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Cross-polarized excitons in carbon nanotubes.

ABSTRACT: Polarization of low-lying excitonic bands in finite-size semiconducting single-walled carbon nanotubes (SWNTs) is studied by using quantum-chemical methodologies. Our calculations elucidate properties of cross-polarized excitons, which lead to the transverse optical absorption of nanotubes and presumably couple to intermediate-frequency modes recently observed in resonance Raman excitation spectroscopy. We identify up to 12 distinct excitonic transitions below the second fundamental band associated with the E(22) van Hove singularity. Calculations for several chiral SWNTs distinguish the optically active "bright" excitonic band polarized parallel to the tube axis and several optically "weak" cross-polarized excitons. The rest are optically (near) forbidden "dark" transitions. An analysis of the transition density matrices related to excitonic bands provides detailed information about delocalization of excitonic wavefunction along the tube. Utilization of the natural helical coordinate system accounting for the tube chirality allows one to disentangle longitudinal and circumferential components. The distribution of the transition density matrix along a tube axis is similar for all excitons. However, four parallel-polarized excitons associated with the E(11) transition are more localized along the circumference of a tube, compared with others related to the E(12) and E(21) cross-polarized transitions. Calculated splitting between optically active parallel- and cross-polarized transitions increases with tube diameter, which compares well with experimental spectroscopic data.

SUBMITTER: Kilina S

PROVIDER: S-EPMC2383959 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Optical absorption is the most fundamental optical property characterizing light-matter interactions in materials and can be most readily compared with theoretical predictions. However, determination of optical absorption cross-section of individual nanostructures is experimentally challenging due to the small extinction signal using conventional transmission measurements. Recently, dramatic increase of optical contrast from individual carbon nanotubes has been successfully achieved with a polarization-based homodyne microscope, where the scattered light wave from the nanostructure interferes with the optimized reference signal (the reflected/transmitted light). Here we demonstrate high-sensitivity absorption spectroscopy for individual single-walled carbon nanotubes by combining the polarization-based homodyne technique with broadband supercontinuum excitation in transmission configuration. To our knowledge, this is the first time that high-throughput and quantitative determination of nanotube absorption cross-section over broad spectral range at the single-tube level was performed for more than 50 individual chirality-defined single-walled nanotubes. Our data reveal chirality-dependent behaviors of exciton resonances in carbon nanotubes, where the exciton oscillator strength exhibits a universal scaling law with the nanotube diameter and the transition order. The exciton linewidth (characterizing the exciton lifetime) varies strongly in different nanotubes, and on average it increases linearly with the transition energy. In addition, we establish an empirical formula by extrapolating our data to predict the absorption cross-section spectrum for any given nanotube. The quantitative information of absorption cross-section in a broad spectral range and all nanotube species not only provides new insight into the unique photophysics in one-dimensional carbon nanotubes, but also enables absolute determination of optical quantum efficiencies in important photoluminescence and photovoltaic processes.

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Cross-polarized excitons in carbon nanotubes.

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