Universal analytic expression of electric-dipole matrix elements for carbon nanotubes (original) (raw)
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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.
Ab initio calculations of optical spectra of a chiral (4,1) carbon nanotube
Physica Status Solidi B-basic Solid State Physics, 2010
We report ab initio calculations of electronic and the linear optical properties of a (4,1) chiral carbon nanotube, using the full-potential linear augmented plane-wave (FP-LAPW) method. The dielectric tensor is derived within the randomphase approximation (RPA). All optical spectra, such as: dielectric function, absorption coefficient, optical conductivity, extinction coefficient, loss function, sum rule, reflectivity, and the refractive index have been calculated for both electric field polarizations, parallel and perpendicular to the tube axis. It is revealed that the optical spectra are anisotropic along these two polarizations. For the parallel polarization, adding the intraband transition contributions, will change the optical spectra of a (4,1) nanotube significantly. The calculated optical gap, E g , electronic dielectric constant, e(1), and the refractive index, n, in the parallel polarization are obtained as 2.6 eV, 1.98, and 1.4, respectively. The results show that for small diameter of SWCNTs the chirality has a strong effect on their optical spectra. Adding the intraband transition contributions showed that the dielectric function has singularity at zero frequency, due to the metallic behavior of a (4,1) chiral nanotube.
Electro-optical properties of single-walled carbon nanotubes
Physica E: Low-dimensional Systems and Nanostructures, 2002
Optical conductivity tensor and electron energy loss function for individual single-wall carbon nanotubes (SWCNT) of arbitrary chirality are found. The reported two types of results obtained in the TEM measurements on the isolated SWCNT of the same diameter are interpreted. The di erence in plasmon excitation probabilities is shown to be related to the di erent numbers of allowed interband transitions in the chiral and achiral tubes, while the peak position shift is to be attributed to the interrelationship between the parities of the electronic states of the armchair tubes and the polarization of the perturbing ÿeld. ?
Theoretical Analysis of the Faraday Effect in Carbon Nanotubes with Arbitrary Chirality
ISRN Condensed Matter Physics, 2013
Using tight-binding model with nearest neighbour interactions, the optical properties of carbon nanotubes under the influence of an external magnetic field are analyzed. First, dipole matrix elements for two cases of light polarized parallel as well as perpendicular to the nanotube axis are analyzed. A close form analytic expression for dipole matrix is obtained for carbon nanotubes with arbitrary chirality in the case of light polarized parallel to the nanotube axis. Then the diagonal and off-diagonal elements of the frequency-dependent susceptibility in the presence of an axial magnetic field are investigated. The off-diagonal elements are applied to calculate the interband Faraday rotation and the Verdet constant. These effects should be clearly detectable under realistic conditions using weak magnetic fields.
Polarized excitons and optical activity in single-wall carbon nanotubes
2018
The polarized excitons and optical activity of single-wall carbon nanotubes (SWNTs) are studied theoretically by π-electron Hamiltonian and helical-rotational symmetry. By taking advantage of the symmetrization, the single-particle energy and properties of a SWNT are characterized with the corresponding helical band structure. The dipole-moment matrix elements, magnetic-moment matrix elements, and the selection rules can also be derived. Based on different selection rules, the optical transitions can be assigned as the parallel-polarized, left-handed circularly-polarized, and right-handed circularly-polarized transitions, where the combination of the last two gives the cross-polarized transition. The absorption and circular dichroism (CD) spectra are simulated by exciton calculation. The calculated results are well comparable with the reported measurements. Built on the foundation, magnetic-field effects on the polarized excitons and optical activity of SWNTs are studied. Dark-bright exciton splitting and interband Faraday effect in the CD spectrum of SWNTs under an axial magnetic field are predicted. The Faraday rotation dispersion can be analyzed according to the selection rules of circular polarizations and the helical band structure.
Theory of optical scattering by carbon nanotubes
Microwave and Optical Technology Letters, 2007
Here, a theory of optical scattering by single-wall carbon nanotube using modal expansion of the scattered and transmitted fields is developed. The effective-boundary condition, derived previously using accurate quantum-mechanical one-electron tight-biding approach, is employed to obtain the unknown coefficients in the series expansion. The complete scattered field is then derived analytically and compared to Rayleigh spectroscopy experiments. Very good agreement with the empirical data is observed. The theory is shown to produce expressions for the dielectric function of carbon nanotubes that can be used for further study of the optical and electronic structure.
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.
Nano Letters, 2003
An atomic dipole interaction model has been used for calculating the second hyperpolarizability of carbon nanotubes on a length scale up to 75 nm. It is demonstrated that an atomistic representation of mesoscale systems such as nanotubes can be used to obtain a cubic response property up to a size of the system where the property scales linearly with increasing size. In particular, it demonstrates that atomistic models are useful also for designing nonlinear molecular materials, where local modifications may give large macroscopic contributions. The saturation length has been calculated for carbon nanotubes. It is found that carbon nanotubes are comparable to conjugated polymers with respect to the magnitude of the second hyperpolarizability and are therefore very promising candidates for future nonlinear optical materials.
Chirality effects in carbon nanotubes
Physical Review B, 2002
We consider chirality related effects in optical, photogalvanic and electrontransport properties of carbon nanotubes. We show that these properties of chiral nanotubes are determined by terms in the electron effective Hamiltonian describing the coupling between the electron wavevector along the tube principal axis and the orbital momentum around the tube circumference. We develop a theory of photogalvanic effects and a theory of dc electric current, which is linear in the magnetic field and quadratic in the bias voltage. Moreover, we present analytic estimations for the natural circular dichroism and magneto-spatial effect in the light absorption.