Ultrafast spectroscopy of excitons in single-walled carbon nanotubes

We studied the femtosecond dynamics of photoexcitations in films containing semiconducting and metallic single-walled carbon nanotubes (SWNTs), using various pump-probe wavelengths and intensities. We found that confined excitons and charge carriers with subpicosecond dynamics dominate the ultrafast response in semiconducting and metallic SWNTs, respectively. Surprisingly, we also found from the exciton excited state absorption bands and multiphoton absorption resonances in the semiconducting nanotubes that transitions between subbands are allowed; this unravels the important role of electron-electron interaction in SWNT optics.     

Theory and ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes

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.     

Elastic exciton-exciton scattering in photoexcited carbon nanotubes

We report on original nonlinear spectral hole-burning experiments in single wall carbon nanotubes that bring evidence of pure dephasing induced by exciton-exciton scattering. We show that the collision-induced broadening in carbon nanotubes is controlled by exciton-exciton scattering as for Wannier excitons in inorganic semiconductors, while the population relaxation is driven by exciton-exciton annihilation as for Frenkel excitons in organic materials. We demonstrate that this singular behavior originates from the intrinsic one-dimensionality of excitons in carbon nanotubes, which display unique hybrid features of organic and inorganic systems.     

Excitons in optical spectra of boron-nitride (BN) nanotubes

Exciton effects are studied in single-wall boron-nitride nanotubes. The Coulomb interaction dependence of the band gap, the optical gap, and the binding energy of excitons are discussed. The optical gap of the (5,0) nanotube is about 6 eV at the on-site interaction U=2t with the hopping integral t=1.1 eV. The binding energy of the exciton is 0.50 eV for these parameters. This energy agrees well with that of other theoretical investigations. We find that the energy gap and the binding energy are almost independent of the geometries of nanotubes. This novel property is in contrast with that of the carbon nanotubes, which show metallic and semiconducting properties depending on the chiralities.     

Stability of high-density one-dimensional excitons in carbon nanotubes under high laser excitation

Through ultrafast pump-probe spectroscopy with intense pump pulses and a wide continuum probe, we show that interband exciton peaks in single-walled carbon nanotubes (SWNTs) are extremely stable under high laser excitations. Estimates of the initial densities of excitons from the excitation conditions, combined with recent theoretical calculations of exciton Bohr radii for SWNTs, suggest that their positions do not change at all even near the Mott density. In addition, we found that the presence of lowest-subband excitons broadens all absorption peaks, including those in the second-subband range, which provides a consistent explanation for the complex spectral dependence of pump-probe signals reported for SWNTs.     

Polaronic exciton in quantum wells wires and nanotubes

We investigate the effect of the longitudinal-optical phonon field on the binding energies of excitons in quantum wells, well-wires and nanotubes based on ionic semiconductors. We take into account the exciton-phonon interaction by using the Aldrich-Bajaj effective potential for Wannier excitons in a polarizable medium. We extend the fractional-dimensional method developed previously for neutral and negatively charged donors to calculate the exciton binding energies in these heterostructures. In this method, the exciton wave function is taken as a product of the ground state functions of the electron polaron and hole polaron with a correlation function that depends only on the electron-hole separation. Starting from the variational principle we derive a one-dimensional differential equation, which is solved numerically by using the trigonometric sweep method. We find that the potential that takes into account polaronic effects always give rise to larger exciton binding energies than those obtained using a Coulomb potential screened by a static dielectric constant. This enhancement of the binding energy is more considerable in quantum wires and nanotubes than in quantum wells. Our results for quantum wells are in a good agreement with previous variational calculations. Also, we present novel curves of the exciton binding energies as a function of the wire and nanotubes radii for different models of the confinement potential.     

Splitting Phenomenon Induced by Magnetic Field in Metallic Carbon Nanotubes

In the framework of the tight-binding model,the excitons states and linear absorption spectra are calculated in the metallic single-walled carbon nanotubes,with the axial magnetic field applied.From our calculations,it is found that for the M_(11) and M_(22) transitions,the exciton states are split into four separate column states by the applied magnetic field due to the symmetry breaking.More interesting is that the splitting can be directly reflected from the linear absorption spectra,which are dominated by four main absorption peaks.In addition,the splitting with increasing the axial magnetic field is also calculated,which increases linearly with the applied magnetic field.The obtained results are expected to be detected by the future experiments.     

