Excitons in carbon nanotubes: An ab initio symmetry-based approach (original) (raw)
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Physical Review B, 2005
We present a recently developed ab initio method based on many-body perturbation theory to calculate the optical absorption spectrum of one-dimensional systems with helical symmetry. Our scheme involves a local, symmetrized basis set which allows for the calculation of large systems otherwise prohibitive in the standard plane-wave approach. It also affords an understanding of the symmetry character of the single-particle states and the excitonic wave functions, which has the advantage of determining in a precise way the selection rules related to the optical transitions of the system in question. We apply our method to single-wall carbon nanotubes of type ͑4,2͒ and present the calculated self-energy corrections, absorption spectra, and excitonic states; we find that GW corrections are substantial and excitonic effects strongly affect the optical properties.
Selection rules for one- and two-photon absorption by excitons in carbon nanotubes
Physical Review B, 2006
Recent optical absorption/emission experiments showed that the lower energy optical transitions in carbon nanotubes are excitonic in nature, as predicted by theory. These experiments were based on the symmetry aspects of free electron-hole states and bound excitonic states. The present work shows, however, that group theory does not predict the selection rules needed to explain the two photon experiments. We obtain the symmetries and selection rules for the optical transitions of excitons in single-wall carbon nanotubes within the approach of the group of the wavevector, thus providing important information for the interpretation of theoretical and experimental optical spectra of these materials.
Exciton binding energies in carbon nanotubes from two-photon photoluminescence
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.
Polarized optical absorption in carbon nanotubes: A symmetry-based approach
2003
Using density functional theory results as input data into the tight binding method for induced representations ͑based on the line group symmetry concept͒ we calculate optical conductivity tensor for single wall carbon nanotubes. Optical transition matrix elements are calculated exactly, out of completely symmetry adapted Bloch eigenfunctions. The results obtained can improve optical spectroscopy method as single-wall carbon nanotubes macroscopic sample characterization tool.
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.
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.
Effect of Exciton-Phonon Coupling in the Calculated Optical Absorption of Carbon Nanotubes
Physical Review Letters, 2005
We find that the optical properties of carbon nanotubes reflect remarkably strong effects of excitonphonon coupling. Tight-binding calculations show that a significant fraction of the spectral weight of the absorption peak is transferred to a distinct exciton+phonon sideband, which is peaked at around 200 meV above the main absorption peak. This sideband provides a distinctive signature of the excitonic character of the optical transition. The exciton-phonon coupling is reflected in a dynamical structural distortion, which contributes a binding energy of up to 100 meV. The distortion is surprisingly long-ranged, and is strongly dependent on chirality.
Diameter and chirality dependence of exciton properties in carbon nanotubes
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.
Exciton Ionization, Franz−Keldysh, and Stark Effects in Carbon Nanotubes
Nano Letters, 2007
We calculate the optical properties of carbon nanotubes in an external static electric field directed along the tube axis. We predict strong Franz-Keldysh oscillations in the first and second band-toband absorption peaks, quadratic Stark effect of the first two excitons, and the field dependence of the bound exciton ionization rate for a wide range of tube chiralities. We find that the phonon assisted mechanism dominates the dissociation rate in electro-optical devices due to the hot optical phonons. We predict a quadratic dependence of the Sommerfeld factor on the electric field and its increase up to 2000% at the critical field of the full exciton dissociation.