Optical excitations of quasi-one-dimensional systems: carbon nanotubes versus polymers and semiconductor wires (original) (raw)
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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.
pi -electron theory of transverse optical excitons in semiconducting single-walled carbon nanotubes
Physical Review B, 2007
We present a quantitative theory of optical absorption polarized transverse to the tube axes in semiconducting single-walled carbon nanotubes. Transverse optical absorption in semiconducting single-walled carbon nanotubes is to an exciton state that is strongly blueshifted, relative to the two lowest longitudinal excitons, by electron-electron interactions. The binding energy of the transverse exciton is considerably smaller than those of the longitudinal excitons. Electron-electron interactions also reduce the relative oscillator strength of the transverse optical absorption. Our theoretical results are in excellent agreement with recent experimental measurements in four chiral nanotubes.
Quasiparticle and Excitonic Effects in the Optical Response of Nanotubes and Nanoribbons
Topics in Applied Physics, 2007
This chapter discusses the effects of many-electron interactions in the photophysics of nanotubes and their consequences on measured properties. The basic theory and key physical differences between two common types of electronic excitations are developed: single-particle excitations (quasiparticles) measured in transport or photoemission experiments, and electron-hole pair excitations (excitonic states) measured in optical experiments. We show, through first-principles calculations, that both quasiparticle and excitonic effects are crucial in understanding the optical response of the carbon nanotubes. These effects change qualitatively the nature of the photoexcited states, leading to extraordinarily strongly bound excitons in both semiconducting and metallic nanotubes and explaining the so-called "ratio problem" in carbon-nanotube spectroscopy. Using simplified models parameterized by the first-principles results, the diameter and family dependences of the exciton properties in carbon nanotubes are further elucidated. We also analyze the symmetries of excitons and their selection rules for one-and two-photon spectroscopy. A method for calculating the radiative lifetime of excitons in carbon nanotubes is also described. In addition, we briefly discuss the effects of pressure and temperature on optical transitions. Finally, we show that many-electron effects are equally dominant in the excitation spectra of other quasi-one-dimensional systems, including the boron-nitride nanotubes, semiconductor nanowires, and graphene nanoribbons.
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.
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.
Bright and Dark Excitons in Semiconductor Carbon: Nanotubes
2008
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.
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.