Selective removal of metallic SWNTs using microwave radiation

We report new method for selectively removing the metallic CNTs from semiconducting CNTs in a powder using high-power microwave radiation in the infrared and radio frequency range of the electromagnetic spectrum. SWNTs in a powder film were heated in a 2.5 GHz microwave oven for a few minutes, and the metallic nanotubes burned more rapidly than the semiconducting nanotubes. Raman data showed that the ratio of metallic to semiconducting nanotubes decreased dramatically after exposure to microwave radiation. Using their more rapid absorption of the radiation energy of the microwaves, we achieved the selective removal of metallic SWNTs from semiconducting SWNTs. This method results in the high-purity of semiconducting SWNTs necessary for sensor and electronic applications.     

Phonon and electronic nonradiative decay mechanisms of excitons in carbon nanotubes

We investigate theoretically the rates of nonradiative decay of excited semiconducting nanotubes by a variety of decay mechanisms and compare them with experimental findings. We find that the multiphonon decay (MPD) of free excitons is too slow to be responsible for the experimentally observed lifetimes. However, MPD lifetimes of localized excitons could be 2-3 orders of magnitude shorter. We also propose a new decay mechanism that relies on a finite doping of nanotubes and involves exciton decay into an optical phonon and an intraband electron-hole pair. The resulting lifetime is in the range of 5 to 100 ps, even for a moderate doping level.     

Structural dependence of exciton in carbon nanotubes

The binding energies and sizes of excitons, and energy splitting of the bright-dark excitons in single-walled carbon nanotubes have been calculated using the nonorthogonal tight-binding model, supplemented by the long-range Coulomb interaction. It is found that the binding energies and the sizes of excitons not only depend on tube's diameter d, but also its chirality. However, the splitting of the bright-dark excitons mostly depends on 1/d². Our obtained results show that the curvature effect is very important for the exciton excitations in the SWNTs, especially in the smaller diameter ones.     

磁场对单壁碳纳米管电子结构和光学性质的影响

采用半经验的模型、用单激发组态相互作用方法计算并讨论了外加轴向磁场对单壁碳纳米管电子结构和光学性质的影响。由于电子电子间相互作用的影响,磁场导致碳纳米管吸收峰能级分裂与磁场不成正比。该结果与简单的能带理论所给出的结果在低磁场情况下有本质的区别,并与实验结果有更高的符合度。该研究进一步证明了电子电子间相互作用以及激子在决定碳纳米管电子结构和光学性质中的重要作用。     

磁场对单壁碳纳米管电子结构和光学性质的影响

我们采用半经验的模型、用单激发组态相互作用方法计算并讨论了外加轴向磁场对单壁碳纳米管电子结构和光学性质的影响。由于电子电子间相互作用的影响，磁场导致碳纳米管吸收峰能级分裂与磁场不成正比。该结果与简单的能带理论所给出的结果在低磁场情况下有本质的区别，并与实验结果有更高的符合度。该研究进一步证明了电子电子间相互作用以及激子在决定碳纳米管电子结构和光学性质中的重要作用。     

On the role of interband surface plasmons in carbon nanotubes

We review the properties of collective surface excitations—excitons and interband plasmons—in single-walled and double-walled carbon nanotubes. We show that an electrostatic field applied perpendicular to the nanotube axis can control the exciton-plasmon coupling in individual small-diameter (≲nm) singlewalled nanotubes, both in the linear excitation regime and in the non-linear excitation regime with the photoinduced biexcitonic states formation. For double-walled carbon nanotubes, we report a profound effect of interband surface plasmons on the inter-tube Casimir force at tube separations similar to their equilibrium distances. Strong overlapping plasmon resonances from both tubes warrant their stronger attraction. Nanotube chiralities possessing such collective excitation features will result in forming the most favorable innerouter tube combination in double-walled carbon nanotubes. These findings pave the way for the development of new generation of tunable optoelectronic and nano-electromechanical device applications with carbon nanotubes.     

