers from nanotubes. The remaining carriers give rise to an induced absorption due to trion formation (binding energy 190 meV). These features show the dynamics of exciton and free carriers populations.

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 Å and 9.0 Å. 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.

Physical Chemistry Chemical Physics, 2009

We review electronic structure calculations of finite-length semiconducting carbon nanotubes using time-dependent density functional theory (TD-DFT) and the time dependent Hartree-Fock (TD-HF) approach coupled with semi-empirical AM1 and ZINDO Hamiltonians. We specifically focus on the energy splitting, relative ordering, and localization properties of optically active (bright) and optically forbidden (dark) states from the lowest excitonic band of the nanotubes. These excitonic states are very important in competing radiative and non-radiative processes in these systems. Our analysis of excitonic transition density matrices demonstrates that pure DFT functionals overdelocalize excitons making an electron-hole pair unbound; consequently, excitonic features are not presented in this method. In contrast, the pure HF and AM1 calculations overbind excitons, inaccurately predicting the lowest energy state as a bright exciton. Changing the AM1 with the ZINDO Hamiltonian in TD-HF calculations predicts the bright exciton as the second state after the dark one. However, in contrast to AM1 calculations, the diameter dependence of the excitation energies obtained by ZINDO does not follow the experimental trends. Finally, the TD-DFT approach incorporating hybrid functionals with a moderate portion of the long-range HF exchange, such as B3LYP, has the most generality and predictive capacity providing a sufficiently accurate description of excitonic structure in finite-size nanotubes. These methods characterize four important lower exciton bands: the lowest state is dark, the upper band is bright, and the two other dark and nearly degenerate excitons lie in between. Although the calculated energy splittings between the lowest dark and the bright excitons are relatively large (B0.1 eV), the dense excitonic manifold below the bright exciton allows for fast non-radiative relaxation leading to the rapid population of the lowest dark exciton. This rationalizes the low luminescence efficiency in nanotubes.

Electroabsorption spectroscopy of well identified index-defined semiconducting carbon nanotubes is reported. The measurement of high definition electroabsorption spectrum allows an direct indexation with unique nanotube chirality. Results show that the electroabsorption is directly proportional to the exciton binding energy of nanotubes. Electroabsorption is a powerfull technique which directly probe into carbon nanotubes excitonic states, and may become a usefull tool for in-situ study of excitons in future nanotube based photonic devices.