Exciton binding energies in carbon nanotubes from two-photon photoluminescence (original) (raw)
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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.
Two‐photon photoluminescence and exciton binding energies in single‐walled carbon nanotubes
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.
Excitonic Effects and Optical Spectra of Single-Walled Carbon Nanotubes
Physical Review Letters, 2004
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.
Excitons in semiconducting single-walled carbon nanotubes
Synthetic Metals, 2005
We report correlated-electron calculations of optically excited states in 10 semiconducting single-walled carbon nanotubes with a wide range of diameters. Optical excitation occurs to excitons whose binding energies decrease with the increasing nanotube diameter, and are smaller than the binding energy of an isolated strand of poly-(paraphenylene vinylene). The ratio of the energy of the second optical exciton polarized along the nanotube axis to that of the lowest exciton is smaller than the value predicted within single-particle theory. The experimentally observed weak photoluminescence is an intrinsic feature of semiconducting nanotubes, and is consequence of dipole-forbidden excitons occurring below the optical exciton. Excited states absorption calculations show photoinduced absorption energies are lower than or comparable to the binding energy of the lowest exciton.
Physical Review Letters, 2004
We report correlated-electron calculations of optically excited states in ten semiconducting single-walled carbon nanotubes with a wide range of diameters. Optical excitation occurs to excitons whose binding energies decrease with the increasing nanotube diameter, and are smaller than the binding energy of an isolated strand of poly-(paraphenylene vinylene). The ratio of the energy of the second optical exciton polarized along the nanotube axis to that of the lowest exciton is smaller than the value predicted within single-particle theory. The experimentally observed weak photoluminescence is an intrinsic feature of semiconducting nanotubes, and is consequence of dipole-forbidden excitons occurring below the optical exciton.
Applied Physics A: Materials Science & Processing, 2004
We present a first-principles study of the effects of many-electron interactions on the optical properties of singlewalled carbon nanotubes. Motivated by recent experiments, we have carried out ab initio calculations on the single-walled carbon nanotubes (3, 3), (5, 0) and (8, 0). The calculations are based on a many-body Green's function approach in which both the quasiparticle (single-particle) excitation spectrum and the optical (electron-hole excitation) spectrum are determined. We show that the optical spectrum of both the semiconducting and metallic nanotubes studied exhibits important excitonic effects due to their quasi-one-dimensional nature. Binding energies for excitonic states range from zero for the metallic (5, 0) tube to nearly 1 eV for the semiconducting (8, 0) tube. Moreover, the metallic (3, 3) tube possesses exciton states bound by nearly 100 meV. Our calculated spectra explain quantitatively the observed features found in the measured spectra.
Low-Lying Exciton States Determine the Photophysics of Semiconducting Single Wall Carbon Nanotubes
Journal of Physical Chemistry C, 2007
A combined experimental and theoretical study of the photophysical properties and excited-state dynamics of semiconducting single-wall carbon nanotubes (SWNTs) is reported. Steady-state and time-resolved fluorescence data as a function of temperature are explained on the basis of a manifold of four low-lying singlet exciton states with kinetically controlled interconversion. Relaxation among these levels is slow and therefore Kasha's rule is not obeyed. Quantum chemical calculations based on time-dependent density functional theory complement the experimental findings. The temperature-dependence of the radiative and nonradiative rate constants are examined.
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.
Direct Experimental Evidence of Exciton-Phonon Bound States in Carbon Nanotubes
Physical Review Letters, 2005
We present direct experimental observation of exciton-phonon bound states in the photoluminescence excitation spectra of isolated single walled carbon nanotubes in aqueous suspension. The photoluminescence excitation spectra from several distinct single-walled carbon nanotubes show the presence of at least one sideband related to the tangential modes, lying {200 meV} above the main absorption/emission peak. Both the energy position and line shapes of the sidebands are in excellent agreement with recent calculations [PRL {\bf 94},027402 (2005)] that predict the existence of exciton-phonon bound states, a sizable spectral weight transfer to these exciton-phonon complexes and that the amount of this transfer depends on the specific nanotube structure and diameter. The observation of these novel exciton-phonon complexes is a strong indication that the optical properties of carbon nanotubes have an excitonic nature and also of the central role played by phonons in describing the excitation and recombination mechanisms in carbon nanotubes.