Observation of charged excitons in hole-doped carbon nanotubes using photoluminescence and absorption spectroscopy

We report the first observation of trions (charged excitons), three-particle bound states consisting of one electron and two holes, in hole-doped carbon nanotubes at room temperature. When p-type dopants are added to carbon nanotube solutions, the photoluminescence and absorption peaks of the trions appear far below the E11 bright exciton peak, regardless of the dopant species. The unexpectedly large energy separation between the bright excitons and the trions is attributed to the strong electron-hole exchange interaction in carbon nanotubes.     

Excitons and many-electron effects in the optical response of single-walled boron nitride nanotubes

We report first-principles calculations of the effects of quasiparticle self-energy and electron-hole interaction on the optical properties of single-walled boron nitride nanotubes. Excitonic effects are shown to be even more important in BN nanotubes than in carbon nanotubes. Electron-hole interactions give rise to complexes of bright (and dark) excitons, which qualitatively alter the optical response. Excitons with a binding energy larger than 2 eV are found in the BN nanotubes. Moreover, unlike the carbon nanotubes, theory predicts that these exciton states are comprised of coherent supposition of transitions from several different subband pairs, giving rise to novel behaviors.     

Quantized bimolecular auger recombination of excitons in single-walled carbon nanotubes

Auger-like exciton-exciton annihilation in isolated single-walled carbon nanotubes (SWNTs) has been studied by femtosecond transient absorption spectroscopy. We observe a quantization of the Auger recombination process and extract dynamics for 2 and 3 electron-hole pair excited states. We further demonstrate that Auger recombination in SWNTs is a two-particle process involving strongly bound excitons and not a three-particle Auger process involving unbound electrons and holes. We thus provide explicit experimental evidence for one-dimensional discrete excitons in SWNTs.     

Exciton hierarchies in gapped carbon nanotubes

We present evidence that the strong electron-electron (e-e) interactions in gapped carbon nanotubes lead to finite hierarchies of excitons within a given nanotube subband. We study these hierarchies by employing a field theoretic reduction of the gapped carbon nanotube permitting e-e interactions to be treated exactly. We analyze this reduction by employing a Wilsonian-like numerical renormalization group. We are so able to determine the gap ratios of the one-photon excitons as a function of the effective strength of interactions. We also determine within the same subband the gaps of the two-photon excitons, the single particle gaps, as well as a subset of the dark excitons. The strong e-e interactions in addition lead to strongly renormalized dispersion relations where the consequences of spin-charge separation can be readily observed.     

Charges on semiconducting nanotubes in polar media: Polarons and excitons

Charge carriers on semiconducting nanotubes immersed in the polar medium such as polar solvents undergo self-trapping into polarons. In the effectively 1d regime polarons are found to have binding energies of approximately 30–35% of the binding energy of excitons. As the thermal dissociation of excitons would occur into polaron pairs, the thermal ionization energy of excitons is substantially reduced, which is expected to lead to enhanced separation of charges.     

Aharonov-Bohm effect for composite particles and collective excitations

The energies of neutral and charged excitons in quantum rings and the plasmon frequencies in nanotubes are analyzed as functions of a magnetic field.     

Extensive limit of a non-extensive entanglement entropy

We report wide-range optical investigations on transparent conducting networks made from separated (semiconducting, metallic) and reference (mixed) single-walled carbon nanotubes, complemented by transport measurements. Comparing the intrinsic frequency-dependent conductivity of the nanotubes with that of the networks, we conclude that higher intrinsic conductivity results in better transport properties, indicating that the properties of the nanotubes are at least as much important as the contacts. We find that HNO₃ doping offers a larger improvement in transparent conductive quality than separation. Spontaneous dedoping occurs in all samples but is most effective in films made of doped metallic tubes, where the sheet conductance returns close to its original value within 24 h.